# kb

id: game-theory-20260505-10
file: data/en.wikipedia.org/wiki/Game_theory-10.md
category: reference
title: Game theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Game_theory
date_saved: 2026-05-05T03:56:32.715747+00:00
instance: kb-cron
parent: game-theory-20260505-0
summary:
=== Trust game === The Trust Game is an experiment designed to measure trust in economic decisions. It is also called "the investment game" and is designed to investigate trust and demonstrate its importance rather than "rationality" of self-interest. The game was designed by Berg Joyce, John Dickhaut and Kevin McCabe in 1995. In the game, one player (the investor) is given a sum of money and must decide how much of it to give to another player (the trustee). The amount given is then tripled by the experimenter. The trustee then decides how much of the tripled amount to return to the investor. If the trustee is completely self-interested, then they would return nothing. However, experiments have shown that this isn't the expected behavior of the trustee. The outcome instead suggests that people are willing to place trust, by risking some amount of money, in the belief that there will be reciprocity. === Cournot Competition === The Cournot competition model involves players choosing quantity of a homogenous product to produce independently and simultaneously, where marginal cost can be different for each firm and the firm's payoff is profit. The production costs are public information and the firm aims to


id: game-theory-20260505-11
file: data/en.wikipedia.org/wiki/Game_theory-11.md
category: reference
title: Game theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Game_theory
date_saved: 2026-05-05T03:56:32.715747+00:00
instance: kb-cron
parent: game-theory-20260505-0
summary:
== See also == Applied ethics – Practical application of moral considerations Bandwidth-sharing game – Type of resource allocation game Chainstore paradox – Game theory paradox Collective intentionality – Social concept in philosophy of mind Core (game theory) – Set in game theory Glossary of game theory Intra-household bargaining Kingmaker scenario – Endgame situation in game theory Law and economics – Analysis of law using economic theory Mutual assured destruction – Doctrine of military strategyPages displaying short descriptions of redirect targets Outline of artificial intelligence Parrondo's paradox – Paradox of combining strategies Precautionary principle – Risk management strategy Quantum refereed game Risk management – Identification, evaluation and control of risks Self-confirming equilibrium – Aspect of game theory Tragedy of the commons – Overuse of a shared resource Traveler's dilemma – Non-zero-sum game thought experiment Wilson doctrine (economics) – Argument in economic theory Compositional game theory Lists List of cognitive biases List of emerging technologies List of games in game theory == Notes == == References == == Further reading == Ben-David, S.; Borodin, A.; Karp, R.; Tardos, G.; Wigderson, A. (January 1994). "On the power of randomization in on-line algorithms". Algorithmica. 11 (1): 2–14. doi:10.1007/BF01294260. S2CID 26771869. Downs, Anthony (1957),


id: game-theory-20260505-12
file: data/en.wikipedia.org/wiki/Game_theory-12.md
category: reference
title: Game theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Game_theory
date_saved: 2026-05-05T03:56:32.715747+00:00
instance: kb-cron
parent: game-theory-20260505-0
summary:
=== Historically important texts === Aumann, R. J.; Shapley, L. S. (1974), Values of Non-Atomic Games, Princeton University Press Cournot, A. Augustin (1838), "Recherches sur les principles mathematiques de la théorie des richesses", Libraire des Sciences Politiques et Sociales Edgeworth, Francis Y. (1881), Mathematical Psychics, London: Kegan Paul Farquharson, Robin (1969), Theory of Voting, Blackwell (Yale U.P. in the U.S.), ISBN 978-0-631-12460-3 Luce, R. Duncan; Raiffa, Howard (1957), Games and decisions: introduction and critical survey, New York: Wiley reprinted edition: R. Duncan Luce; Howard Raiffa (1989), Games and decisions: introduction and critical survey, New York: Dover Publications, ISBN 978-0-486-65943-5 Maynard Smith, John (1982), Evolution and the theory of games, Cambridge University Press, ISBN 978-0-521-28884-2 Nash, John (1950), "Equilibrium points in n-person games", Proceedings of the National Academy of Sciences of the United States of America, 36 (1): 48–49, Bibcode:1950PNAS...36...48N, doi:10.1073/pnas.36.1.48, PMC 1063129, PMID 16588946 Shapley, L.S. (1953), A Value for n-person Games, In: Contributions to the Theory of Games volume II, H. W. Kuhn and A. W. Tucker (eds.) Shapley, L. S. (October 1953). "Stochastic Games". Proceedings of the National Academy of Sciences. 39 (10): 1095–1100. Bibcode:1953PNAS...39.1095S. doi:10.1073/pnas.39.10.1095. PMC 1063912. PMID 16589380. von Neumann, John (1928), "Zur Theorie der Gesellschaftsspiele",


id: grammar-systems-theory-20260505-0
file: data/en.wikipedia.org/wiki/Grammar_systems_theory-0.md
category: reference
title: Grammar systems theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Grammar_systems_theory
date_saved: 2026-05-05T03:56:33.967957+00:00
instance: kb-cron
parent: grammar-systems-theory-20260505-0
summary:
Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-called sequential form that represents an environment. Grammar systems can thus be used as a formalization of decentralized or distributed systems of agents in artificial intelligence. Let A {\displaystyle \mathbb {A} } be a simple reactive agent moving on the table and trying not to fall down from the table with two reactions, t for turning and ƒ for moving forward. The set of possible behaviors of A {\displaystyle \mathbb {A} } can then be described as formal language L A = { ( f m t n f r ) + : 1 ≤ m ≤ k ; 1 ≤ n ≤ ℓ ; 1 ≤ r ≤ k } , {\displaystyle \mathbb {L_{A}} =\{(f^{m}t^{n}f^{r})^{+}:1\leq m\leq k;1\leq n\leq \ell ;1\leq r\leq k\},} where ƒ can be done maximally k times and t can be done maximally ℓ times considering the dimensions of the table. Let G A {\displaystyle \mathbb {G_{A}} } be a formal grammar which generates language L A {\displaystyle \mathbb {L_{A}} } . The behavior of A


id: homeokinetics-20260505-0
file: data/en.wikipedia.org/wiki/Homeokinetics-0.md
category: reference
title: Homeokinetics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Homeokinetics
date_saved: 2026-05-05T03:56:35.253721+00:00
instance: kb-cron
parent: homeokinetics-20260505-0
summary:
Homeokinetics is the study of self-organizing, complex systems. Standard physics studies systems at separate levels, such as atomic physics, nuclear physics, biophysics, social physics, and galactic physics. Homeokinetic physics studies the up-down processes that bind these levels. Tools such as mechanics, quantum field theory, and the laws of thermodynamics provide the key relationships. The subject, described as the physics and thermodynamics associated with the up down movement between levels of systems, originated in the late 1970s work of American physicists Harry Soodak and Arthur Iberall. Complex systems are universes, galaxies, social systems, people, or even those that seem as simple as gases. The basic premise is that the entire universe consists of atomistic-like units bound in interactive ensembles to form systems, level by level, in a nested hierarchy. Homeokinetics treats all complex systems on an equal footing, animate and inanimate, providing them with a common viewpoint. The complexity in studying how they work is reduced by the emergence of common languages in all complex systems. == History == Arthur Iberall, Warren McCulloch and Harry Soodak developed the concept of homeokinetics as a new branch of physics. It began through Iberall's biophysical research for the NASA exobiology program into the dynamics


id: image-analysis-20260505-0
file: data/en.wikipedia.org/wiki/Image_analysis-0.md
category: reference
title: Image analysis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Image_analysis
date_saved: 2026-05-05T03:56:36.441246+00:00
instance: kb-cron
parent: image-analysis-20260505-0
summary:
Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detectors and neural networks are inspired by human visual perception models. == Digital == Digital Image Analysis or Computer Image Analysis is when a computer or electrical device automatically studies an image to obtain useful information from it. Note that the device is often a computer but may also be an electrical circuit, a digital camera or a mobile phone. It involves the fields of computer or machine vision, and medical imaging, and makes heavy use of pattern recognition, digital


