This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable...This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable information.This method can also deal with the uncertain problem which has both positive evidence and negative evidence at the same time.10-elements linguistic truthvalued intuitionistic fuzzy first-order logic system has been established in the intuitionistic fuzzy algebra.展开更多
Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-va...Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-valued first-order logic, we discussed the satisfiable problem of 6-elements linguistic truth-valued first-order logic and proposed a resolution method of 6-elements linguistic truth-valued firstorder logic. Then the resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.展开更多
I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself o...I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself of the functional and logic paradigms. The purpose of this note, proceeding from the algebraic oersoective, is to formulize the first-order mathematical展开更多
Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for qua...Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for quantifiers;and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.展开更多
Using Boolean operations and concatenation product w.r.t special trees,quantifier hierarchies are given by way of alternate existential and universal quantifiers for the first-order definable tree languages.
Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although...Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.展开更多
Parametric logic is introduced. The language, semantics and axiom system of parametric logic are defined. Completeness theorem of parametric logic is provided. Parametric logic has formal ability powerful enough to ca...Parametric logic is introduced. The language, semantics and axiom system of parametric logic are defined. Completeness theorem of parametric logic is provided. Parametric logic has formal ability powerful enough to capture a wide class of logic as its special cases, and therefore can be viewed as a uniform basis for modern logics.展开更多
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main r...The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.展开更多
Context-awareness enhances human-centric, intelligent behavior in a smart environment; however context-awareness is not widely used due to the lack of effective infrastructure to support context-aware applications. Th...Context-awareness enhances human-centric, intelligent behavior in a smart environment; however context-awareness is not widely used due to the lack of effective infrastructure to support context-aware applications. This paper presents an agent-based middleware for providing context-aware services for smart spaces to afford effective support for context acquisition, representation, interpretation, and utilization to applications. The middleware uses a formal context model, which combines first order probabilistic logic （FOPL） and web ontology language （OWL） ontologies, to provide a common understanding of contextual information to facilitate context modeling and reasoning about imperfect and ambiguous contextual information and to enable context knowledge sharing and reuse. A context inference mechanism based on an extended Bayesian network approach is used to enable automated reactive and deductive reasoning. The middleware is used in a case study in a smart classroom, and performance evaluation result shows that the context reasoning algorithm is good for non-time-critical applications and that the complexity is highly sensitive to the size of the context dataset.展开更多
To solve the shortage problem of the semantic descrip- tion scope and verification capability existed in the security policy, a semantic description method for the security policy based on ontology is presented. By de...To solve the shortage problem of the semantic descrip- tion scope and verification capability existed in the security policy, a semantic description method for the security policy based on ontology is presented. By defining the basic elements of the security policy, the relationship model between the ontology and the concept of security policy based on the Web ontology language （OWL） is established, so as to construct the semantic description framework of the security policy. Through modeling and reasoning in the Protege, the ontology model of authorization policy is proposed, and the first-order predicate description logic is introduced to the analysis and verification of the model. Results show that the ontology-based semantic description of security policy has better flexibility and practicality.展开更多
A program construction method based on Gamma language is proposed. The problemto be solved is specified by first-order predicate logic and a semantic verification program isconstructed directly from the specification....A program construction method based on Gamma language is proposed. The problemto be solved is specified by first-order predicate logic and a semantic verification program isconstructed directly from the specification. Ways for improving efficiency of the program arealso studied. The method differs from the one proposed by Manna and Waldinger, where aprogram is extracted from the proof of the existence of an object meeting the given specification.On the other hand, it also differs from the classical one used for deriving Gamma programsof Banatre and Le Metayer, which consists in decomposing the specification into an invariantand a termination condition.展开更多
基金This work is partly supported by National Nature Science Foundation of China (Grant No.61105059,61175055,61173100), International Cooperation and Exchangeof the National Natural Science Foundation of China (Grant No.61210306079),Sichuan Key Technology Research and Development Program (Grant No.2011FZ0051),Radio Administration Bureau of MIIT of China (Grant No.[2011]146), China Institution of Communications (Grant No.[2011]051), and Sichuan Key Laboratory of Intelligent Network Information Processing (Grant No.SGXZD1002-10),Liaoning Excellent Talents in University (LJQ2011116).
文摘This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable information.This method can also deal with the uncertain problem which has both positive evidence and negative evidence at the same time.10-elements linguistic truthvalued intuitionistic fuzzy first-order logic system has been established in the intuitionistic fuzzy algebra.
