Abstract
.The theory which is outlined in this lecture, call it RCC for short, is a system of reasoning and computation which is not in the traditional spirit. In large measure, RCC is oriented toward reasoning and computation in an environment of uncertainty, imprecision and partiality of truth. The centerpiece of RCC is the concept of a restriction—a basic concept which is deceptively simple. Informally, a restriction is an answer to a question of the form: What is the value of a variable, X? More concretely, a restriction, R(X), is a limitation on the values which X can take. A restriction is precisiated if R(X) is mathematically well defined; otherwise it is unprecisiated. Generally, restrictions which are described in a natural language are unprecisiated. A restriction is precisiable if it lends itself to precisiation. A restriction is singular if R(X) is a singleton; otherwise it is nonsingular. Nonsingularity implies uncertainty. Examples. Robert is staying at a hotel in Berkeley. He asks the concierge, “How long will it take me to drive to SF Airport?” Possible answers: one hour; one hour plus minus fifteen minutes; about one hour; usually about one hour, etc. Each of these answers is a restriction on the variable, Driving time. The first two answers are precisiated restrictions. The last two answers are unprecisiated. Another example. The concept of a restriction is considerably more general than the concept of an interval, set, fuzzy set and probability distribution. In one form or another, much of human cognition involves restrictions, particularly in the realms of everyday reasoning and decisionmaking. Humans have a remarkable capability to reason and, to some degree, compute with restrictions. What is needed is a theory which formalizes this capability. RCC may be viewed as a step in this direction. What should be noted is that existing approaches to reasoning and computation, other than RCC, do not have the capability of reasoning and computation with restrictions which are described in a natural language.