id: information-theory-20260505-0
file: data/en.wikipedia.org/wiki/Information_theory-0.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
Information theory is the mathematical study of the quantification, storage, and communication of a particular type of mathematically defined information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. Information theory was initially formed in the context of telecommunication but soon found a wide range of other applications. It is now at the intersection of mathematics, statistics and computer science, and has applications in diverse fields ranging from electrical engineering and physics to neurobiology. As a simple example of the concept, if one flips a fair coin and does not yet know the outcome (heads or tails), then they lack a certain amount of information. After looking at the coin, they gain information about the outcome. For a fair coin, the probability of either heads or tails is 1/2 and the amount of information is expressed as − log 2 ⁡ ( 1 / 2 ) {\displaystyle -\log _{2}(1/2)} = 1 bit of information. A key concept in information theory is information entropy. In Shannon's formulation entropy is equal to the lack of information about an event. In the above


id: information-theory-20260505-1
file: data/en.wikipedia.org/wiki/Information_theory-1.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
The landmark event establishing the discipline of information theory and bringing it to immediate worldwide attention was the publication of Claude Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948. Historian James Gleick rated the paper as the most important development of 1948, noting that the paper was "even more profound and more fundamental" than the transistor. He came to be known as the "father of information theory". Shannon outlined some of his initial ideas of information theory as early as 1939 in a letter to Vannevar Bush. Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs, all implicitly assuming events of equal probability. Harry Nyquist's 1924 paper, Certain Factors Affecting Telegraph Speed, contains a theoretical section quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation W = K log m (recalling the Boltzmann constant), where W is the speed of transmission of intelligence, m is the number of different voltage levels to choose from at each time step, and K is a constant. Ralph Hartley's 1928 paper, Transmission of Information, uses the word information as


id: information-theory-20260505-2
file: data/en.wikipedia.org/wiki/Information_theory-2.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
Intuitively, the entropy H ( X ) {\displaystyle H(X)} of a discrete random variable X is a measure of the amount of uncertainty associated with the value of X {\displaystyle X} when only its distribution is known. A high entropy indicates the outcomes are more evenly distributed, making the result harder to predict. For example, if one transmits 1000 bits (0s and 1s), and the value of each of these bits is known to the receiver (has a specific value with certainty) ahead of transmission, no information is transmitted. If, however, each bit is independently and equally likely to be 0 or 1, 1000 shannons of information (more often called bits) have been transmitted. ==== Properties ==== A key property of entropy is that it is maximized when all the messages in the message space are equiprobable. For a source with n possible symbols, where p i = 1 n {\textstyle p_{i}={\frac {1}{n}}} for all i {\displaystyle i} , the entropy is given by: H ( X ) = log 2 ⁡ ( n ) {\displaystyle H(X)=\log _{2}(n)} This maximum value represents the most unpredictable state. For a source that emits a sequence of N {\displaystyle N} symbols that are


id: information-theory-20260505-3
file: data/en.wikipedia.org/wiki/Information_theory-3.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
=== Mutual information (transinformation) === Mutual information measures the amount of information that can be obtained about one random variable by observing another. It is important in communication where it can be used to maximize the amount of information shared between sent and received signals. The mutual information of X relative to Y is given by: I ( X ; Y ) = E X , Y [ S I ( x , y ) ] = ∑ x , y p ( x , y ) log ⁡ p ( x , y ) p ( x ) p ( y ) {\displaystyle I(X;Y)=\mathbb {E} _{X,Y}[SI(x,y)]=\sum _{x,y}p(x,y)\log {\frac {p(x,y)}{p(x)\,p(y)}}} where SI (Specific mutual Information) is the pointwise mutual information. A basic property of the mutual information is that: I ( X ; Y ) = H ( X ) − H ( X | Y ) . {\displaystyle I(X;Y)=H(X)-H(X|Y).\,} That is, knowing Y {\textstyle Y} , we can save an average of I(X; Y) bits in encoding X {\displaystyle X} compared to not knowing Y {\displaystyle Y} . Mutual information is symmetric: I ( X ; Y ) = I ( Y ; X ) = H ( X


id: information-theory-20260505-4
file: data/en.wikipedia.org/wiki/Information_theory-4.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
I ( X n → Y n ) ≜ ∑ i = 1 n I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{n}\to Y^{n})\ \triangleq \ \sum _{i=1}^{n}I(X^{i};Y_{i}|Y^{i-1})} , where I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{i};Y_{i}|Y^{i-1})} is the conditional mutual information I ( X 1 , X 2 , . . . , X i ; Y i | Y 1 , Y 2 , . . . , Y i − 1 ) {\displaystyle I(X_{1},X_{2},...,X_{i};Y_{i}|Y_{1},Y_{2},...,Y_{i-1})} . In contrast to mutual information, directed information is not symmetric. The I ( X n → Y n ) {\displaystyle I(X^{n}\to Y^{n})} measures the information bits that are transmitted causally from X n {\displaystyle X^{n}} to Y n {\displaystyle Y^{n}} . The Directed information has many applications in problems where causality plays an important role such as capacity of channel with feedback, capacity of discrete memoryless networks with feedback, gambling with causal side information, compression with causal side information, real-time control communication settings, and in statistical physics. === Other quantities === Other important information theoretic quantities include the Rényi entropy and the Tsallis entropy (generalizations of the concept


id: information-theory-20260505-5
file: data/en.wikipedia.org/wiki/Information_theory-5.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
→ Message W Encoder f n → E n c o d e d s e q u e n c e X n Channel p ( y | x ) → R e c e i v e d s e q u e n c e Y n Decoder g n → E s t i m a t e d m e s s a g e W ^ {\displaystyle {\xrightarrow[{\text{Message}}]{W}}{\begin{array}{|c| }\hline {\text{Encoder}}\\f_{n}\\\hline \end{array}}{\xrightarrow[{\mathrm {Encoded \atop sequence} }]{X^{n}}}{\begin{array}{|c| }\hline {\text{Channel}}\\p(y|x)\\\hline \end{array}}{\xrightarrow[{\mathrm {Received \atop sequence} }]{Y^{n}}}{\begin{array}{|c| }\hline {\text{Decoder}}\\g_{n}\\\hline \end{array}}{\xrightarrow[{\mathrm {Estimated \atop message} }]{\hat {W}}}} Here X {\displaystyle X} represents the space of messages transmitted, and Y {\textstyle Y} the space of messages received during a unit time over our channel. Let p(y|x) be the conditional probability distribution function of Y {\textstyle Y} given X {\displaystyle X} . We will consider p(y|x) to be an inherent fixed property of our communications channel (representing the nature of the noise of our channel). Then the joint distribution of X {\displaystyle X} and Y {\textstyle Y} is completely determined by our channel and by our choice of f(x), the marginal distribution of messages we choose to send over the channel. Under these


id: information-theory-20260505-6
file: data/en.wikipedia.org/wiki/Information_theory-6.md
category: reference
title: Information theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Information_theory
date_saved: 2026-05-05T03:56:37.735412+00:00
instance: kb-cron
parent: information-theory-20260505-0
summary:
Information theoretic concepts apply to cryptography and cryptanalysis. Turing's information unit, the ban, was used in the Ultra project, breaking the German Enigma machine code and hastening the end of World War II in Europe. Shannon himself defined an important concept now called the unicity distance. Based on the redundancy of the plaintext, it attempts to give a minimum amount of ciphertext necessary to ensure unique decipherability. Information theory leads us to believe it is much more difficult to keep secrets than it might first appear. A brute force attack can break systems based on asymmetric key algorithms or on most commonly used methods of symmetric key algorithms (sometimes called secret key algorithms), such as block ciphers. The security of all such methods comes from the assumption that no known attack can break them in a practical amount of time. Information theoretic security refers to methods such as the one-time pad that are not vulnerable to such brute force attacks. In such cases, the positive conditional mutual information between the plaintext and ciphertext (conditioned on the key) can ensure proper transmission, while the unconditional mutual information between the plaintext and ciphertext remains zero, resulting in absolutely secure communications. In other


id: logic-20260505-0
file: data/en.wikipedia.org/wiki/Logic-0.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ∧ {\displaystyle \land } (and) or → {\displaystyle \to


