Finite Approximations of Predicate Circumscription

概要

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Predicate Circumscription is a fundamental for malization of common sense reasoning. In this paper, we study a new approximation formula of it. In our previous works, we investigated Lifschitz's pointwise circumscription and its generalization, which functions as a finite approximation to predicate circumscription in the first-order framework. In this paper, at first, we study the ability of the generalized pointwise circumscription more closely, and give a simple example which shows that it cannot be complete even when a minimized predicate has only finite extension on the minimal models. Next, we introduce a new approximation formula, called finite constructive circumscription, in order to overcome that limitation. Finally, we compare expressive power of the two approximation methods with of predicate circumscription schema, and propose a open problem that should be solved to clarify that the completeness of predicate circumscription schema with respect to minimal model semantics.
社団法人電子情報通信学会の論文
1999-02-25