基金This work is partly supported by National Nature Science Foundation of China (Grant No.61105059,61175055,61173100), International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No.61210306079), Sichuan Key Technology Research and Development Program (Grant No.2011FZ0051), Radio Administration Bureau of MIIT of China (Grant No.[2011]146), China Institution of Communications (Grant No.[2011]051), and Sichuan Key Laboratory of Intelligent Network Information Processing (Grant No.SGXZD1002-10),Liaoning Excellent Talents in University (LJQ2011116).
文摘Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-valued first-order logic, we discussed the satisfiable problem of 6-elements linguistic truth-valued first-order logic and proposed a resolution method of 6-elements linguistic truth-valued firstorder logic. Then the resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.
基金Project supported by the National High Technique Planning Foundation
文摘I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself of the functional and logic paradigms. The purpose of this note, proceeding from the algebraic oersoective, is to formulize the first-order mathematical
基金the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2010KF-06)Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901).
文摘Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for quantifiers;and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.
基金Project supported by the National Natural Science Foundation of China.
文摘Using Boolean operations and concatenation product w.r.t special trees,quantifier hierarchies are given by way of alternate existential and universal quantifiers for the first-order definable tree languages.
文摘Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.
基金the National Natural Science Foundation of Chinathe National Hi-Tech R&D (863) Program+1 种基金 the National Fundamental Research (Climbing) ProgramLi Kasheng's Academic Foundation
文摘Parametric logic is introduced. The language, semantics and axiom system of parametric logic are defined. Completeness theorem of parametric logic is provided. Parametric logic has formal ability powerful enough to capture a wide class of logic as its special cases, and therefore can be viewed as a uniform basis for modern logics.
基金Supported by the National Science Foundation of China under Grant Nos.11235003 and 11475023National Social Sciences Foundation of China under Grant No.14BZX078+1 种基金the Research Fund for the Doctoral Program of Higher Education of Chinathe Undergraduate Training Program of Beijing
文摘The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.
基金Supported by the Basic Research Foundation of Tsinghua Na-tional Laboratory for Information Science and Technology (TNList)the National High-Tech Research and Development (863) Program of China (No. 2006AA01Z198)
文摘Context-awareness enhances human-centric, intelligent behavior in a smart environment; however context-awareness is not widely used due to the lack of effective infrastructure to support context-aware applications. This paper presents an agent-based middleware for providing context-aware services for smart spaces to afford effective support for context acquisition, representation, interpretation, and utilization to applications. The middleware uses a formal context model, which combines first order probabilistic logic （FOPL） and web ontology language （OWL） ontologies, to provide a common understanding of contextual information to facilitate context modeling and reasoning about imperfect and ambiguous contextual information and to enable context knowledge sharing and reuse. A context inference mechanism based on an extended Bayesian network approach is used to enable automated reactive and deductive reasoning. The middleware is used in a case study in a smart classroom, and performance evaluation result shows that the context reasoning algorithm is good for non-time-critical applications and that the complexity is highly sensitive to the size of the context dataset.
基金Supported by the National Natural Science Foundation of China(61462020,61363006,61163057)the Guangxi Experiment Center of Information Science Foundation(20130329)the Guangxi Natural Science Foundation(2014GXNSFAA118375)
文摘To solve the shortage problem of the semantic descrip- tion scope and verification capability existed in the security policy, a semantic description method for the security policy based on ontology is presented. By defining the basic elements of the security policy, the relationship model between the ontology and the concept of security policy based on the Web ontology language （OWL） is established, so as to construct the semantic description framework of the security policy. Through modeling and reasoning in the Protege, the ontology model of authorization policy is proposed, and the first-order predicate description logic is introduced to the analysis and verification of the model. Results show that the ontology-based semantic description of security policy has better flexibility and practicality.
文摘A program construction method based on Gamma language is proposed. The problemto be solved is specified by first-order predicate logic and a semantic verification program isconstructed directly from the specification. Ways for improving efficiency of the program arealso studied. The method differs from the one proposed by Manna and Waldinger, where aprogram is extracted from the proof of the existence of an object meeting the given specification.On the other hand, it also differs from the classical one used for deriving Gamma programsof Banatre and Le Metayer, which consists in decomposing the specification into an invariantand a termination condition.
