Abstraction and ACT-R

Outline

Motivations for the Theory– Architecture– Abstraction

Production Rules

ACT-R Architecture of Cognition

Architecture

• There is a distinction between brain architecture and cognitive architecture.

• This is a difference between the physical description of the system, and the functional properties that it enables.

• Some examples…

• The common feature to each is in the method of abstraction.– Moving from a more complex, lower level

system of interaction, to a higher level language in which those lower level features are typed.

Some Characteristic features of Abstraction.

Constraints on the Abstraction• Typing

– Lower level features are given higher level types

• Simplification– The higher level abstraction is obligated to

simplify conceptual complexity

• Morphism– There must be a mapping. – ‘Many to one’

Production Systems

Comprise a language with sentences of the formIf <<condition>> then <<event/action>>

Developed by Emil Post (1943), also known as ‘Post Production Rules’

Turing Complete

Solve a Linear Equation

• If the expression has X = N, where N is a number, THEN halt and check by substituting N in the original equation

• If there is a term in X on the right-hand side, THEN subtract it from both sides, and collect the terms.

• IF there is a numerical term on the left hand side, THEN subtract it from both sides, and collect the terms

• IF the equation has the form NX = M, N = 1, THEN divide both sides by N

• If the expression has X = N, where N is a number, THEN halt and check by substituting N in the original equation

• If there is a term in X on the right-hand side, THEN subtract it from both sides, and collect the terms.

• IF there is a numerical term on the left hand side, THEN subtract it from both sides, and collect the terms

• IF the equation has the form NX = M, N = 1, THEN divide both sides by N

• X = 2X + 5

• X – 2X = 2X – 2X + 5

• -X = 5

• X = -5

ACT-R(Adaptive Control of Thought-Rational)

• Modules

• Buffers

• Productions

Modules - Fodor (Modularity of Mind)

• Features– Functional

separation

Domain specific• Interaction between

modules

Buffers

• Active Content• Interface• Interaction between

modules– Provides the link

Productions

• If <<condition>> then <<result>>

• State Change– Contents of Buffer

– Contents of Modules

Learning

• Adaptive control – Update

• Goal structures

• Declarative memory contents

• Productions

Structure of Declarative Module

‘Chunks’ – A collection of related information.

Action023:isa chaseagent dogobject cat

Fact3+4:isa addition-factaddend1 threeaddend2 foursum seven

Summary

• Cognitive Science and Act-R benefit by engaging in abstraction

• By matches conditions set by contents in the buffer, and specifying to changes in that content. Act-R models cognition.