Usuality, regularity, and fuzzy set logic

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Most varieties of approximate reasoning in knowledge-based systems rely on if-then rules using some form of material implication in many-valued logic. We review material implication under three major logical systems: propositional logic, predicate logic, and set logic. Difficulties in the use of each of these for approximate reasoning are discussed. Recent work by Zadeh and others in the concepts of usuality, regularity, and dispositional reasoning supports a new approach to approximate reasoning based on fuzzy set logic and regularity. This approach resembles nonmonotonic logic schemes such as circumscription but differs in focusing on degrees of regularity and abnormality rather than using a two-valued logic. Regularity-conditioned inferences preserve important aspects for fuzzy modus ponens while eliminating the questionable inference modes of confirmation, denial, presumption, and prejudice. We conclude the discussion with an example based on the relation between fast driving and poor fuel efficiency.