A new look at fuzzy-logic inference

The modus ponens, the inference primitive, and many more complex inferences, are not, as logic operations, reducible to expressions involving logic functions exclusively. Some of the consequences of this observation are considered for inference in fuzzy logic. The author constructs a fuzzy modus ponens and other rules of inference which include modus tollens and reductio ad absurdum. These in turn are based on a choice for the operation of implication which preserves the symmetry implicit in its definition. Extensions including conditional quantification, cut rules, 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 can be affected in fuzzy logic if, as in classical logic, one ventures outside the scope of (fuzzy) logic operations