id: logic-20260505-1
file: data/en.wikipedia.org/wiki/Logic-1.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Formal logic uses formal languages to express, analyze, and clarify arguments. They normally have a very limited vocabulary and exact syntactic rules. These rules specify how their symbols can be combined to construct sentences, so-called well-formed formulas. This simplicity and exactness of formal logic make it capable of formulating precise rules of inference. They determine whether a given argument is valid. Because of the reliance on formal language, natural language arguments cannot be studied directly. Instead, they need to be translated into formal language before their validity can be assessed. The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is a logical formal system. Distinct logics differ from each other concerning the rules of inference they accept as valid and the formal languages used to express them. Starting in the late 19th century, many new formal systems have been proposed. There are disagreements about what makes a formal system a logic. For example, it has been suggested that only logically complete systems, like first-order logic, qualify as logics. For such reasons, some theorists deny that higher-order logics are logics in the strict sense. === Informal logic === When


id: logic-20260505-2
file: data/en.wikipedia.org/wiki/Logic-2.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Premises and conclusions are the basic parts of inferences or arguments and therefore play a central role in logic. In the case of a valid inference or a correct argument, the conclusion follows from the premises, or in other words, the premises support the conclusion. For instance, the premises "Mars is red" and "Mars is a planet" support the conclusion "Mars is a red planet". For most types of logic, it is accepted that premises and conclusions have to be truth-bearers. This means that they have a truth value: they are either true or false. Contemporary philosophy generally sees them either as propositions or as sentences. Propositions are the denotations of sentences and are usually seen as abstract objects. For example, the English sentence "the tree is green" is different from the German sentence "der Baum ist grün" but both express the same proposition. Propositional theories of premises and conclusions are often criticized because they rely on abstract objects. For instance, philosophical naturalists usually reject the existence of abstract objects. Other arguments concern the challenges involved in specifying the identity criteria of propositions. These objections are avoided by seeing premises and conclusions not as propositions but as sentences, i.e. as


id: logic-20260505-3
file: data/en.wikipedia.org/wiki/Logic-3.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Logic is commonly defined in terms of arguments or inferences as the study of their correctness. An argument is a set of premises together with a conclusion. An inference is the process of reasoning from these premises to the conclusion. But these terms are often used interchangeably in logic. Arguments are correct or incorrect depending on whether their premises support their conclusion. Premises and conclusions, on the other hand, are true or false depending on whether they are in accord with reality. In formal logic, a sound argument is an argument that is both correct and has only true premises. Sometimes a distinction is made between simple and complex arguments. A complex argument is made up of a chain of simple arguments. This means that the conclusion of one argument acts as a premise of later arguments. For a complex argument to be successful, each link of the chain has to be successful. Arguments and inferences are either correct or incorrect. If they are correct then their premises support their conclusion. In the incorrect case, this support is missing. It can take different forms corresponding to the different types of reasoning. The strongest form of support corresponds to deductive reasoning.


id: logic-20260505-4
file: data/en.wikipedia.org/wiki/Logic-4.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
==== Ampliative ==== Ampliative arguments are arguments whose conclusions contain additional information not found in their premises. In this regard, they are more interesting since they contain information on the depth level and the thinker may learn something genuinely new. But this feature comes with a certain cost: the premises support the conclusion in the sense that they make its truth more likely but they do not ensure its truth. This means that the conclusion of an ampliative argument may be false even though all its premises are true. This characteristic is closely related to non-monotonicity and defeasibility: it may be necessary to retract an earlier conclusion upon receiving new information or in light of new inferences drawn. Ampliative reasoning plays a central role in many arguments found in everyday discourse and the sciences. Ampliative arguments are not automatically incorrect. Instead, they just follow different standards of correctness. The support they provide for their conclusion usually comes in degrees. This means that strong ampliative arguments make their conclusion very likely while weak ones are less certain. As a consequence, the line between correct and incorrect arguments is blurry in some cases, such as when the premises offer weak but non-negligible


id: logic-20260505-5
file: data/en.wikipedia.org/wiki/Logic-5.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
=== Definitory and strategic rules === The main focus of most logicians is to study the criteria according to which an argument is correct or incorrect. A fallacy is committed if these criteria are violated. In the case of formal logic, they are known as rules of inference. They are definitory rules, which determine whether an inference is correct or which inferences are allowed. Definitory rules contrast with strategic rules. Strategic rules specify which inferential moves are necessary to reach a given conclusion based on a set of premises. This distinction does not just apply to logic but also to games. In chess, for example, the definitory rules dictate that bishops may only move diagonally. The strategic rules, on the other hand, describe how the allowed moves may be used to win a game, for instance, by controlling the center and by defending one's king. It has been argued that logicians should give more emphasis to strategic rules since they are highly relevant for effective reasoning. === Formal systems === A formal system of logic consists of a formal language together with a set of axioms and a proof system used to draw inferences from these axioms. In logic, axioms


id: logic-20260505-6
file: data/en.wikipedia.org/wiki/Logic-6.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
In Aristotelian logic, the subject can be universal, particular, indefinite, or singular. For example, the term "all humans" is a universal subject in the proposition "all humans are mortal". A similar proposition could be formed by replacing it with the particular term "some humans", the indefinite term "a human", or the singular term "Socrates". Aristotelian logic only includes predicates for simple properties of entities. But it lacks predicates corresponding to relations between entities. The predicate can be linked to the subject in two ways: either by affirming it or by denying it. For example, the proposition "Socrates is not a cat" involves the denial of the predicate "cat" to the subject "Socrates". Using combinations of subjects and predicates, a great variety of propositions and syllogisms can be formed. Syllogisms are characterized by the fact that the premises are linked to each other and to the conclusion by sharing one term in each case. Thus, these three propositions contain three terms, referred to as major term, minor term, and middle term. The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how the propositions are formed. For example, the syllogism "all men are


id: logic-20260505-7
file: data/en.wikipedia.org/wiki/Logic-7.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Modal logic is an extension of classical logic. In its original form, sometimes called "alethic modal logic", it introduces two new symbols: ◊ {\displaystyle \Diamond } expresses that something is possible while ◻ {\displaystyle \Box } expresses that something is necessary. For example, if the formula B ( s ) {\displaystyle B(s)} stands for the sentence "Socrates is a banker" then the formula ◊ B ( s ) {\displaystyle \Diamond B(s)} articulates the sentence "It is possible that Socrates is a banker". To include these symbols in the logical formalism, modal logic introduces new rules of inference that govern what role they play in inferences. One rule of inference states that, if something is necessary, then it is also possible. This means that ◊ A {\displaystyle \Diamond A} follows from ◻ A {\displaystyle \Box A} . Another principle states that if a proposition is necessary then its negation is impossible and vice versa. This means that ◻ A {\displaystyle \Box A} is equivalent to ¬ ◊ ¬ A {\displaystyle \lnot \Diamond \lnot A} . Other forms of modal logic introduce similar symbols but associate different meanings with them to apply modal logic to other fields. For example, deontic logic concerns


id: logic-20260505-8
file: data/en.wikipedia.org/wiki/Logic-8.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Informal logic is usually carried out in a less systematic way. It often focuses on more specific issues, like investigating a particular type of fallacy or studying a certain aspect of argumentation. Nonetheless, some frameworks of informal logic have also been presented that try to provide a systematic characterization of the correctness of arguments. The pragmatic or dialogical approach to informal logic sees arguments as speech acts and not merely as a set of premises together with a conclusion. As speech acts, they occur in a certain context, like a dialogue, which affects the standards of right and wrong arguments. A prominent version by Douglas N. Walton understands a dialogue as a game between two players. The initial position of each player is characterized by the propositions to which they are committed and the conclusion they intend to prove. Dialogues are games of persuasion: each player has the goal of convincing the opponent of their own conclusion. This is achieved by making arguments: arguments are the moves of the game. They affect to which propositions the players are committed. A winning move is a successful argument that takes the opponent's commitments as premises and shows how one's own conclusion follows


