Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the taut...Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.展开更多
In fuzzy set theory, instead of the underlying membership set being a two-valued set it is a multi-valued set that generally has the structure of a lattice L with a minimal element O and the maximal element I. Further...In fuzzy set theory, instead of the underlying membership set being a two-valued set it is a multi-valued set that generally has the structure of a lattice L with a minimal element O and the maximal element I. Furthermore if ∧, ∨, → and ┐ are defined in the set L, then we can use these operations to define, as in the ordinary set theory, operations on fuzzy subsets. In this paper we give a model of the Lattice-Valued Logic with set of agents. Any agents know the logic value of a sentence p. The logic value is compatible with all of the accessible conceptual models or worlds of p inside the agent. Agent can be rational or irrational in the use of the logic operation. Every agent of n agents can have the same set of conceptual models for p and know the same logic for p in this case the agents form a consistent group of agents. When agents have different conceptual models for p, different subgroup of agents know different logic value for p. In this case the n agents are inconsistent in the expression of the logic value for p. The valuation structure of set of agents can be used as a semantic model for the Lattice-valued Logic and fuzzy logic.展开更多
As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice impl...As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice implication algebra.In this principle,the resolution level is an ideal of lattice implication algebra,instead of an element in truth-value field.Moreover,the soundness theorem is given.In the light of lifting lemma,the completeness theorem is established.This can provide a new tool for automated reasoning.展开更多
In this paper, closure operators of lattice-valued propositional logic LP（X） are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP（X） is investi...In this paper, closure operators of lattice-valued propositional logic LP（X） are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP（X） is investigated. At the same time, a tool for checking compactness of LP（X） is given.展开更多
We have given a semantic extension of lattice-valued propositional logic LP（X） in [6]. In this paper, we investigate its corresponding syntactic extension of LP（X） and give the relations between these two extensions.
Lattice-valued logic plays an important role in multi-valued logic systems. A lattice valued logic system lp(X) is constructed. The syntax of lp(X) is discussed. It may be more convenient in application and study espe...Lattice-valued logic plays an important role in multi-valued logic systems. A lattice valued logic system lp(X) is constructed. The syntax of lp(X) is discussed. It may be more convenient in application and study especially in the case that the valuation domain is finite lattice implication algebra.展开更多
This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a cha...This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.展开更多
It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular...It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular, it demonstrates several basic equivalent characterizations on the retriev-ability of (?) valued automata. Finally, the connections of the homomorphisms between two eeeeeeeeee valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.展开更多
In this paper, the syntactical problenss of lattice- valued proptnitional logicsystem LP(X) are discuased , the soundness theorem and the deduction thooremare given, and the adequaey problem of LP(X) is solved with sl...In this paper, the syntactical problenss of lattice- valued proptnitional logicsystem LP(X) are discuased , the soundness theorem and the deduction thooremare given, and the adequaey problem of LP(X) is solved with slishtrestriction.展开更多
We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
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
We give two generalizations of Tarski’s fixpoint theorem in the setting of residuated lattices and use them to establish van Emdem-Kowalski’s least fixpoint semantics for residuated lattice-valued logic programs.
