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Symbolic representation of probabilistic worlds
1Department of Psychology, Center for Cognitive Science, Rutgers University-New Brunswick, 152 Frelinghuysen Rd., Piscataway, NJ 08854, United States. jacob@ruccs.rutgers.edu
Cognition
|January 25, 2012
Summary
This study introduces a quantitative measure for symbolic representation effectiveness. It finds that symbolic representation is warranted in modal environments, where it minimizes information loss, supporting cognitive science assumptions.
Area of Science:
- Cognitive Science
- Mathematical Psychology
- Information Theory
Background:
- Symbolic representation is central to cognitive science but lacks mathematical validation.
- Previous discussions focused on philosophical aspects, not quantitative effectiveness.
Purpose of the Study:
- To introduce a quantitative measure for the effectiveness of symbolic representation.
- To establish formal constraints for warranted symbolic representation.
- To explore the relationship between environmental probability distributions and representational accuracy.
Main Methods:
- Development of a novel quantitative measure for symbolic representation effectiveness.
- Analysis of environmental probability distributions, specifically modal versus arbitrary distributions.
- Formal derivation of constraints for warranted representation.
Main Results:
- Symbolic representation is generally not warranted for arbitrary probability distributions.
- Effectiveness is contingent on the probabilistic structure of the environment.
- Modal environments, characterized by narrow component distributions, allow for representation with minimal information loss.
Conclusions:
- The effectiveness of symbolic representation is mathematically defined by environmental structure.
- Modal environments are crucial for supporting symbolic representation, including propositional forms and logical relations.
- The assumption of a modal environment is a tacit foundation for symbolic reasoning in cognitive science.
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