id: logic-20260505-9
file: data/en.wikipedia.org/wiki/Logic-9.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
The term "mathematical logic" is sometimes used as a synonym of "formal logic". But in a more restricted sense, it refers to the study of logic within mathematics. Major subareas include model theory, proof theory, set theory, and computability theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or to establish logic-based foundations of mathematics. The latter was a major concern in early 20th-century mathematical logic, which pursued the program of logicism pioneered by philosopher-logicians such as Gottlob Frege, Alfred North Whitehead, and Bertrand Russell. Mathematical theories were supposed to be logical tautologies, and their program was to show this by means of a reduction of mathematics to logic. Many attempts to realize this program failed, from the crippling of Frege's project in his Grundgesetze by Russell's paradox, to the defeat of Hilbert's program by Gödel's incompleteness theorems. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic. They include Cantor's theorem, the status of the Axiom of Choice, the question


id: logic-20260505-10
file: data/en.wikipedia.org/wiki/Logic-10.md
category: reference
title: Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Logic
date_saved: 2026-05-05T03:56:39.118518+00:00
instance: kb-cron
parent: logic-20260505-0
summary:
Logic was developed independently in several cultures during antiquity. One major early contributor was Aristotle, who developed term logic in his Organon and Prior Analytics. He was responsible for the introduction of the hypothetical syllogism and temporal modal logic. Further innovations include inductive logic as well as the discussion of new logical concepts such as terms, predicables, syllogisms, and propositions. Aristotelian logic was highly regarded in classical and medieval times, both in Europe and the Middle East. It remained in wide use in the West until the early 19th century. It has now been superseded by later work, though many of its key insights are still present in modern systems of logic. Ibn Sina (Avicenna) was the founder of Avicennian logic, which replaced Aristotelian logic as the dominant system of logic in the Islamic world. It influenced Western medieval writers such as Albertus Magnus and William of Ockham. Ibn Sina wrote on the hypothetical syllogism and on the propositional calculus. He developed an original "temporally modalized" syllogistic theory, involving temporal logic and modal logic. He also made use of inductive logic, such as his methods of agreement, difference, and concomitant variation, which are critical to the scientific method. Fakhr al-Din


id: mathematical-linguistics-20260505-0
file: data/en.wikipedia.org/wiki/Mathematical_linguistics-0.md
category: reference
title: Mathematical linguistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_linguistics
date_saved: 2026-05-05T03:56:40.346427+00:00
instance: kb-cron
parent: mathematical-linguistics-20260505-0
summary:
Mathematical linguistics is the application of mathematics to model phenomena and solve problems in general linguistics and theoretical linguistics. Mathematical linguistics has a significant amount of overlap with computational linguistics. == Discrete mathematics == Discrete mathematics is used in language modeling, including formal grammars, language representation, and historical linguistic trends. === Set theory === Semantic classes, word classes, natural classes, and the allophonic variations of each phoneme in a language are all examples of applied set theory. Set theory and concatenation theory are used extensively in phonetics and phonology. === Combinatorics === In phonotactics, combinatorics is useful for determining which sequences of phonemes are permissible in a given language, and for calculating the total number of possible syllables or words, based on a given set of phonological constraints. Combinatorics on words can reveal patterns within words, morphemes, and sentences. === Finite-state transducers === Context-sensitive rewriting rules of the form a → b / c _ d, used in linguistics to model phonological rules and sound change, are computationally equivalent to finite-state transducers, provided that application is nonrecursive, i.e. the rule is not allowed to rewrite the same substring twice. Weighted FSTs found applications in natural language processing, including machine translation,


id: mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Mathematics-0.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
Mathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory (the study of integers and their properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the study of approximating continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that are either abstractions from nature or purely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove the properties of objects through proofs, which consist of a succession of applications of deductive rules to already established results. These results, called theorems, include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are


id: mathematics-20260505-1
file: data/en.wikipedia.org/wiki/Mathematics-1.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
Geometry is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines, angles and circles, which were developed mainly for the needs of surveying and architecture, but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs, which require that every assertion must be proved. For example, it is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results (theorems) and a few basic statements. The basic statements are not subject to proof because they are self-evident (postulates), or are part of the definition of the subject of study (axioms). This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane (plane geometry) and the three-dimensional Euclidean space. Euclidean geometry was developed without change of methods or scope until the 17th century, when René Descartes introduced what is now called Cartesian coordinates. This constituted a


id: mathematics-20260505-2
file: data/en.wikipedia.org/wiki/Mathematics-2.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
group theory field theory vector spaces, whose study is essentially the same as linear algebra ring theory commutative algebra, which is the study of commutative rings, includes the study of polynomials, and is a foundational part of algebraic geometry homological algebra Lie algebra and Lie group theory Boolean algebra, which is widely used for the study of the logical structure of computers The study of types of algebraic structures as mathematical objects is the purpose of universal algebra and category theory. The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces; this particular area of application is called algebraic topology. === Calculus and analysis === Calculus, formerly called infinitesimal calculus, was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz. It is fundamentally the study of the relationship between variables that depend continuously on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis" is commonly used for advanced


id: mathematics-20260505-3
file: data/en.wikipedia.org/wiki/Mathematics-3.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Part of computational mathematics involves numerical analysis, which is the study of methods for problems in analysis using functional analysis and approximation theory. Numerical analysis broadly includes the study of approximation and discretization, with special focus on rounding errors. Numerical analysis and, more broadly, scientific computing, also study non-analytic topics of mathematical science, especially algorithmic-matrix-and-graph theory. Other areas of computational mathematics include computer algebra and symbolic computation. == History == === Etymology === The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning 'something learned, knowledge, mathematics', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning 'mathematical science'. It entered the English language during the Late Middle English period through French and Latin. Traditionally, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely the first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and English, until around


id: mathematics-20260505-4
file: data/en.wikipedia.org/wiki/Mathematics-4.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. The Greek and Arabic mathematical texts were in turn translated to Latin during the Middle Ages and made available in Europe. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe, with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation, the introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them


id: mathematics-20260505-5
file: data/en.wikipedia.org/wiki/Mathematics-5.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
== Relationship with sciences == Mathematics is used in most sciences for modeling phenomena, which then allows predictions to be made from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model. Inaccurate predictions, rather than being caused by invalid mathematical concepts, imply the need to change the mathematical model used. For example, the perihelion precession of Mercury could only be explained after the emergence of Einstein's general relativity, which replaced Newton's law of gravitation as a better mathematical model. There is still a philosophical debate whether mathematics is a science. However, in practice, mathematicians are typically grouped with scientists, and mathematics shares much in common with the physical sciences. Like them, it is falsifiable, which means in mathematics that, if a result or a theory is wrong, this can be proved by providing a counterexample. Similarly as in science, theories and results (theorems) are often obtained from experimentation. In mathematics, the experimentation may consist of computation on selected examples or of the study of figures or other representations of mathematical objects (often mind representations without physical support). For example, when asked how he came


id: mathematics-20260505-6
file: data/en.wikipedia.org/wiki/Mathematics-6.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
=== Unreasonable effectiveness === The unreasonable effectiveness of mathematics is a phenomenon that was named and first made explicit by physicist Eugene Wigner. It is the fact that many mathematical theories (even the "purest") have applications outside their initial object. These applications may be completely outside their initial area of mathematics, and may concern physical phenomena that were completely unknown when the mathematical theory was introduced. Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. A second historical example is the theory of ellipses. They were studied by the ancient Greek mathematicians as conic sections (that is, intersections of cones with planes). It was almost 2,000 years later that Johannes Kepler discovered that the trajectories of the planets are ellipses. In the 19th century, the internal development of geometry (pure mathematics) led to definition and study of non-Euclidean geometries, spaces of dimension higher than three and manifolds. At this time, these concepts seemed totally disconnected from the physical reality, but at the beginning of the


