Elimination of Predicate Quantifiers

Abstract

Formulae of higher-order predicate logic are difficult to handle with automated inference systems. Some of these formulae, however, are equivalent to formulae of first-order predicate logic or even propositional logic. For example the formula of second-order predicate logic P (P P) is trivially equivalent to the propositional constant false. In applications where formulae of higher-order predicate logic occur naturally it is very useful to determine whether the given formula is in fact equivalent to a simpler formula of first-order or propositional logic. Typical applications where this occurs are predicate minimization by circumscription, correspondence theory in non-classical logic, and simple versions of set theory. In these areas we are faced with formulae of second-order predicate logic with existentially or universally quantified predicate variables and we want to simplify them by computing equivalent first-order formulae.KeywordsModal LogicPredicate LogicCorrespondence TheoryPredicate VariableQuantifier EliminationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.