Outline of a Theory of Usuality Based on Fuzzy Logic
The concept of usuality relates to propositions which are usually true or, more precisely, to events which have a high probability of occurrence. For example, usually Cait is very cheerful, usually a TV set weighs about fifty pounds, etc. Such propositions are said to be usuality-qualified. A usuality-qualified proposition may be expressed in the form usually (X is F), in which X is a variable taking values in a universe of discourse U and F is a fuzzy subset of U which may be interpreted as a usual value of X. In general, a usual value of variable, X, is not unique, and any fuzzy subset of U qualifies to a degree to be a usual value of X. A usuality qualified proposition in which usually is implicit rather than explicit is said to be a disposition. Simple examples of dispositions are snow is white, a cup of coffee costs about fifty cents and Swedes are taller than Italians.
In this paper, we outline a theory of usuality in which the point of departure is a method of representing the meaning of usuality-qualified propositions. Based on this method, a system of inference for usuality-qualified propositions may be developed. As examples, a dispositional version of the Aristotelian Barbara syllogism as well as a dispositional version of the modus ponens are described. Such dispositional rules of inference are of direct relevance to commonsense reasoning and, in particular, to commonsense decision analysis. A potentially important application area for the theory of usuality is the management of uncertainty in expert systems.
KeywordsMembership Function Fuzzy Logic Fuzzy Number Fuzzy Subset USUALITY Base
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