A KEY TO FUZZY-LOGIC INFERENCE

Classically, whether to effect inference, one uses a small set of axioms and modus ponens, or a set of rules of inference including modus ponens, one is going beyond what can be derived with the explicit operations of logic alone. Carrying this concept over to fuzzy logic we construct a fuzzy modus ponens and other rules of inference that include modus tollens and reductio ad absurdum. These in turn are based on (and greatly facilitated by) a choice for the operation of implication that preserves the (logic) symmetry implicit in its definition. Extensions including conditional quantification, cut rules (single, multiple, and implicitory), and fuzzy mathematical induction are sketched. As an example, a fuzzy-logic treatment of the Yale shooting problem is discussed. The results suggest that the implicit processes of inference, as distinct from the explicit processes of decision (control) theory and systems theory, can be effected in fuzzy logic if, as in classical logic, one ventures outside the scope of (fuzzy) logic operations.