Distributive Normal Forms in First-Order Logic

Abstract

Publisher Summary This chapter discusses distributive normal forms in first-order logic. It also carries the theory further by studying some of their most important properties. The chapter describes and proves semantically complete a disproof procedure that is connected especially closely with their structure. The chapter mainly highlights first-order logic, although similar normal forms are easily seen to exist elsewhere—for example, in higher-order logics and in modal logics. The reason for the restriction is that the properties of these parallel normal forms are so different as to make a separate treatment advisable. The distributive normal forms of first-order logic are generalizations of the well-known complete normal forms of propositional logic and of monadic first-order logic. Disjunctions of certain conjunctions or constituents depends on features called their “parameters”: (1) The set of all the predicates occurring in it, (2) The set of all the free individual symbols occurring in it, (3) the maximal length of sequences of nested quantifiers occurring in it.