id: mathematics-20260505-7
file: data/en.wikipedia.org/wiki/Mathematics-7.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
Often the fundamental postulate of mathematical economics is that of the rational individual actor – Homo economicus (lit. 'economic man'). In this model, the individual seeks to maximize their self-interest, and always makes optimal choices using perfect information. This atomistic view of economics allows it to relatively easily mathematize its thinking, because individual calculations are transposed into mathematical calculations. Such mathematical modeling allows one to probe economic mechanisms. Some reject or criticize the concept of Homo economicus. Economists note that real people have limited information, make poor choices, and care about fairness and altruism, not just personal gain. Without mathematical modeling, it is hard to go beyond statistical observations or untestable speculation. Mathematical modeling allows economists to create structured frameworks to test hypotheses and analyze complex interactions. Models provide clarity and precision, enabling the translation of theoretical concepts into quantifiable predictions that can be tested against real-world data. At the start of the 20th century, there was a development to express historical movements in formulas. In 1922, Nikolai Kondratiev discerned the ~50-year-long Kondratiev cycle, which explains phases of economic growth or crisis. Towards the end of the 19th century, mathematicians extended their analysis into geopolitics. Peter Turchin developed cliodynamics in


id: mathematics-20260505-8
file: data/en.wikipedia.org/wiki/Mathematics-8.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, without any use of empirical evidence and intuition. Rigorous reasoning is not specific to mathematics, but, in mathematics, the standard of rigor is much higher than elsewhere. Despite mathematics' concision, rigorous proofs can require hundreds of pages to express, such as the 255-page Feit–Thompson theorem. The emergence of computer-assisted proofs has allowed proof lengths to further expand. The result of this trend is a philosophy of the quasi-empiricist proof that can not be considered infallible, but has a probability attached to it. The concept of rigor in mathematics dates back to ancient Greece, where their society encouraged logical, deductive reasoning. However, this rigorous approach would tend to discourage exploration of new approaches, such as irrational numbers and concepts of infinity. The method of demonstrating rigorous proof was enhanced in the sixteenth century through the use of symbolic notation. In the 18th century, social transition led to mathematicians earning their keep through teaching, which led to more careful thinking about the underlying concepts of mathematics. This produced more rigorous approaches, while transitioning from geometric


id: mathematics-20260505-9
file: data/en.wikipedia.org/wiki/Mathematics-9.md
category: reference
title: Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics
date_saved: 2026-05-05T03:56:46.299650+00:00
instance: kb-cron
parent: mathematics-20260505-0
summary:
=== Psychology (aesthetic, creativity and intuition) === The validity of a mathematical theorem relies only on the rigor of its proof, which could theoretically be done automatically by a computer program. This does not mean that there is no place for creativity in a mathematical work. On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process. An extreme example is Apery's theorem: Roger Apery provided only the ideas for a proof, and the formal proof was given only several months later by three other mathematicians. Creativity and rigor are not the only psychological aspects of the activity of mathematicians. Some mathematicians can see their activity as a game, more specifically as solving puzzles. This aspect of mathematical activity is emphasized in recreational mathematics. Mathematicians can find an aesthetic value to mathematics. Like beauty, it is hard to define, it is commonly related to elegance, which involves qualities like simplicity, symmetry, completeness, and generality. G. H. Hardy in A Mathematician's Apology expressed the belief that the aesthetic considerations are, in themselves, sufficient to justify the


id: formal-ontology-20260505-0
file: data/en.wikipedia.org/wiki/Formal_ontology-0.md
category: reference
title: Formal ontology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Formal_ontology
date_saved: 2026-05-05T03:56:47.552517+00:00
instance: kb-cron
parent: formal-ontology-20260505-0
summary:
In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased (domain- and application-independent) view on reality, which can help the modeler of domain- or application-specific ontologies to avoid possibly erroneous ontological assumptions encountered in modeling large-scale ontologies. By maintaining an independent view on reality, a formal (upper level) ontology gains the following properties: indefinite expandability: the ontology remains consistent with increasing content. content and context independence: any kind of 'concept' can find its place. accommodate different levels of granularity. == Historical background == Theories on how to conceptualize reality date back as far as Plato and Aristotle. The term 'formal ontology' itself was coined by Edmund Husserl in the second edition of his Logical Investigations (1900–01), where it refers to an ontological counterpart of formal logic. Formal ontology for Husserl embraces an axiomatized mereology and a theory of dependence relations, for example between the qualities of an object and the object itself. 'Formal' signifies not the use of a formal-logical language, but rather: non-material, or in other words domain-independent (of universal application). Husserl's ideas on formal ontology were developed especially by his Polish


id: formal-ontology-20260505-1
file: data/en.wikipedia.org/wiki/Formal_ontology-1.md
category: reference
title: Formal ontology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Formal_ontology
date_saved: 2026-05-05T03:56:47.552517+00:00
instance: kb-cron
parent: formal-ontology-20260505-0
summary:
=== Formal ontology as a crossmapping hub: crossmapping taxonomies, databases and nonformal ontologies === Aligning terminologies and ontologies is not an easy task. The divergence of the underlying meaning of word descriptions and terms within different information sources is a well known obstacle for direct approaches to data integration and mapping. One single description may have a completely different meaning in one data source when compared with another. This is because different databases/terminologies often have a different viewpoint on similar items. They are usually built with a specific application-perspective in mind and their hierarchical structure represents this. A formal ontology, on the other hand, represents entities without a particular application scope. Its hierarchy reflects ontological principles and a basic class-subclass relation between its concepts. A consistent framework like this is ideal for crossmapping data sources. However, one cannot just integrate these external data sources in the formal ontology. A direct incorporation would lead to corruption of the framework and principles of the formal ontology. A formal ontology is a great crossmapping hub only if a complete distinction between the content and structure of the external information sources and the formal ontology itself is maintained. This is possible by specifying a


id: organoid-intelligence-20260505-0
file: data/en.wikipedia.org/wiki/Organoid_intelligence-0.md
category: reference
title: Organoid intelligence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Organoid_intelligence
date_saved: 2026-05-05T03:56:48.926200+00:00
instance: kb-cron
parent: organoid-intelligence-20260505-0
summary:
Organoid intelligence (OI) is an emerging field of study in computer science and biology that develops and studies biological wetware computing using 3D cultures of human brain cells (or brain organoids) and brain-machine interface technologies. Such technologies may be referred to as OIs or the nervous filesystem. Organoid intelligent computer systems can be an example of biohybrid systems. == Differences with non-organic computing == As opposed to traditional non-organic silicon-based approaches, OI seeks to use lab-grown cerebral organoids to serve as "biological hardware". While these structures are still far from being able to think like a regular human brain and do not yet possess strong computing capabilities, OI research currently offers the potential to improve the understanding of brain development, learning and memory, potentially finding treatments for neurological disorders such as dementia. Thomas Hartung, a professor from Johns Hopkins University, argued in 2023 that "while silicon-based computers are certainly better with numbers, brains are better at learning." He noted that transistor density in computer chip may be approaching its limits, whereas brains, being wired differently, are more energy-efficient and can store large amounts of information. Some researchers claim that even though human brains are slower than machines at processing simple


id: oxford-model-20260505-0
file: data/en.wikipedia.org/wiki/Oxford_model-0.md
category: reference
title: Oxford model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Oxford_model
date_saved: 2026-05-05T03:56:50.239737+00:00
instance: kb-cron
parent: oxford-model-20260505-0
summary:
The Oxford Model or the Oxford macro econometric Model was a Macroeconomic model created by Lawrence Klein and Sir James Ball. It included a Phillips-type relation and led to an "explosion" of macroeconometric forecasting. == References ==


id: pattern-recognition-20260505-0
file: data/en.wikipedia.org/wiki/Pattern_recognition-0.md
category: reference
title: Pattern recognition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pattern_recognition
date_saved: 2026-05-05T03:56:51.565383+00:00
instance: kb-cron
parent: pattern-recognition-20260505-0
summary:
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition focuses more on the signal and also takes acquisition and signal processing into consideration. It originated in engineering, and the term is popular in the context of computer vision: a leading computer vision conference is named Conference on Computer Vision and Pattern Recognition. In machine learning, pattern recognition is the


