A Computational Theory of Dispositions

A COMPUTATIONAL THEORY OF DISPOSITIONS Lotfi A. Zadeh Computer Science Division University of California, Berkeley, California 94720, U.S.A. ABSTRACT Informally, a disposition is a proposition which is prepon- derantly, but no necessarily always, true. For example, birds can fly is a disposition, as are the propositions Swedes are blond and Spaniards are dark. An idea which underlies the theory described in this paper is that a disposition may be viewed as a proposition with implicit fuzzy quantifiers which are approximations to all and always, e.g., almost all, almost always, most, frequently, etc. For example, birds can fly may be interpreted as the result of supressing the fuzzy quantifier most in the proposi- tion most birds can fly. Similarly, young men like young women may be read as most young men like mostly young women. The process of transforming a disposition into a proposition is referred to as ezplicitation or restoration. Explicitation sets the stage for representing the meaning of a proposition through the use of test-score semantics (Zadeh, 1978, 1982). In this approach to semantics, the mean- ing of a proposition, p, is represented as a procedure which tests, scores and aggregates the elastic constraints which are induced by p. The paper closes with a description of an approach to reasoning with dispositions which is based on the concept of a fuzzy syllogism. Syllogistic reasoning with dispositions has an important bearing on commonsense reasoning as well as on the management of uncertainty in expert systems. As a sim- ple application of the techniques described in this paper, we formulate a definition of typicality- a concept which plays an important role in human cognition and is of relevance to default reasoning. 1. Introduction Informally, a disposition is a proposition which is prepon- derantly, but not necessarily always, true. Simple examples of dispositions are: Smoking is addictive, exercise is good for your health, long sentences are more difficult to parse than short sen- tences, overeating causes obesity, Trudi is always right, etc. Dispositions play a central role in human reasoning, since much of human knowledge and, especially, commousense knowledge, may be viewed as a collection of dispositions. The concept of a disposition gives rise to a number of related concepts among which is the concept of a dispositional predicate. Familiar examples of unary predicates of this type are: Healthy, honest, optimist, safe, etc., with binary disposi- tional predicates exemplified by: taller than in Swedes are taller than Frenchmen, like in Italians are like Spaniards, like in youn 9 men like young women, and smokes in Ron smokes cigarettes. Another related concept is that of a dispositional command {or imperative) which is exemplified by proceed with caution, avoid overexertion, keep under refrigeration, be frank, etc. To Protessor Nancy Cartwright. Research supported in part by NASA Grant NCC2-275 and NSF Grant IST-8320416. The basic idea underlying the approach described in this paper is that a disposition may be viewed as a proposition with suppressed, or, more generally, implicit fuzzy quantifiers such as most~ almost …

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