Reasoning and Rationality

Emily SlusserFebruary 13th 2006

Charter, N. &Oaksford, M. (1999). Ten years of the rational analysis of cognition. Trends in Cognitive Science, 3, 57-65.

Rational Analysis

Style of explanation in cognitive sciences (J.R. Anderson and Milson)

But what is rational analysis exactly?

How does it relate to other approaches in cognitive sciences?

How does it apply in practice?

Mechanistic & Purposive Explanation

MechanisticInternal causal structure

PurposiveWhat problem does it solve?

What is its function?

Methodology(Anderson, J.R.)

1) Goals of the cognitive system

2) Environment to which the system has adopted (formal model)

3) Computational Limitations (minimal assumptions)

4) Derive optimal behavior function

5) Empirical data to see if predictions are confirmed

6) Iteration to refine the theory

Rational Analysis and Evolutionary Psychology Adaptation arises through evolution

Adaptive throughout evolutionary history but counteradaptive in contemporary environment

Need-probability Rarity assumption

Wason card task -> enhanced reasoning ability social reasoning module

The Role of Optimality

Some things to consider…

How to compute the optimal solution?

Is this analysis necessary?

Two or more ‘good’ but very different solutions

Note of caution but nothing more…

Memory

1) Goals - Efficient retrieval of relevant information

2) Environment - Determines need-probability

3) Computational Limitations - Memory searched sequentially

4) Optimization - Memory system should stop retrieval when

p G < C

5) Data - Need probability is a decreasing power function of time

6) Iteration - Empirical basis of ‘environment’

Need-Probability & Power Functions

S availability of memory structure

p need probability

Hs history factor

a(Qs) context factor

Relationship between retention interval and need-probability

yuck

Wason Card Selection Task

Ap

2q

Knot p

7not q

‘If there is an A on one side,

then there is a 2 on the other side’

If p, then q

Wason Card Selection Task

Ap

2q

Knot p

7not q

2 A? ?

Wason Card Selection Task

Borrowed Car

‘If you borrow my car,

then you must fill up the gas tank’

If p, then q

Full Gas Tank

Empty Gas Tank

Did Not Borrow Car

Reasoning – Optimal Data Selection (ODS)

1) Goals – Greatest expected informativeness (EIg) and independence of antecedent (p) and consequent (q)

2) Environment – When P(p) and P(q) are low then EIg(q) > EIg (not q) (rarity assumption)

3) Computational Limitations – Cost of examining data (as little as possible is examined)

4) Optimization – EIg(p) > EIg(q) > EIg(not q) > EIg(not p)

5) Data – Performance approximates Baysian optimal data selection

6) Iteration – Performance will change if rarity assumption is violated

Optimal Data Selection

Expected information gain

Frequency of card selection

Human performance approximates

Baysian optimal data selection

Conclusions

Question: How do arbitrary mechanisms & arbitraryperformance limitations add up to a successful system?

Answer: Rational Analysis

Identifies specific mechanisms, specific problems, and include environment

Optimal behavior functions

Source of constraint and novel empirical predictions

Further Questions

What are the limits of rational analysis?

How can rational analysis be integrated with related work in perception and motor control?

How does rational analysis relate to proposed cognitive architectures?

Can learning be given a rational analysis?

How constrained is rational analysis?

Happy Valentine’s Day (tomorrow)