id: pattern-recognition-20260505-1
file: data/en.wikipedia.org/wiki/Pattern_recognition-1.md
category: reference
title: Pattern recognition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pattern_recognition
date_saved: 2026-05-05T03:56:51.565383+00:00
instance: kb-cron
parent: pattern-recognition-20260505-0
summary:
Many common pattern recognition algorithms are probabilistic in nature, in that they use statistical inference to find the best label for a given instance. Unlike other algorithms, which simply output a "best" label, often probabilistic algorithms also output a probability of the instance being described by the given label. In addition, many probabilistic algorithms output a list of the N-best labels with associated probabilities, for some value of N, instead of simply a single best label. When the number of possible labels is fairly small (e.g., in the case of classification), N may be set so that the probability of all possible labels is output. Probabilistic algorithms have many advantages over non-probabilistic algorithms: They output a confidence value associated with their choice. (Note that some other algorithms may also output confidence values, but in general, only for probabilistic algorithms is this value mathematically grounded in probability theory. Non-probabilistic confidence values can in general not be given any specific meaning, and only used to compare against other confidence values output by the same algorithm.) Correspondingly, they can abstain when the confidence of choosing any particular output is too low. Because of the probabilities output, probabilistic pattern-recognition algorithms can be more effectively


id: pattern-recognition-20260505-2
file: data/en.wikipedia.org/wiki/Pattern_recognition-2.md
category: reference
title: Pattern recognition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pattern_recognition
date_saved: 2026-05-05T03:56:51.565383+00:00
instance: kb-cron
parent: pattern-recognition-20260505-0
summary:
p ( l a b e l | x , θ ) = p ( x | l a b e l , θ ) p ( l a b e l | θ ) ∑ L ∈ all labels p ( x | L ) p ( L | θ ) . {\displaystyle p({\rm {label}}|{\boldsymbol {x}},{\boldsymbol {\theta }})={\frac {p({{\boldsymbol {x}}|{\rm {label,{\boldsymbol {\theta }}}}})p({\rm {label|{\boldsymbol {\theta }}}})}{\sum _{L\in {\text{all labels}}}p({\boldsymbol {x}}|L)p(L|{\boldsymbol {\theta }})}}.} When the labels are continuously distributed (e.g., in regression analysis), the denominator involves integration rather than summation: p ( l a b e l | x , θ ) = p ( x | l a b e l , θ ) p ( l a b e l | θ ) ∫ L ∈ all labels p ( x | L ) p ( L | θ ) d ⁡ L . {\displaystyle p({\rm {label}}|{\boldsymbol {x}},{\boldsymbol {\theta }})={\frac {p({{\boldsymbol {x}}|{\rm {label,{\boldsymbol {\theta }}}}})p({\rm {label|{\boldsymbol {\theta }}}})}{\int _{L\in {\text{all labels}}}p({\boldsymbol {x}}|L)p(L|{\boldsymbol {\theta }})\operatorname {d} L}}.} The value of θ {\displaystyle {\boldsymbol {\theta }}} is typically learned using maximum a posteriori (MAP) estimation. This finds the best value that simultaneously meets two conflicting objects: To perform as well


id: pattern-recognition-20260505-3
file: data/en.wikipedia.org/wiki/Pattern_recognition-3.md
category: reference
title: Pattern recognition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pattern_recognition
date_saved: 2026-05-05T03:56:51.565383+00:00
instance: kb-cron
parent: pattern-recognition-20260505-0
summary:
identification and authentication: e.g., license plate recognition, fingerprint analysis, face detection/verification, and voice-based authentication. medical diagnosis: e.g., screening for cervical cancer (Papnet), breast tumors or heart sounds; defense: various navigation and guidance systems, target recognition systems, shape recognition technology etc. mobility: advanced driver assistance systems, autonomous vehicle technology, etc. In psychology, pattern recognition is used to make sense of and identify objects, and is closely related to perception. This explains how the sensory inputs humans receive are made meaningful. Pattern recognition can be thought of in two different ways. The first concerns template matching and the second concerns feature detection. A template is a pattern used to produce items of the same proportions. The template-matching hypothesis suggests that incoming stimuli are compared with templates in the long-term memory. If there is a match, the stimulus is identified. Feature detection models, such as the Pandemonium system for classifying letters (Selfridge, 1959), suggest that the stimuli are broken down into their component parts for identification. One observation is a capital E having three horizontal lines and one vertical line. == Algorithms == Algorithms for pattern recognition depend on the type of label output, on whether learning is supervised or unsupervised, and on


id: perceptual-control-theory-20260505-0
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-0.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
Perceptual control theory (PCT) is a model of behavior based on the properties of negative feedback control loops. A control loop maintains a sensed variable at or near a reference value by means of the effects of its outputs upon that variable, as mediated by physical properties of the environment. In engineering control theory, reference values are set by a user outside the system. An example is a thermostat. In a living organism, reference values for controlled perceptual variables are endogenously maintained. Biological homeostasis and reflexes are simple, low-level examples. The discovery of mathematical principles of control introduced a way to model a negative feedback loop closed through the environment (circular causation), which spawned perceptual control theory. It differs fundamentally from some models in behavioral and cognitive psychology that model stimuli as causes of behavior (linear causation). PCT research is published in experimental psychology, neuroscience, ethology, anthropology, linguistics, sociology, robotics, developmental psychology, organizational psychology and management, and a number of other fields. PCT has been applied to design and administration of educational systems, and has led to a psychotherapy called the method of levels. == Principles and differences from other theories == The perceptual control theory is deeply rooted in


id: perceptual-control-theory-20260505-1
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-1.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
== Example == A simple negative feedback control system is a cruise control system for a car. A cruise control system has a sensor which "perceives" speed as the rate of spin of the drive shaft directly connected to the wheels. It also has a driver-adjustable 'goal' specifying a particular speed. The sensed speed is continuously compared against the specified speed by a device (called a "comparator") which subtracts the currently sensed input value from the stored goal value. The difference (the error signal) determines the throttle setting (the accelerator depression), so that the engine output is continuously varied to prevent the speed of the car from increasing or decreasing from that desired speed as environmental conditions change. If the speed of the car starts to drop below the goal-speed, for example when climbing a hill, the small increase in the error signal, amplified, causes engine output to increase, which keeps the error very nearly at zero. If the speed begins to exceed the goal, e.g. when going down a hill, the engine is throttled back so as to act as a brake, so again the speed is kept from departing more than a barely detectable amount from the goal


id: perceptual-control-theory-20260505-2
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-2.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
== Mathematics == To illustrate the mathematical calculations employed in a PCT simulation, consider a pursuit tracking task in which the participant keeps a mouse cursor aligned with a moving target on a computer monitor. The model assumes that a perceptual signal within the participant represents the magnitude of the input quantity qi. (This has been demonstrated to be a rate of firing in a neuron, at least at the lowest levels.) In the tracking task, the input quantity is the vertical distance between the target position T and the cursor position C, and the random variation of the target position acts as the disturbance d of that input quantity. This suggests that the perceptual signal p quantitatively represents the cursor position C minus the target position T, as expressed in the equation p=C–T. Between the perception of target and cursor and the construction of the signal representing the distance between them there is a delay of τ milliseconds, so that the working perceptual signal at time t represents the target-to-cursor distance at a prior time, t – τ. Consequently, the equation used in the model is 1. p(t) = C(t–τ) – T(t–τ) The negative feedback control system receives a


id: perceptual-control-theory-20260505-3
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-3.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
== Distinctions from engineering control theory == In the artificial systems that are specified by engineering control theory, the reference signal is considered to be an external input to the 'plant'. In engineering control theory, the reference signal or set point is public; in PCT, it is not, but rather must be deduced from the results of the test for controlled variables, as described above in the methodology section. This is because in living systems a reference signal is not an externally accessible input, but instead originates within the system. In the hierarchical model, error output of higher-level control loops, as described in the next section below, evokes the reference signal r from synapse-local memory, and the strength of r is proportional to the (weighted) strength of the error signal or signals from one or more higher-level systems. In engineering control systems, in the case where there are several such reference inputs, a 'Controller' is designed to manipulate those inputs so as to obtain the effect on the output of the system that is desired by the system's designer, and the task of a control theory (so conceived) is to calculate those manipulations so as to avoid instability and oscillation.