In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neit...In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neither of the ideas holds,which makes it difficult to give a natural semantics for connexive logic.By combining Kleene's three valued logic and Lewis'conditional logic,we propose a new natural semantics for connexive logic.We give four ax-iomatic systems characterizing different classes of selection models in the new semantics.We prove soundness and completeness of these logics and compare them with some comexive 1og-ics in the literature.展开更多
As Model-Based Systems Engineering(MBSE)was applied to the Electric Multiple Unit(EMU)braking system control logic,a preliminary exploration was conducted for bullet train braking system control logic research using a...As Model-Based Systems Engineering(MBSE)was applied to the Electric Multiple Unit(EMU)braking system control logic,a preliminary exploration was conducted for bullet train braking system control logic research using an MBSE practice framework.The framework mainly includes the requirement analysis phase,functional analysis phase,and design phase.Systems Modeling Language(SysML)was used as the modeling language,and Cameo Systems Modeler(CSM)was employed as the modeling tool.By integrating the EMU braking system control logic and utilizing a top-down design approach,the implementation of MBSE in the bullet train braking system was analyzed and studied.The results show that,according to the MBSE practice framework,a unified description of the requirement analysis,functional analysis,and design synthesis of the EMU braking system control logic can be achieved.Additionally,the correlation and traceability between models can be established.展开更多
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
Institutional logic theory,a pivotal framework within organizational studies,delineates the multifaceted and intricate logics that underpin organizational fields.This theoretical perspective elucidates the manner in w...Institutional logic theory,a pivotal framework within organizational studies,delineates the multifaceted and intricate logics that underpin organizational fields.This theoretical perspective elucidates the manner in which diverse individuals or groups within an organization internalize and manifest distinct institutional logics,alongside the ensuing political and cultural conflicts.Furthermore,the theory endeavors to elucidate the complexities inherent in institutional logic across organizational fields,examining the reflection of these logics among various individuals or groups and their associated political and cultural dichotomies.Central to this discourse is the acknowledgment of the core systems that constitute the fabric of a country,encompassing the state,market,familial structures,corporate entities,professional bodies,and religious institutions.These components not only coexist with inherent conflicts but also exhibit a high degree of interdependence,underlined by their shared institutional logics.This literature attempts to review and analysis institutional logic in the field of entrepreneurship and integrates institutional logic into entrepreneurs’personal background,experience,and other social characteristics,and study how institutional logic operates.It is recommended that future researchers take entrepreneurs as the research object and conduct more in-depth research on the evolution of organizational response strategies when political and cultural conflicts occur between different groups within the enterprise,combined with institutional logic theory.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
The ancient tacit knowledge behind the logic system permeated the culture and promoted numerous impactful inventions throughout the history. Traditional Chinese medicine with its effectiveness should also have stemmed...The ancient tacit knowledge behind the logic system permeated the culture and promoted numerous impactful inventions throughout the history. Traditional Chinese medicine with its effectiveness should also have stemmed out from such logic system. This article aims to rearticulate the underlying lucid multi-dimensional logic system, which faded in obscurity only because of time-out loss of the mid-right concept. Retracing this past tacit but important concept could uncover a multi-dimensional system over a point relating to all matters while capturing the central core of the matter. The seemingly unmanageable multidimensional logic was strengthened by verification processes which affirmed its further extensions, and made up the language of the people, the concepts of yin-yang(阴阳), and the development of extensions of Ba Gua(八卦) derivatives, which furthered the interpretation of the space-time properties and Chinese medicine.展开更多
As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Int...As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.展开更多
文摘Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.
文摘In fuzzy set theory, instead of the underlying membership set being a two-valued set it is a multi-valued set that generally has the structure of a lattice L with a minimal element O and the maximal element I. Furthermore if ∧, ∨, → and ┐ are defined in the set L, then we can use these operations to define, as in the ordinary set theory, operations on fuzzy subsets. In this paper we give a model of the Lattice-Valued Logic with set of agents. Any agents know the logic value of a sentence p. The logic value is compatible with all of the accessible conceptual models or worlds of p inside the agent. Agent can be rational or irrational in the use of the logic operation. Every agent of n agents can have the same set of conceptual models for p and know the same logic for p in this case the agents form a consistent group of agents. When agents have different conceptual models for p, different subgroup of agents know different logic value for p. In this case the n agents are inconsistent in the expression of the logic value for p. The valuation structure of set of agents can be used as a semantic model for the Lattice-valued Logic and fuzzy logic.
基金the National Natural Science Foundation of China(No.61175055)the Sichuan Key Technology Research and Development Program(No.2011FZ0051)
文摘As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice implication algebra.In this principle,the resolution level is an ideal of lattice implication algebra,instead of an element in truth-value field.Moreover,the soundness theorem is given.In the light of lifting lemma,the completeness theorem is established.This can provide a new tool for automated reasoning.
基金Supported by the National Natural Science Foundation of China(60474022)
文摘In this paper, closure operators of lattice-valued propositional logic LP（X） are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP（X） is investigated. At the same time, a tool for checking compactness of LP（X） is given.
基金Supported by the National Natural Science Foundation of China(60474022)
文摘We have given a semantic extension of lattice-valued propositional logic LP（X） in [6]. In this paper, we investigate its corresponding syntactic extension of LP（X） and give the relations between these two extensions.
基金The National Science Fund of China(No.60074014,60474022)The Project Fund of Zhejiang Science and Technology Depart ment,China(No.2005C31005)
文摘Lattice-valued logic plays an important role in multi-valued logic systems. A lattice valued logic system lp(X) is constructed. The syntax of lp(X) is discussed. It may be more convenient in application and study especially in the case that the valuation domain is finite lattice implication algebra.
