CogSci C131

Production systems and cognitive architectures

Tom Griffiths

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Token manipulation systems

System is defined fully by a set of tokens starting positions for those tokens formal rules stating how token positions can

be changed into other token positions Rules depend only on current positions,

and define only the next positions

Example 2: Formal logic Pieces Starting positions Formal rules

P, Q, , , , , (, )

well-formed formulas e.g., P Q

e.g., P Q P Q

Outline

Production systems

Break

Cognitive architectures

The World

Logic

P Q

P

Q

Facts Inference Rules

Herb Simon and Allen Newell

Logic Theorist (Newell & Simon, 1956)

The first AI system Found proofs by using heuristics to search the large space

Heuristics inspired by human problem-solving strategies

Symposium on Information Theory

Often considered the birth of cognitive science (on 9/11/56, at MIT)

Three famous papers presented: Allen Newell & Herbert Simon, The Logic Theory

Machine: A complex information processing system Noam Chomsky, Three models of language George Miller, The magical number seven

The World

Logic

P Q

P

Q

Facts Inference Rules

The World

Early AI systems Workspace Operations

Actions

Observations

Facts

Goals

Operations

Production systems

Operations are encoded in IF THEN form

Production fires when IF condition is satisfied, executes instructions following THEN

String World

The world is a string of characters e.g. ABC

Facts are properties of the string e.g. initial substrings

Actions are rewriting parts of the string e.g. AB -> BA

A production system

P1: $$ -> *P2: *$ -> *P3: *x -> x*P4: * -> null & haltP5: $xy -> y$xP6: null -> $

Where: x and y can be any letter * and $ are reserved symbols null is the empty symbol halt ends execution

Some challenges

How do we decide which production to apply, when many are possible? execute the first execute at random execute via some complicated criterion

Should we allow any IF THEN rule to be in our set of rules?

thought string = computation;disp(string);

Minds and computers are both formal systems

ACT-R (Anderson, 1993)

Outside World

Working Memory

Declarative Memory

Production Memory

Encoding Performance

Storage

Retrieval Execution

Match

Application

John Anderson

Declarative memory Facts are represented by chunks Chunks are activated by context

organized in a semantic network, which we will talk about later in the semester

Procedural memory

Skills and strategies used in solving problems are represented as productions

Hierarchy of goals viewed as one of the key characteristics of human behavior

Productions differ in time to execute

Learning

People can acquire new chunks through perceptual experience, or via productions

People can form new productions by generalizing from experience

Learning

People can acquire new chunks through perceptual experience, or via productions

People can form new productions by generalizing from experience

Sets of productions can be compiled into more efficient productions

Compiling productions

If certain productions regularly fire other productions, then those productions can be collapsed

Can be executed by another production

The power-law of practice

(Siebel, 1963)

1023 alternative choice task

(Ohlsson, 1992)

Asimovs books

time = practice- log(time) = -log(practice)

The promise of production systems

All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition (Anderson, 1996, p. 356) Simons (1981) metaphor of the ant

Just a matter of more rules

Same philosophy has been applied to AI

The Cyc project aims to collect rules for common sense reasoning

You can download a version with 300,000 concepts, 2,000,000 facts

Doug Lenat

The promise of production systems

All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition (Anderson, 1996, p. 356) Simons metaphor of the ant

Productions can modify productions

The World

Early AI systems Workspace

Operations

Actions

Observations

Facts

Goals

Operations

The promise of production systems

All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition (Anderson, 1996, p. 356) Simons (1981) metaphor of the ant

Productions can modify productions A programming language for human thought

just a matter of figuring out the productions!

Chatbots and productions

Break

Up next: Cognitive architectures

Computation

Alan Turing (1912-1954)

Computer architecture

John von Neumann

What architecture underlies cognition? How can we characterize human information

processing in terms of memory symbols operations interpretation interaction with the world

Cashing out the idea of cognition as a formal system, explicitly analogous to computers

ACT-R (Anderson, 1993)

Outside World

Working Memory

Declarative Memory

Production Memory

Encoding Performance

Storage

Retrieval Execution

Match

Application

John Anderson

SOAR (Newell, Rosenbloom, Polk, and Laird, 1987)

Outside World

Senses Muscles

Perceptual Systems

Motor Systems

Working Memory

Production Memory Chunking

Decision

Execution

Allen Newell

Why study cognitive architecture?

Estimate parameters characterizing human information processing how long does each operation take?

Additive factors analysis

Assuming that each operation takes a fixed amount of time, estimate times by manipulating operations involved

H P Z

Probe: Q

Probe: L

M

H P R

Probe: B

V N A S C

Additive factors analysis

Assuming that each operation takes a fixed amount of time, estimate times by manipulating operations involved

So estimate time for productions, to build up to really complex tasks

(Sternberg, 1967)

Why study cognitive architecture? Estimate parameters characterizing

human information processing how long does each operation take?

Figure out whats going wrong

Why study cognitive architecture? Estimate parameters characterizing

human information processing how long does each operation take?

Figure out whats going wrong Unified theories of cognition

rather than lots of different models, lots of programs in a common language

shared components across different models, connections between problems

What kind of explanations do we get?

What sort of unified theory do we develop?

Marrs three levels

Computation What is the goal of the computation, why is it

appropriate, and what is the logic of the strategy by which it can be carried out?

Representation and algorithm What is the representation for the input and

output, and the algorithm for the transformation? Implementation

How can the representation and algorithm be realized physically?

cons

train

s co

nstra

ins

What kind of explanations do we get?

What sort of unified theory do we develop?

Even if production systems are the right way to characterize human cognition, all we get is a mechanistic story a program for every problem describes how people do what they do not why people behave in a particular way

Thursday

Formal systems and language you get to read Chomsky! think about different proposals for formal systems

that can capture the structure of human languages