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.

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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

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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 -gt enhanced reasoning ability
• social reasoning module

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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

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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 lt C
• 5) Data - Need probability is a decreasing power
  function of time
• 6) Iteration - Empirical basis of environment

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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
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Wason Card Selection Task
A p
2 q
K not p
7 not q
If there is an A on one side, then there is a
2 on the other side If p, then q
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Wason Card Selection Task
A p
2 q
K not p
7 not q
2
A
?
?
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Wason Card Selection Task
Borrowed Car
Empty Gas Tank
Full Gas Tank
Did Not Borrow Car
If you borrow my car, then you must fill up
the gas tank If p, then q
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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) gt EIg (not q)
• (rarity assumption)
• 3) Computational Limitations Cost of examining
  data
• (as little as possible is examined)
• 4) Optimization EIg(p) gt EIg(q) gt EIg(not q) gt
  EIg(not p)
• 5) Data Performance approximates Baysian
  optimal data selection
• 6) Iteration Performance will change if rarity
  assumption is violated

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Optimal Data Selection

• Expected information gain
• Frequency of card selection
• Human performance approximates
• Baysian optimal data selection

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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

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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 Valentines Day (tomorrow)