id: perceptual-control-theory-20260505-4
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-4.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
The reorganization concept has led to a method of psychotherapy called the method of levels (MOL). Using MOL, the therapist aims to help the patient shift his or her awareness to higher levels of perception in order to resolve conflicts and allow reorganization to take place. == Neuroscience == === Learning === Currently, no one theory has been agreed upon to explain the synaptic, neuronal or systemic basis of learning. Prominent since 1973, however, is the idea that long-term potentiation (LTP) of populations of synapses induces learning through both pre- and postsynaptic mechanisms. LTP is a form of Hebbian learning, which proposed that high-frequency, tonic activation of a circuit of neurones increases the efficacy with which they are activated and the size of their response to a given stimulus as compared to the standard neurone (Hebb, 1949). These mechanisms are the principles behind Hebb's famously simple explanation: "Those that fire together, wire together". LTP has received much support since it was first observed by Terje Lømo in 1966 and is still the subject of many modern studies and clinical research. However, there are possible alternative mechanisms underlying LTP, as presented by Enoki, Hu, Hamilton and Fine in 2009, published in


id: perceptual-control-theory-20260505-5
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-5.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
=== Hierarchical organisation === Botvinick in 2008 proposed that one of the founding insights of the cognitive revolution was the recognition of hierarchical structure in human behavior. Despite decades of research, however, the computational mechanisms underlying hierarchically organized behavior are still not fully understood. Bedre, Hoffman, Cooney & D'Esposito in 2009 proposed that the fundamental goal in cognitive neuroscience is to characterize the functional organization of the frontal cortex that supports the control of action. Recent neuroimaging data has supported the hypothesis that the frontal lobes are organized hierarchically, such that control is supported in progressively caudal regions as control moves to more concrete specification of action. However, it is still not clear whether lower-order control processors are differentially affected by impairments in higher-order control when between-level interactions are required to complete a task, or whether there are feedback influences of lower-level on higher-level control. Botvinik in 2008 found that all existing models of hierarchically structured behavior share at least one general assumption – that the hierarchical, part–whole organization of human action is mirrored in the internal or neural representations underlying it. Specifically, the assumption is that there exist representations not only of low-level motor behaviors, but also separable representations


id: perceptual-control-theory-20260505-6
file: data/en.wikipedia.org/wiki/Perceptual_control_theory-6.md
category: reference
title: Perceptual control theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perceptual_control_theory
date_saved: 2026-05-05T03:56:52.953091+00:00
instance: kb-cron
parent: perceptual-control-theory-20260505-0
summary:
== Current situation and prospects == The preceding explanation of PCT principles provides justification of how this theory can provide a valid explanation of neural organisation and how it can explain some of the current issues of conceptual models. Perceptual control theory currently proposes a hierarchy of 11 levels of perceptions controlled by systems in the human mind and neural architecture. These are: intensity, sensation, configuration, transition, event, relationship, category, sequence, program, principle, and system concept. Diverse perceptual signals at a lower level (e.g. visual perceptions of intensities) are combined in an input function to construct a single perception at the higher level (e.g. visual perception of a color sensation). The perceptions that are constructed and controlled at the lower levels are passed along as the perceptual inputs at the higher levels. The higher levels in turn control by adjusting the reference levels (goals) of the lower levels, in effect telling the lower levels what to perceive. While many computer demonstrations of principles have been developed, the proposed higher levels are difficult to model because too little is known about how the brain works at these levels. Isolated higher-level control processes can be investigated, but models of an extensive hierarchy


id: prescriptive-analytics-20260505-0
file: data/en.wikipedia.org/wiki/Prescriptive_analytics-0.md
category: reference
title: Prescriptive analytics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Prescriptive_analytics
date_saved: 2026-05-05T03:56:54.207294+00:00
instance: kb-cron
parent: prescriptive-analytics-20260505-0
summary:
Prescriptive analytics is a form of business analytics which suggests decision options for how to take advantage of a future opportunity or mitigate a future risk and shows the implication of each decision option. It enables an enterprise to consider "the best course of action to take" in the light of information derived from descriptive and predictive analytics. == Overview == Prescriptive analytics is the third and final phase of business analytics, which also includes descriptive and predictive analytics. Referred to as the "final frontier of analytic capabilities", prescriptive analytics entails the application of mathematical and computational sciences and suggests decision options for how to take advantage of the results of descriptive and predictive phases. The first stage of business analytics is descriptive analytics, which still accounts for the majority of all business analytics today. Descriptive analytics looks at past performance and understands that performance by mining historical data to look for the reasons behind past success or failure. Most management reporting – such as sales, marketing, operations, and finance – uses this type of post-mortem analysis. The next phase is predictive analytics. Predictive analytics answers the question of what is likely to happen. This is where historical data is


id: prescriptive-analytics-20260505-1
file: data/en.wikipedia.org/wiki/Prescriptive_analytics-1.md
category: reference
title: Prescriptive analytics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Prescriptive_analytics
date_saved: 2026-05-05T03:56:54.207294+00:00
instance: kb-cron
parent: prescriptive-analytics-20260505-0
summary:
=== Unconventional Resource Development === With the value of the end product determined by global commodity economics, the basis of competition for operators in upstream E&P is the ability to effectively deploy capital to locate and extract resources more efficiently, effectively, predictably, and safely than their peers. In unconventional resource plays, operational efficiency and effectiveness is diminished by reservoir inconsistencies, and decision-making impaired by high degrees of uncertainty. These challenges manifest themselves in the form of low recovery factors and wide performance variations. Prescriptive Analytics software can accurately predict production and prescribe optimal configurations of controllable drilling, completion, and production variables by modeling numerous internal and external variables simultaneously, regardless of source, structure, size, or format. Prescriptive analytics software can also provide decision options and show the impact of each decision option so the operations managers can proactively take appropriate actions, on time, to guarantee future exploration and production performance, and maximize the economic value of assets at every point over the course of their serviceable lifetimes. === Oilfield Equipment Maintenance === In the realm of oilfield equipment maintenance, Prescriptive Analytics can optimize configuration, anticipate and prevent unplanned downtime, optimize field scheduling, and improve maintenance planning. According to General Electric,


id: queueing-theory-20260505-0
file: data/en.wikipedia.org/wiki/Queueing_theory-0.md
category: reference
title: Queueing theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Queueing_theory
date_saved: 2026-05-05T03:56:55.531499+00:00
instance: kb-cron
parent: queueing-theory-20260505-0
summary:
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang, who created models to describe the system of incoming calls at the Copenhagen Telephone Exchange Company. These ideas were seminal to the field of teletraffic engineering and have since seen applications in telecommunications, traffic engineering, computing, project management, and particularly industrial engineering, where they are applied in the design of factories, shops, offices, and hospitals. == Description == Queueing theory is one of the major areas of study in the discipline of management science. Through management science, businesses are able to solve a variety of problems using different scientific and mathematical approaches. Queueing analysis is the probabilistic analysis of waiting lines, and thus the results, also referred to as the operating characteristics, are probabilistic rather than deterministic. The probability that n customers are in the queueing system, the average number of customers in the queueing


id: queueing-theory-20260505-1
file: data/en.wikipedia.org/wiki/Queueing_theory-1.md
category: reference
title: Queueing theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Queueing_theory
date_saved: 2026-05-05T03:56:55.531499+00:00
instance: kb-cron
parent: queueing-theory-20260505-0
summary:
P n = λ n − 1 λ n − 2 ⋯ λ 0 μ n μ n − 1 ⋯ μ 1 P 0 = P 0 ∏ i = 0 n − 1 λ i μ i + 1 {\displaystyle P_{n}={\frac {\lambda _{n-1}\lambda _{n-2}\cdots \lambda _{0}}{\mu _{n}\mu _{n-1}\cdots \mu _{1}}}P_{0}=P_{0}\prod _{i=0}^{n-1}{\frac {\lambda _{i}}{\mu _{i+1}}}} . The condition ∑ n = 0 ∞ P n = P 0 + P 0 ∑ n = 1 ∞ ∏ i = 0 n − 1 λ i μ i + 1 = 1 {\displaystyle \sum _{n=0}^{\infty }P_{n}=P_{0}+P_{0}\sum _{n=1}^{\infty }\prod _{i=0}^{n-1}{\frac {\lambda _{i}}{\mu _{i+1}}}=1} leads to P 0 = 1 1 + ∑ n = 1 ∞ ∏ i = 0 n − 1 λ i μ i + 1 {\displaystyle P_{0}={\frac {1}{1+\sum _{n=1}^{\infty }\prod _{i=0}^{n-1}{\frac {\lambda _{i}}{\mu _{i+1}}}}}} which, together with the equation for P n {\displaystyle P_{n}} ( n ≥ 1 ) {\displaystyle (n\geq 1)} , fully describes the required steady state probabilities. === Kendall's notation === Single queueing nodes are usually described using Kendall's notation in the form A/S/c where A describes the distribution of durations between each arrival to the queue, S the distribution of service times for


