FUZZY-SETS IN APPROXIMATE REASONING .2. LOGICAL APPROACHES

This second part of an overview of fuzzy set-based methods for approximate reasoning is devoted to deductive approaches dealing with knowledge bases made of a collection of symbolic expressions (e.g. logical formulas) to which numerical weights are attached. Then such a knowledge base can be viewed as a fuzzy set of formulae (especially if the weights belong to the interval [0, 1]). An important distinction is made, in the interpretation of the weights, between degrees of truth and degrees of uncertainty; the former can be assumed to behave in a fully compositional way while the latter cannot. Rule-based inference systems where fuzzy set operations are used for propagating and combining 'certainty factors', are briefly discussed. Then an extensive survey of truth-functional fuzzy logic is provided, and it is followed by a brief presentation of possibilistic logic, a possibility theory-based logic of uncertainty (which is not compositional with respect to every connective). In both cases, the automated deduction and logic programming aspects are emphasized while purely logical considerations which are not directly relevant for approximate reasoning, are not developed.