The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of t...The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.展开更多
Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC* , gives it...Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC* , gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zom lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason’s result.展开更多
Global property is the necessary condition which must be satisfied by the provable formulas. It can help to find out some unprovable formula that does not satisfy some global property before proving it using formal au...Global property is the necessary condition which must be satisfied by the provable formulas. It can help to find out some unprovable formula that does not satisfy some global property before proving it using formal automated rea-soning systems, thus the efficiency of the whole system is improved. This paper presents some global properties of valid formulas in modal logic K. Such prop-erties are structure characters of formulas, so they are simple and easy to check.At the same time, some global properties of K unsatisfiable formula set are also given.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 transitiongraphs 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 transitiongraphs with assignment. It is shown that the satisfiability of the two-variable sub-logic HML(FO2) ofHML(FO) is decidable, and the complexity discussed. Finally, a decision procedure for model checkingthe 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
Business letter with friendly modality is an effective means to represent the best advantage of one's self and firm. The paper in vestigates modality in business letter according to Halliday's view on modality...Business letter with friendly modality is an effective means to represent the best advantage of one's self and firm. The paper in vestigates modality in business letter according to Halliday's view on modality. The modal devices mainly cover modal operator, modal ad junct, and modal cohesion. By means of binary approach modal logic is tentative divided into: perfective and imperfective; positive and neg ative; subjective and objective or explicit and implicit; high, median and low value. Modal devices or modal logic has formal and semantic level. Modality is regarded as a potential analyzing method to business text in this paper. The significance of the study is for understanding modal expression in business letter, meanwhile, this is a way to better understand modal logic, and to better use modal device in business let ter.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10331010 and 10771129)the Foundation of 211 Constructionof Shaanxi Normal University
文摘The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
文摘Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC* , gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zom lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason’s result.
文摘Global property is the necessary condition which must be satisfied by the provable formulas. It can help to find out some unprovable formula that does not satisfy some global property before proving it using formal automated rea-soning systems, thus the efficiency of the whole system is improved. This paper presents some global properties of valid formulas in modal logic K. Such prop-erties are structure characters of formulas, so they are simple and easy to check.At the same time, some global properties of K unsatisfiable formula set are also given.
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 transitiongraphs with assignment. It is shown that the satisfiability of the two-variable sub-logic HML(FO2) ofHML(FO) is decidable, and the complexity discussed. Finally, a decision procedure for model checkingthe 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.
文摘Business letter with friendly modality is an effective means to represent the best advantage of one's self and firm. The paper in vestigates modality in business letter according to Halliday's view on modality. The modal devices mainly cover modal operator, modal ad junct, and modal cohesion. By means of binary approach modal logic is tentative divided into: perfective and imperfective; positive and neg ative; subjective and objective or explicit and implicit; high, median and low value. Modal devices or modal logic has formal and semantic level. Modality is regarded as a potential analyzing method to business text in this paper. The significance of the study is for understanding modal expression in business letter, meanwhile, this is a way to better understand modal logic, and to better use modal device in business let ter.
