In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset ...In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset spaces which are more general than topological spaces.The minimal modal logic which is strongly sound and complete with respect to the class of subset spaces is found.Soundness and completeness results of some famous modal logics(e.g.S4,S5 and Tr)with respect to various important classes of subset spaces(eg intersection structures and complete fields of sets)are also proved.In the meantime,some known results,e.g.the soundness and completeness of Tr with respect to the class of discrete topological spaces,are proved directly using some modifications of the method of canonical mode1,without a detour via neighbourhood semantics or relational semantics.展开更多
In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided i...In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.展开更多
SOA is built upon and evolving from older concepts of distributed computing and modular programming, OWL-S plays a key role in describing behaviors of web services, which are the essential of the SOA software. Althoug...SOA is built upon and evolving from older concepts of distributed computing and modular programming, OWL-S plays a key role in describing behaviors of web services, which are the essential of the SOA software. Although OWL-S has given semantics to concepts by ontology technology, it gives no semantics to control-flow and data-flow. This paper presents a formal semantics framework for OWL-S sub-set, including its abstraction, syntax, static and dynamic seman-tics by rewrite logic. Details of a consistent transformation from OWL-S SOS of control-flow to corresponding rules and equations, and dataflow semantics including “Precondition”, “Result” and “Binding” etc. are explained. This paper provides a possibility for formal verification and reliability evaluation of software based on SOA.展开更多
The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-latt...The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field,and the syntax and semantic of the logical system are discussed,respectively.展开更多
Traditional AI systems are brittle in the sense that they fail miserably whenpresented with problems even slightly outside of their limited range of expertise.A powerful, extensible strategy of Distributed Artificial ...Traditional AI systems are brittle in the sense that they fail miserably whenpresented with problems even slightly outside of their limited range of expertise.A powerful, extensible strategy of Distributed Artificial Intelligence (DAI) forovercoming such bounds is to put the system in a society of systems. So theability to coordinate group activities of individuals and to communicate betweeneach other is necessary for a language describing DAI systems. Agent-orientedlanguage NUML is such a language. It is a specific kind of object-orientedlanguage. To give formal semantics to NUML, there is the problem to for-malise object-oriented programming paradigm which is still open. The theoryof higher-order rr-calculus is a concurrent computation model with sufficientcapability, which provides us a mathematical tool to do the formalization. Thispaper tries to use higher-order T-calculus to formalise NUML.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
Using Kripke semantics, we have identified and reduced an epistemic incompleteness in the metaphor commonly employed in Social Networks Analysis (SNA), which basically compares information flows with current flows in ...Using Kripke semantics, we have identified and reduced an epistemic incompleteness in the metaphor commonly employed in Social Networks Analysis (SNA), which basically compares information flows with current flows in advanced centrality measures. Our theoretical approach defines a new paradigm for the semantic and dynamic analysis of social networks including shared content. Based on our theoretical findings, we define a semantic and predictive model of dynamic SNA for Enterprises Social Networks (ESN), and experiment it on a real dataset.展开更多
基金supported by the National Social Science Fund of China(No.20CZX048)。
文摘In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset spaces which are more general than topological spaces.The minimal modal logic which is strongly sound and complete with respect to the class of subset spaces is found.Soundness and completeness results of some famous modal logics(e.g.S4,S5 and Tr)with respect to various important classes of subset spaces(eg intersection structures and complete fields of sets)are also proved.In the meantime,some known results,e.g.the soundness and completeness of Tr with respect to the class of discrete topological spaces,are proved directly using some modifications of the method of canonical mode1,without a detour via neighbourhood semantics or relational semantics.
基金supported by the Chinese Ministry of Education of Humanities and Social Science Project(23YJC72040003)the Key Project of Chinese Ministry of Education(22JJD720021)supported by the Natural Science Foundation of Shandong Province,China(project number:ZR2023QF021)。
文摘In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.
文摘SOA is built upon and evolving from older concepts of distributed computing and modular programming, OWL-S plays a key role in describing behaviors of web services, which are the essential of the SOA software. Although OWL-S has given semantics to concepts by ontology technology, it gives no semantics to control-flow and data-flow. This paper presents a formal semantics framework for OWL-S sub-set, including its abstraction, syntax, static and dynamic seman-tics by rewrite logic. Details of a consistent transformation from OWL-S SOS of control-flow to corresponding rules and equations, and dataflow semantics including “Precondition”, “Result” and “Binding” etc. are explained. This paper provides a possibility for formal verification and reliability evaluation of software based on SOA.
基金the National Natural Science Foundation of China(No.61175055)the Scientific Research Fund of Sichuan Provincial Education Department(11ZB023)the Sichuan Key Technology Research and Development Program(No.2011FZ0051)
文摘The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field,and the syntax and semantic of the logical system are discussed,respectively.
文摘Traditional AI systems are brittle in the sense that they fail miserably whenpresented with problems even slightly outside of their limited range of expertise.A powerful, extensible strategy of Distributed Artificial Intelligence (DAI) forovercoming such bounds is to put the system in a society of systems. So theability to coordinate group activities of individuals and to communicate betweeneach other is necessary for a language describing DAI systems. Agent-orientedlanguage NUML is such a language. It is a specific kind of object-orientedlanguage. To give formal semantics to NUML, there is the problem to for-malise object-oriented programming paradigm which is still open. The theoryof higher-order rr-calculus is a concurrent computation model with sufficientcapability, which provides us a mathematical tool to do the formalization. Thispaper tries to use higher-order T-calculus to formalise NUML.
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Using Kripke semantics, we have identified and reduced an epistemic incompleteness in the metaphor commonly employed in Social Networks Analysis (SNA), which basically compares information flows with current flows in advanced centrality measures. Our theoretical approach defines a new paradigm for the semantic and dynamic analysis of social networks including shared content. Based on our theoretical findings, we define a semantic and predictive model of dynamic SNA for Enterprises Social Networks (ESN), and experiment it on a real dataset.
