Abstract

Some higher-order formulas are equivalent to formulas of first-order predicate logic or even propositional logic. In applications where formulas of higherorder 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 prepositional logic. Typical applications where this occurs are predicate minimization by circumscription, correspondence theory in non-classical logics and simple versions of set theory. In these areas we are faced with formulas of second-order predicate logic with existentially or universally quantified predicate variables and want to simplify them by computing equivalent first-order formulas.

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