id: queueing-theory-20260505-2
file: data/en.wikipedia.org/wiki/Queueing_theory-2.md
category: reference
title: Queueing theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Queueing_theory
date_saved: 2026-05-05T03:56:55.531499+00:00
instance: kb-cron
parent: queueing-theory-20260505-0
summary:
M stands for Markov or memoryless, and means arrivals occur according to a Poisson process D stands for deterministic, and means jobs arriving at the queue require a fixed amount of service k describes the number of servers at the queueing node (k = 1, 2, 3, ...) If the node has more jobs than servers, then jobs will queue and wait for service. The M/G/1 queue was solved by Felix Pollaczek in 1930, a solution later recast in probabilistic terms by Aleksandr Khinchin and now known as the Pollaczek–Khinchine formula. After the 1940s, queueing theory became an area of research interest to mathematicians. In 1953, David George Kendall solved the GI/M/k queue and introduced the modern notation for queues, now known as Kendall's notation. In 1957, Pollaczek studied the GI/G/1 using an integral equation. John Kingman gave a formula for the mean waiting time in a G/G/1 queue, now known as Kingman's formula. Leonard Kleinrock worked on the application of queueing theory to message switching in the early 1960s and packet switching in the early 1970s. His initial contribution to this field was his doctoral thesis at the Massachusetts Institute of Technology in 1962, published in book form in


id: queueing-theory-20260505-3
file: data/en.wikipedia.org/wiki/Queueing_theory-3.md
category: reference
title: Queueing theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Queueing_theory
date_saved: 2026-05-05T03:56:55.531499+00:00
instance: kb-cron
parent: queueing-theory-20260505-0
summary:
=== Mean-field limits === Mean-field models consider the limiting behaviour of the empirical measure (proportion of queues in different states) as the number of queues m approaches infinity. The impact of other queues on any given queue in the network is approximated by a differential equation. The deterministic model converges to the same stationary distribution as the original model. === Heavy traffic/diffusion approximations === In a system with high occupancy rates (utilisation near 1), a heavy traffic approximation can be used to approximate the queueing length process by a reflected Brownian motion, Ornstein–Uhlenbeck process, or more general diffusion process. The number of dimensions of the Brownian process is equal to the number of queueing nodes, with the diffusion restricted to the non-negative orthant. === Fluid limits === Fluid models are continuous deterministic analogs of queueing networks obtained by taking the limit when the process is scaled in time and space, allowing heterogeneous objects. This scaled trajectory converges to a deterministic equation which allows the stability of the system to be proven. It is known that a queueing network can be stable but have an unstable fluid limit. === Queueing applications === Queueing theory finds widespread application in computer science and


id: risk-analysis-business-20260505-0
file: data/en.wikipedia.org/wiki/Risk_analysis_(business)-0.md
category: reference
title: Risk analysis (business)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Risk_analysis_(business)
date_saved: 2026-05-05T03:56:56.759751+00:00
instance: kb-cron
parent: risk-analysis-business-20260505-0
summary:
Risk analysis is the process of identifying and assessing risks that may jeopardize an organization's success. It typically fits into a larger risk management framework. Diligent risk analysis helps construct preventive measures to reduce the probability of incidents from occurring, as well as counter-measures to address incidents as they develop to minimize negative impacts on the organization. A popular method to perform risk analysis on IT systems is called facilitated risk analysis process (FRAP). == Facilitated risk analysis process == FRAP analyzes one system, application or segment of business processes at a time. FRAP assumes that additional efforts to develop precisely quantified risks are not cost-effective because: such estimates are time-consuming risk documentation becomes too voluminous for practical use specific loss estimates are generally not needed to determine if controls are needed. without assumptions, there is little risk analysis After identifying and categorizing risks, a team identifies the controls that could mitigate the risk. The decision for what controls are needed lies with the business manager. The team's conclusions as to what risks exist and what controls needed are documented, along with a related action plan for control implementation. Three of the most important risks a software company faces are:


id: statistics-20260505-0
file: data/en.wikipedia.org/wiki/Statistics-0.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
Statistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. Statistics is deeply related to subjects like physics, chemistry, geography, geopolitics, and especially mathematics. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main


id: statistics-20260505-1
file: data/en.wikipedia.org/wiki/Statistics-1.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
==== Sampling ==== When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models. To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative sampling ensures that inferences and conclusions can safely be extended from the sample to the population as a whole. A major problem lies in determining the extent to which the chosen sample is actually representative. Statistics offers methods to estimate and correct for any bias in the sample and data collection procedures. There are also methods of experimental design that can lessen these issues at the outset of a study, strengthening its ability to discern truths about the population. Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid only when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory


id: statistics-20260505-2
file: data/en.wikipedia.org/wiki/Statistics-2.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables


id: statistics-20260505-3
file: data/en.wikipedia.org/wiki/Statistics-3.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
===== Null hypothesis and alternative hypothesis ===== Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time. The alternative hypothesis is the name of the hypothesis that contradicts the null hypothesis. The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H0, asserts that the defendant is innocent, whereas the alternative hypothesis, H1, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H0 (the status quo) stands in opposition to H1 and is maintained unless H1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H0" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily accept H0 but fails to reject H0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors. The null hypothesis cannot be proven true because it is already assumed to be true when the test


id: statistics-20260505-4
file: data/en.wikipedia.org/wiki/Statistics-4.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
The standard approach is to test a null hypothesis against an alternative hypothesis. A critical region is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true (statistical significance) and the probability of type II error is the probability that the estimator does not belong to the critical region given that the alternative hypothesis is true. The statistical power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false. Referring to statistical significance does not necessarily mean that the overall result is significant in real-world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that it is unlikely to help the patient noticeably. Although in principle the acceptable level of statistical significance may be subject to debate, the significance level is the largest p-value that allows the test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the


id: statistics-20260505-5
file: data/en.wikipedia.org/wiki/Statistics-5.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel), probability theory as a mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli's posthumous work Ars Conjectandi. This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it a decade earlier in 1795. In the 1830s-1850s, "statistical offices" and national "statistical societies" were founded in Europe and America, and in the mid-19th century, the idea arose of "organized contacts between the statisticians of different countries although informal contacts occurred earlier". In those days, the name "statistics" referred mainly to "matters of state", and British statisticians were often called "statists". Belgian scientist Adolphe Quetelet (1796–1874) introduced the notion of the "average man" (l'homme


id: statistics-20260505-6
file: data/en.wikipedia.org/wiki/Statistics-6.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
=== Statistics in academia === Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. Business statistics applies statistical methods in econometrics, auditing and production and operations, including services improvement and marketing research. A study of two journals in tropical biology found that the 12 most frequent statistical tests are: analysis of variance (ANOVA), chi-squared test, Student's t-test, linear regression, Pearson's correlation coefficient, Mann-Whitney U test, Kruskal-Wallis test, Shannon's diversity index, Tukey's range test, cluster analysis, Spearman's rank correlation coefficient and principal component analysis. A typical statistics course covers descriptive statistics, probability, binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation. Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of free statistics software. === Statistical computing === The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as


id: statistics-20260505-7
file: data/en.wikipedia.org/wiki/Statistics-7.md
category: reference
title: Statistics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistics
date_saved: 2026-05-05T03:56:59.364659+00:00
instance: kb-cron
parent: statistics-20260505-0
summary:
Who says so? (Do they have an axe to grind?) How do they know? (Do they have the resources to know the facts?) What's missing? (Do they give us a complete picture?) Did someone change the subject? (Do they offer us the right answer to the wrong problem?) Does it make sense? (Is their conclusion logical and consistent with what we already know?) === Misinterpretation: correlation === The concept of correlation is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a data set often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death, might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. == See also == Foundations and major


