By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S...By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.展开更多
A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the th...A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the theorems relating it to major nonmonotonic logics are proved.It directly formalizes the intuition of nonmonotonic reasoning.Among other things,it provides us a first-order extension of default logic and autoepistemic logic,and simultaneously has the capability of circumscription to infer universal statement.It has important applications in logic programming and deductive data base.As a result,it provides a uniform basis for various nonmonotonic logics,from which the correspondent relationship among major nonmonotonic logics can coincide.展开更多
文摘By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.
基金Project in part supported by the National Natural Science Foundation of China, the National Hi-Tech 863 Programme, the National Project of Fundamental Research (Climbing)and by Guangdong Natural Science Foundation.
文摘A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the theorems relating it to major nonmonotonic logics are proved.It directly formalizes the intuition of nonmonotonic reasoning.Among other things,it provides us a first-order extension of default logic and autoepistemic logic,and simultaneously has the capability of circumscription to infer universal statement.It has important applications in logic programming and deductive data base.As a result,it provides a uniform basis for various nonmonotonic logics,from which the correspondent relationship among major nonmonotonic logics can coincide.
