Coverage and Competency in Formal Theories: A Commonsense Theory of Memory

The utility of formal theories of commonsense reasoning will depend both on their competency in solving problems and on their conceptual coverage. We argue that the problems of coverage and competency can be decoupled and solved with dierent methods for a given commonsense domain. We describe a methodology for identifying the coverage requirements of theories through the large-scale analysis of planning strategies, with further refinements made by collecting and categorizing instances of natural language expressions pertaining to the domain. We demonstrate the eectiveness of this methodology in identifying the representational coverage requirements of theories of the commonsense psychology of human memory. We then apply traditional methods of formalization to produce a formal first-order theory of commonsense memory with a high degree of competency and coverage. 1 Coverage and Competency While much research in commonsense reasoning has been directed at describing axiomatic content theories in specific areas, of equal concern are the research methods that are used to develop these content theories. Davis (1998) reflects back on the methodological problems that have hindered progress and recommends a research program based on microworlds. He argues that the goal of commonsense reasoning research is the generation of competency theories that can answer commonsense problems that people are able to solve. By emphasizing reasoning competency, Davis makes a strong case for focusing on the function of axiomatic theories rather than their form. However, while the representational form may be indeterminate with respect to its function, representation itself has an even broader role to play across the full spectrum of cognitive behavior, beyond the commonsense reasoning functions of explanation, prediction, planning and design. What is needed of commonsense theories is not only competency, but also enough coverage over the breadth of commonsense concepts to enable use in computational models of memory retrieval, language understanding, perception, similarity, among other cognitive functions. A conservative commonsense reasoning researcher might argue that coverage is an additional constraint on an already difficult task, and is best addressed after suitable competency theories have been put forth. We argue that without addressing the issue of coverage first, competency theories will be intolerant of elaboration and dicult to integrate with each other or within larger cognitive models. This paper presents a new methodology for authoring formal commonsense theories. The basis of our approach is the tenet that the problems of coverage and competency should be decoupled and addressed by entirely dierent methods. Our approach begins by outlining the coverage requirements of commonsense theories through the analysis of a corpus of strategies. These requirements are elaborated to handle distinctions made in natural language, as evidenced through the analysis of large English text corpora. We then address the specification of a formal notation (here, first-order predicate calculus) and of a full axiomatic theory. Section 2 of this paper describes the methods used to solve the coverage problem in the domains of commonsense psychology. Section 3 elaborates on the role of natural language in refining these representations, with an example domain of the commonsense psychology of memory. Section 4 presents a formal, axiomatic theory of the com