非再帰的な述語サーカムスクリプションの一階論理式への等価変換

概要

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In this paper, we present a method which transforms predicate circumscription into a first-order sentence if its condition sentence is non-recursive with respect to predicates to be minimized. So far, fundamentally, the concept of the recursion in aribitrary first-order formulas has not been so clear. Therefore, at first, we consider and formalize this concept. Next, we define a computational condition that a formula is non-recursive with respect to predicates, and give an equivalent transformation method of non-recursive predicate circumscription into first-order sentences. A non-recursive formula A with respect to predicates p_1,…,p_n is defined only by the relations between positive and negative occurrences of p_1,…,p_n in A, without considering the number of the occurrences or the kinds of the quantification. Therefore, this transfomation method can deal with complex predicate circumscription such that its condition sentence is non-definite with respect to minimized predicates, or is quantified with both existential and universal quantifiers in any forms.
1990-07-01