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More on Bounding Introspection in Modal Nonmonotonic Logics

Authors:	Xishun Zhao Decheng Ding

Institution:	(1) Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

Abstract:	Abstract By ${\user1{\mathcal{L}}}$ we denote the set of all propositional formulas. Let ${\user1{\mathcal{C}}}$ be the set of all clauses. Define ${\user1{\mathcal{C}}}_{0} = {\user1{\mathcal{C}}} \cup {\left\{ {\neg L\eta :\eta \in {\user1{\mathcal{C}}}} \right\}}$ . In Sec. 2 of this paper we prove that for normal modal logics ${\user1{\mathcal{S}}}$ , the notions of ${\left( {{\user1{\mathcal{S}}},{\user1{\mathcal{C}}}_{0} } \right)}$ -expansions and ${\user1{\mathcal{S}}}$ -expansions coincide. In Sec. 3, we prove that if I consists of default clauses then the notions of ${\user1{\mathcal{S}}}$ -expansions for I and ${\left( {{\user1{\mathcal{S}}},{\user1{\mathcal{C}}}} \right)}$ -expansions for I coincide. To this end, we first show, in Sec. 3, that the notion of ${\user1{\mathcal{S}}}$ -expansions for I is the same as that of ${\left( {{\user1{\mathcal{S}}},{\user1{\mathcal{L}}}} \right)}$ -expansions for I. The project is supported by NSFC

Keywords:	Modal nonmonotonic logic Expansion Bounding Introspection Default clause
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