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
A semantic interpretation of a first order extension of Hennessy-Milner logic for value-passing processes, named HML(FO), is presented. The semantics is based on symbolic transition graphs with assignment. It is shown...A semantic interpretation of a first order extension of Hennessy-Milner logic for value-passing processes, named HML(FO), is presented. The semantics is based on symbolic transition graphs with assignment. It is shown that the satisfiability of the two-variable sub-logic HML(FO2) of HML(FO) is decidable, and the complexity discussed. Finally, a decision procedure for model checking the value-passing processes with respect to HML(FO2) is obtained.展开更多
Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of ...Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.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.
基金This work was partially supported by the National Natural Science Foundationof China (Grant No. 69833020) the National High Technology Development Program of China (Grant No. 2002AA144050)the National Grand Fundamental Research 973 Program of China
文摘A semantic interpretation of a first order extension of Hennessy-Milner logic for value-passing processes, named HML(FO), is presented. The semantics is based on symbolic transition graphs with assignment. It is shown that the satisfiability of the two-variable sub-logic HML(FO2) of HML(FO) is decidable, and the complexity discussed. Finally, a decision procedure for model checking the value-passing processes with respect to HML(FO2) is obtained.
文摘Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.
