kb/data/en.wikipedia.org/wiki/Conversation_theory-3.md

title	chunk	source	category	tags	date_saved	instance
Conversation theory	4/5	https://en.wikipedia.org/wiki/Conversation_theory	reference	science, encyclopedia	2026-05-05T07:11:08.773848+00:00	kb-cron

And where a concept is defined as an operation that is substitutable for the below ordered-pair:

    C
    O
    N
    ≜
    P
    R
    O
    C
    =
    ⟨
    P
    R
    O
    G
    ,
    I
    N
    T
    E
    R
    ⟩
  

{\displaystyle CON\triangleq PROC=\langle PROG,INTER\rangle }

Whose contents are defined as:

            I
            N
            T
            E
            R
          
          
            ≜
          
          
            λ
            (
            x
            )
          
        
        
          
            P
            R
            O
            G
          
          
            ≜
          
          
            π
            (
            x
            )
          
        
      
    
  

{\displaystyle {\begin{array}{lcl}INTER&\triangleq &\lambda (x)\\PROG&\triangleq &\pi (x)\end{array}}}

Such that a program is defined as a calculus or set of rules

    π
  

{\displaystyle \pi }

that operates on some input, and an interpretation is conceived of as a compiler

    λ
  

{\displaystyle \lambda }

that attempts to compile said input into an executable form. A concept—as thus defined—is considered by Pask to be an

    L
  

{\displaystyle L}

-procedure or process, which is embodied by its underlying processor called an

    L
  

{\displaystyle L}

-processor. When said form has been compiled by said processor, then the concept may be executed to produce a topic relation, which may be sufficiently written as:

    A
    P
    (
    λ
    (
    π
    (
    
      R
      
        H
      
    
    )
    )
    )
    =
    A
    P
    (
    C
    O
    N
    (
    
      R
      
        H
      
    
    )
    )
    ⇒
    
      R
      
        H
      
    
  

{\displaystyle AP(\lambda (\pi (R_{H})))=AP(CON(R_{H}))\Rightarrow R_{H}}

Which represents one such representation of the basic logical form of a concept within conversation theory. In later work, Pask envisaged conceptualisation as a parallel rather than a serial process: That within a conversational system, conversations may or may not be taking place at any given time. Because of this, he demarcates the application operator

    A
    P
  

{\displaystyle AP}

and the execution operator

    &
  

{\displaystyle \&}

to indicate when the activation of a concept is necessarily activated or when it is sufficiently activated within a conversational system.

==== Protologic ==== The protologic or protolanguage (simplified often as Lp), is a sister theory of conversation theory which contains a system of rules of inference governing conceptual formulation and modulation. The rules and principles governing conceptualisation within the protologic are often illustrated as entailment structures, which are representational snapshots that may help visualize an organized and publicly available collection of resultant knowledge within conversation theory. The entailment structure a graph composed of a series of nodes and arrows representing a series of topic relations and the derivations of such topic relations.

===== Entailment Derivation =====

===== Collective Derivation =====

===== Disjunct Derivation =====

===== Analogy Derivation =====

=== Cognitive Reflector === From conversation theory, Pask developed what he called a "Cognitive Reflector". This is a virtual machine for selecting and executing concepts or topics from an entailment mesh shared by at least a pair of participants. It features an external modelling facility on which agreement between, say, a teacher and pupil may be shown by reproducing public descriptions of behaviour. We see this in essay and report writing or the "practicals" of science teaching.

Lp was Pask's protolanguage which produced operators like Ap which concurrently executes the concept, Con, of a Topic, T, to produce a Description, D. Thus:

    A
    P
    (
    C
    O
    N
    )
    ⇒
    D
    (
    T
    )
  

{\displaystyle AP(CON)\Rightarrow D(T)}

where => stands for produces. A succinct account of these operators is presented in Pask Amongst many insights he points out that three indexes are required for concurrent execution, two for parallel and one to designate a serial process. He subsumes this complexity by designating participants A, B, etc. In Commentary toward the end of Pask, he states:

The form not the content of the theories (conversation theory and interactions of actors theory) return to and is congruent with the forms of physical theories; such as wave particle duality (the set theoretic unfoldment part of conversation theory is a radiation and its reception is the interpretation by the recipient of the descriptions so exchanged, and vice versa). The particle aspect is the recompilation by the listener of what a speaker is saying. Theories of many universes, one at least for each participant A and one to participant B- are bridged by analogy. As before this is the truth value of any interaction; the metaphor for which is culture itself.

=== Learning strategies ===

In order to facilitate learning, Pask argued that subject matter should be represented in the form of structures which show what is to be learned. These structures exist in a variety of different levels depending upon the extent of the relationships displayed. The critical method of learning according to Conversation Theory is "teachback" in which one person teaches another what they have learned. Pask identified two different types of learning strategies: