---
title: "Probabilistic logic"
chunk: 1/2
source: "https://en.wikipedia.org/wiki/Probabilistic_logic"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:44:54.389289+00:00"
instance: "kb-cron"
---

Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computational complexities of their probabilistic and logical components.  Other difficulties include the possibility of counter-intuitive results, such as in case of belief fusion in Dempster–Shafer theory. Source trust and epistemic uncertainty about the probabilities they provide, such as defined in subjective logic, are additional elements to consider. The need to deal with a broad variety of contexts and issues has led to many different proposals.

== Logical background ==
There are numerous proposals for probabilistic logics. Very roughly, they can be categorized into two different classes: those logics that attempt to make a probabilistic extension to logical entailment, such as Markov logic networks, and those that attempt to address the problems of uncertainty and lack of evidence (evidentiary logics).
That the concept of probability can have different meanings may be understood by noting that, despite the mathematization of probability in the Enlightenment, mathematical probability theory remains, to this very day, entirely unused in criminal courtrooms, when evaluating the "probability" of the guilt of a suspected criminal.
More precisely, in evidentiary logic, there is a need to distinguish the objective truth of a statement from our decision about the truth of that statement, which in turn must be distinguished from our confidence in its truth: thus, a suspect's real guilt is not necessarily the same as the judge's decision on guilt, which in turn is not the same as assigning a numerical probability to the commission of the crime, and deciding whether it is above a numerical threshold of guilt.  The verdict on a single suspect may be guilty or not guilty with some uncertainty, just as the flipping of a coin may be predicted as heads or tails with some uncertainty.  Given a large collection of suspects, a certain percentage may be guilty, just as the probability of flipping "heads" is one-half. However, it is incorrect to take this law of averages with regard to a single criminal (or single coin-flip): the criminal is no more "a little bit guilty" than predicting a single coin flip to be "a little bit heads and a little bit tails": we are merely uncertain as to which it is.  Expressing uncertainty as a numerical probability may be acceptable when making scientific measurements of physical quantities, but it is merely a mathematical model of the uncertainty we perceive in the context of "common sense" reasoning and logic.  Just as in courtroom reasoning, the goal of employing uncertain inference is to gather evidence to strengthen the confidence of a proposition, as opposed to performing some sort of probabilistic entailment.

== Historical context ==
Historically, attempts to quantify probabilistic reasoning date back to antiquity. There was a particularly strong interest starting in the 12th century, with the work of the Scholastics, with the invention of the half-proof (so that two half-proofs are sufficient to prove guilt), the elucidation of moral certainty (sufficient certainty to act upon, but short of absolute certainty), the development of Catholic probabilism (the idea that it is always safe to follow the established rules of doctrine or the opinion of experts, even when they are less probable), the case-based reasoning of casuistry, and the scandal of Laxism (whereby probabilism was used to give support to almost any statement at all, it being possible to find an expert opinion in support of almost any proposition.).

== Modern proposals ==
Below is a list of proposals for probabilistic and evidentiary extensions to classical and predicate logic.