Symbolic modeling
In my pre-connectionist days, I studied rule- and frame-based techniques. One effort concerned propagation of uncertainty in rule-based reasoning, addressing the issues of how uncertain evidence in a rule’s antecedents affects the rule’s conclusion and how to combine evidence across rules having the same uncertain conclusion. Experimental results showed that the certainty of the antecedents in a rule can be summarized by the maximum certainty of disjunctively connected antecedents and minimum of conjunctively connected antecedents, and that the maximum certainty of a rule’s conclusion can be scaled by multiplication with the results of that summary. For combining evidence across rules, our results favored Heckerman’s modified certainty model, which sums the certainties contributed by each of two rules and divides by 1 plus their product.
With former graduate student Joseph Vybihal, I worked on analogical reasoning, the process of finding and adapting old solutions to solve new problems. Instead of the more common emphasis on analogical mapping, we focused on search for the most useful analogy. Our psychological research uncovered a search strategy that begins by generalizing on the properties of the target problem and then eventually specializes on examples of some higher-level concept, thus locating siblings of the target problem. Simulations demonstrated that this search pattern lessened and, in some cases, solved the related problems of analogical mapping and adaptation.
These symbolic models yield an idealized picture of cognitive processes at a relatively high level of description. What they fail to provide is a picture of the micro-structure of cognition, of the approximate and variable nature of cognition, and of procedural learning. All of these problems led to my current work on connectionist modeling.
With former graduate student Joseph Vybihal, I worked on analogical reasoning, the process of finding and adapting old solutions to solve new problems. Instead of the more common emphasis on analogical mapping, we focused on search for the most useful analogy. Our psychological research uncovered a search strategy that begins by generalizing on the properties of the target problem and then eventually specializes on examples of some higher-level concept, thus locating siblings of the target problem. Simulations demonstrated that this search pattern lessened and, in some cases, solved the related problems of analogical mapping and adaptation.
These symbolic models yield an idealized picture of cognitive processes at a relatively high level of description. What they fail to provide is a picture of the micro-structure of cognition, of the approximate and variable nature of cognition, and of procedural learning. All of these problems led to my current work on connectionist modeling.
- Shultz, T. R. (1990). Managing uncertainty in rule based cognitive models. Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (pp. 21-26). Schenectady, NY: GE Corporate Research and Development.
- Shultz, T. R., Zelazo, P. D., & Engelberg, D. J. (1989). Managing uncertainty in rule-based reasoning. Proceedings of the Eleventh Annual Conference of the Cognitive Science Society (pp. 227-234). Hillsdale, NJ: Erlbaum.
- Vybihal, J., & Shultz, T. R. (1989). Search in analogical reasoning. Proceedings of the Eleventh Annual Conference of the Cognitive Science Society (pp. 948-955). Hillsdale, NJ: Erlbaum.
