production systems
DESCRIPTION
Production SystemsTRANSCRIPT
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CogSci C131
Production systems and cognitive architectures
Tom Griffiths
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Admin
Problem set 0 is due 5pm Friday! Python transition class 4:30 today in
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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
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Example 2: Formal logic Pieces Starting positions Formal rules
P, Q, , , , , (, )
well-formed formulas e.g., P Q
e.g., P Q P Q
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Outline
Production systems
Break
Cognitive architectures
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The World
Logic
P Q
P
Q
Facts Inference Rules
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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
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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
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The World
Logic
P Q
P
Q
Facts Inference Rules
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The World
Early AI systems Workspace Operations
Actions
Observations
Facts
Goals
Operations
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Production systems
Operations are encoded in IF THEN form
Production fires when IF condition is satisfied, executes instructions following THEN
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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
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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
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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?
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thought string = computation;disp(string);
Minds and computers are both formal systems
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ACT-R (Anderson, 1993)
Outside World
Working Memory
Declarative Memory
Production Memory
Encoding Performance
Storage
Retrieval Execution
Match
Application
John Anderson
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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
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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
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Learning
People can acquire new chunks through perceptual experience, or via productions
People can form new productions by generalizing from experience
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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
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Compiling productions
If certain productions regularly fire other productions, then those productions can be collapsed
Can be executed by another production
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The power-law of practice
(Siebel, 1963)
1023 alternative choice task
(Ohlsson, 1992)
Asimovs books
time = practice- log(time) = -log(practice)
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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
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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
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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
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The World
Early AI systems Workspace
Operations
Actions
Observations
Facts
Goals
Operations
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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!
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Chatbots and productions
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Break
Up next: Cognitive architectures
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Computation
Alan Turing (1912-1954)
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Computer architecture
John von Neumann
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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
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ACT-R (Anderson, 1993)
Outside World
Working Memory
Declarative Memory
Production Memory
Encoding Performance
Storage
Retrieval Execution
Match
Application
John Anderson
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SOAR (Newell, Rosenbloom, Polk, and Laird, 1987)
Outside World
Senses Muscles
Perceptual Systems
Motor Systems
Working Memory
Production Memory Chunking
Decision
Execution
Allen Newell
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Why study cognitive architecture?
Estimate parameters characterizing human information processing how long does each operation take?
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Additive factors analysis
Assuming that each operation takes a fixed amount of time, estimate times by manipulating operations involved
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H P Z
Probe: Q
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Probe: L
M
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H P R
Probe: B
V N A S C
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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)
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Why study cognitive architecture? Estimate parameters characterizing
human information processing how long does each operation take?
Figure out whats going wrong
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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
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What kind of explanations do we get?
What sort of unified theory do we develop?
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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
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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
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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