A Computational Theory Of Dispositions

1. I n t r o d u c t i o n Informally, a disposition is a proposition which is preponderantly, 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 sentences, 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 dispositional 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 all, almost always, usually, rarely, much of the time, etc . To illustrate, the disposition gestating causes obesity may be viewed as the result of suppression of the fuzzy quantifier most in the proposition most of those who overeat are obese. Similarly, the disposition young men like young women may be interpreted as most young men like mostly young women. It should be stressed, however, that restoration (or ezplicitation) -viewed as the inverse of suppression is an interpretation-dependent process in the sense that, in general, a disposition may be interpreted in different ways depending on the manner in which the fuzzy quantifiers are restored and defined. The implicit presence of fuzzy quantifiers stands in the way of representing the meaning of dispositional concepts through the use of conventional methods based on truthconditional, possible-world or model-theoretic semantics (Cresswell, 1973; McCawley, 1981; Miller and Johnson-Laird, 1970),~-tn the computational approach which is described in this paper, a fuzzy quantifier is manipulated as a fuzzy number. This idea serves two purposes. First, it provides a basis for representing the meaning of dispositions; and second, it opens a way of reasoning with dispositions through the use of a collection of syllogisms. This aspect of the concept of a disposition is of relevance to default reasoning and nonmonotonic logic (McCarthy, 1980; McDermott and Doyle, 1980; McDermott, 1982; Reiter, 1983). To illustrate the manner in which fuzzy quantifiers may be manipulated as fuzzy numbers, assume that, after restoration, two dispositions d I and d 2 may be expressed as propositions of the form Pl A Qt A t s are BI s (1.1) P2 A = Q2 Be s are CI s , (1.2) in which Ql and Q2 are fuzzy quantifiers, and A, B and C are fuzzy predicates. For example, Pl &most students are undergraduates (1.3) P2 ~ most undergraduates are young . By treating Pl and P2 as the major and minor premises in a syllogism, the following chaining syllogism may be established if B C A (Zadeh, 1983): 1. In the literature of linguistics, logic and philosophy of languages, fuzzy quantifiers are usually referred to as ~agne or generalized quantifiers (Barwise and Cooper, 1981; Peterson, 1979). In the approach described in this paper, a fuszy quantifier is interpreted as a fuzzy number which provides an approximate characterization of absolute or relative cardinality.