基金This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004) the National Key Project for Basic Research (Grant No.1998030509) the National Natural Science Foundation of China (Grant No. 69823001).
文摘This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.
基金This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004)the National Key Project for Basic Research (Grant No. 1998030509).
文摘It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular, it demonstrates several basic equivalent characterizations on the retriev-ability of (?) valued automata. Finally, the connections of the homomorphisms between two eeeeeeeeee valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.
文摘In this paper, the syntactical problenss of lattice- valued proptnitional logicsystem LP(X) are discuased , the soundness theorem and the deduction thooremare given, and the adequaey problem of LP(X) is solved with slishtrestriction.
基金supported by the National Foundation for Distionguished Young Scholars(Grant No:69725004)Rrsearch and Development Project of High-Technology(Grant No:863-306-ZT06-04-3)+1 种基金Foundation of Natural Sciences(Grant No:6982001) of ChinaFOK Ying-Tung Edu
文摘We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
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We give two generalizations of Tarski’s fixpoint theorem in the setting of residuated lattices and use them to establish van Emdem-Kowalski’s least fixpoint semantics for residuated lattice-valued logic programs.
基金supported by the MOE Project of Humanities and Social Sciences of China(Grant No.21YJA72040001)。
文摘In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neither of the ideas holds,which makes it difficult to give a natural semantics for connexive logic.By combining Kleene's three valued logic and Lewis'conditional logic,we propose a new natural semantics for connexive logic.We give four ax-iomatic systems characterizing different classes of selection models in the new semantics.We prove soundness and completeness of these logics and compare them with some comexive 1og-ics in the literature.
文摘As Model-Based Systems Engineering(MBSE)was applied to the Electric Multiple Unit(EMU)braking system control logic,a preliminary exploration was conducted for bullet train braking system control logic research using an MBSE practice framework.The framework mainly includes the requirement analysis phase,functional analysis phase,and design phase.Systems Modeling Language(SysML)was used as the modeling language,and Cameo Systems Modeler(CSM)was employed as the modeling tool.By integrating the EMU braking system control logic and utilizing a top-down design approach,the implementation of MBSE in the bullet train braking system was analyzed and studied.The results show that,according to the MBSE practice framework,a unified description of the requirement analysis,functional analysis,and design synthesis of the EMU braking system control logic can be achieved.Additionally,the correlation and traceability between models can be established.
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.
文摘Institutional logic theory,a pivotal framework within organizational studies,delineates the multifaceted and intricate logics that underpin organizational fields.This theoretical perspective elucidates the manner in which diverse individuals or groups within an organization internalize and manifest distinct institutional logics,alongside the ensuing political and cultural conflicts.Furthermore,the theory endeavors to elucidate the complexities inherent in institutional logic across organizational fields,examining the reflection of these logics among various individuals or groups and their associated political and cultural dichotomies.Central to this discourse is the acknowledgment of the core systems that constitute the fabric of a country,encompassing the state,market,familial structures,corporate entities,professional bodies,and religious institutions.These components not only coexist with inherent conflicts but also exhibit a high degree of interdependence,underlined by their shared institutional logics.This literature attempts to review and analysis institutional logic in the field of entrepreneurship and integrates institutional logic into entrepreneurs’personal background,experience,and other social characteristics,and study how institutional logic operates.It is recommended that future researchers take entrepreneurs as the research object and conduct more in-depth research on the evolution of organizational response strategies when political and cultural conflicts occur between different groups within the enterprise,combined with institutional logic theory.
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The ancient tacit knowledge behind the logic system permeated the culture and promoted numerous impactful inventions throughout the history. Traditional Chinese medicine with its effectiveness should also have stemmed out from such logic system. This article aims to rearticulate the underlying lucid multi-dimensional logic system, which faded in obscurity only because of time-out loss of the mid-right concept. Retracing this past tacit but important concept could uncover a multi-dimensional system over a point relating to all matters while capturing the central core of the matter. The seemingly unmanageable multidimensional logic was strengthened by verification processes which affirmed its further extensions, and made up the language of the people, the concepts of yin-yang(阴阳), and the development of extensions of Ba Gua(八卦) derivatives, which furthered the interpretation of the space-time properties and Chinese medicine.
文摘As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.
