An Equivalent Transformation of Parallel Circumscription into First-Order Formulas

Abstract

Parallel circumscription is an extension of predicate circumscription by adding parameters, which are predicates allowed to vary in the process in minimization. It is a very useful and important tool for commonsense reasoning. But, unfortunately, its direct computation is very difficult, because it is formulated as a higher-order formula. In this paper, we present an equivalent transformation method of parallel circumscription into first-order formulas. We have already presented a fundamental method for eliminating parameters of parallel circumscription and a method for transforming predicate circumscription into first-order formulas. Each of them is stronger than the well known Lifschitz's method. In this paper, based on these results, we give a sufficient condition for transforming parallel circumscription into first-order formulas, and present a transformation method which consists of the above two methods. This method can transform a complex parallel circumscription such that its condition sentence is quantified by both ∃ and ∀ quantifiers.