Reasoning and Rationality

1. Reasoning and Rationality Emily Slusser February 13th 2006 Charter, N. &Oaksford, M. (1999). Ten years of the rational analysis of cognition. Trends in Cognitive Science, 3, 57-65.

2. 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?

3. Mechanistic & Purposive Explanation Mechanistic Internal causal structure Purposive What problem does it solve? What is its function?

4. Methodology(Anderson, J.R.) • Goals of the cognitive system • Environment to which the system has adopted (formal model) • Computational Limitations (minimal assumptions) • Derive optimal behavior function • Empirical data to see if predictions are confirmed • Iteration to refine the theory

5. 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

6. 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…

7. 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’

8. Need-Probability & Power Functions S availability of memory structure pneed probability Hshistory factor a(Qs)context factor Relationship between retention interval and need-probability yuck

9. Wason Card Selection Task A p K not p 2 q 7 not q ‘If there is an A on one side, then there is a 2 on the other side’ If p, then q

10. Wason Card Selection Task A p K not p 2 q 7 not q 2 ? A ?

11. Wason Card Selection Task Borrowed Car Empty Gas Tank Did Not Borrow Car Full Gas Tank ‘If you borrow my car, then you must fill up the gas tank’ If p, then q

12. 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

13. Optimal Data Selection Expected information gain Frequency of card selection Human performance approximates Baysian optimal data selection

14. Conclusions Question: How do arbitrary mechanisms & arbitrary performance 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

15. 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)