Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because th...Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.展开更多
This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke se...This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke semantics to axiomatize lattice structures,we focus on the modal characterization of bounded lattices and their extensions relevant to logical systems.By introducing nullary modalities 1(maximum element)and 0(minimum element),we first establish a modal axiomatic system for bounded lattices.Subsequently,we provide pure formula characterizations of complementation and orthocomplementation relations in lattices,along with corresponding completeness results.As key applications,we present modal characterizations of fundamental logical algebraic structures:Boolean algebras,orthomodular lattices,and Heyting algebras.The last section develops novel axiomatization results for atomic lattices and atomless lattices.Throughout this work,all axiomatic systems are shown to be strongly complete via pureformula extensions,demonstrating how hybrid modal languages with nullary operators can uniformly capture boundary elements,complementation properties,and latticetheoretic operations central to both classical and nonclassical logics.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
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 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
Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative ...Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.展开更多
Modal logic characterization in a higher-order setting is usually not a trivial task because higher-order process-passing is quite different from first-order name-passing. We study the logical characterization of high...Modal logic characterization in a higher-order setting is usually not a trivial task because higher-order process-passing is quite different from first-order name-passing. We study the logical characterization of higherorder processes constrained by linearity. Linearity respects resource-sensitiveness and does not allow processes to duplicate themselves arbitrarily. We provide a modal logic that characterizes linear higher-order processes,particularly the bisimulation called local bisimulation over them. More importantly, the logic has modalities for higher-order actions downscaled to resembling first-order ones in Hennessy-Milner logic, based on a formulation exploiting the linearity of processes.展开更多
Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner,the need for extending classical logic to construct new multi-valued optical models bec...Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner,the need for extending classical logic to construct new multi-valued optical models becomes a challenging and promising research area.This paper establishes a novel octal-valued logic design model with new optical gates construction based on the hypothesis of Light Color State Model to provide an efficient solution to the limitations of computational processing inherent in the electronics computing.We provide new mathematical definitions for both of the binary OR function and the PLUS operation in multi valued logic that is used as the basis of novel construction for the optical full adder model.Four case studies were used to assure the validity of the proposed adder.These cases proved that the proposed optical 8-valued logic models provide significantly more information to be packed within a single bit and therefore the abilities of data representation and processing is increased.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
The idea that approximate exactness is the most we can and should expect scientific theories to yield underlies the formation and application of the multi-valued logic of approximation discussed in this paper. In this...The idea that approximate exactness is the most we can and should expect scientific theories to yield underlies the formation and application of the multi-valued logic of approximation discussed in this paper. In this logic, inexactness （measured by truth values） is controlled and minimized by means of uniquely designed deductions. We show how the notion of equality （including substitution of equals） is handled within this logic and we apply it to certain principles and interpretations of quantum theory.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
This paper proposes the use of the current signal to express logic values and establishes the theory of grounded current switches suitable for I2L circuits.Based on the advantage that current signals are easy to be ad...This paper proposes the use of the current signal to express logic values and establishes the theory of grounded current switches suitable for I2L circuits.Based on the advantage that current signals are easy to be added, the design technique of I2L circuits by means of the multi-valued current signal is proposed.It is shown that simpler structure of I2L circuits can be obtained with this technique.展开更多
As an emerging memory device,memristor shows great potential in neuromorphic computing applications due to its advantage of low power consumption.This review paper focuses on the application of low-power-based memrist...As an emerging memory device,memristor shows great potential in neuromorphic computing applications due to its advantage of low power consumption.This review paper focuses on the application of low-power-based memristors in various aspects.The concept and structure of memristor devices are introduced.The selection of functional materials for low-power memristors is discussed,including ion transport materials,phase change materials,magnetoresistive materials,and ferroelectric materials.Two common types of memristor arrays,1T1R and 1S1R crossbar arrays are introduced,and physical diagrams of edge computing memristor chips are discussed in detail.Potential applications of low-power memristors in advanced multi-value storage,digital logic gates,and analogue neuromorphic computing are summarized.Furthermore,the future challenges and outlook of neuromorphic computing based on memristor are deeply discussed.展开更多
To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended ...To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.展开更多
基金National Natural Science Foundation of China(No.61164009)the Science and Technology Research Project,Department of Education of Jiangxi Province,China(No.GJJ14420)Natural Science Foundation of Jiangxi Province,China(No.20132BAB206026)
文摘Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.
基金supported by China Postdoctoral Science Foundation(2024M750225).
文摘This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke semantics to axiomatize lattice structures,we focus on the modal characterization of bounded lattices and their extensions relevant to logical systems.By introducing nullary modalities 1(maximum element)and 0(minimum element),we first establish a modal axiomatic system for bounded lattices.Subsequently,we provide pure formula characterizations of complementation and orthocomplementation relations in lattices,along with corresponding completeness results.As key applications,we present modal characterizations of fundamental logical algebraic structures:Boolean algebras,orthomodular lattices,and Heyting algebras.The last section develops novel axiomatization results for atomic lattices and atomless lattices.Throughout this work,all axiomatic systems are shown to be strongly complete via pureformula extensions,demonstrating how hybrid modal languages with nullary operators can uniformly capture boundary elements,complementation properties,and latticetheoretic operations central to both classical and nonclassical logics.
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.
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Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.
基金the National Natural Science Foundation of China(Nos.61202023,61261130589 and61173048)the PACE Project(No.12IS02001)the Specialized Research Fund for the Doctoral Program of Higher Edueation of China(No.20120073120031)
文摘Modal logic characterization in a higher-order setting is usually not a trivial task because higher-order process-passing is quite different from first-order name-passing. We study the logical characterization of higherorder processes constrained by linearity. Linearity respects resource-sensitiveness and does not allow processes to duplicate themselves arbitrarily. We provide a modal logic that characterizes linear higher-order processes,particularly the bisimulation called local bisimulation over them. More importantly, the logic has modalities for higher-order actions downscaled to resembling first-order ones in Hennessy-Milner logic, based on a formulation exploiting the linearity of processes.
文摘Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner,the need for extending classical logic to construct new multi-valued optical models becomes a challenging and promising research area.This paper establishes a novel octal-valued logic design model with new optical gates construction based on the hypothesis of Light Color State Model to provide an efficient solution to the limitations of computational processing inherent in the electronics computing.We provide new mathematical definitions for both of the binary OR function and the PLUS operation in multi valued logic that is used as the basis of novel construction for the optical full adder model.Four case studies were used to assure the validity of the proposed adder.These cases proved that the proposed optical 8-valued logic models provide significantly more information to be packed within a single bit and therefore the abilities of data representation and processing is increased.
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The idea that approximate exactness is the most we can and should expect scientific theories to yield underlies the formation and application of the multi-valued logic of approximation discussed in this paper. In this logic, inexactness （measured by truth values） is controlled and minimized by means of uniquely designed deductions. We show how the notion of equality （including substitution of equals） is handled within this logic and we apply it to certain principles and interpretations of quantum theory.
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.
文摘This paper proposes the use of the current signal to express logic values and establishes the theory of grounded current switches suitable for I2L circuits.Based on the advantage that current signals are easy to be added, the design technique of I2L circuits by means of the multi-valued current signal is proposed.It is shown that simpler structure of I2L circuits can be obtained with this technique.
基金supported by the NSFC(12474071)Natural Science Foundation of Shandong Province(ZR2024YQ051)+5 种基金Open Research Fund of State Key Laboratory of Materials for Integrated Circuits(SKLJC-K2024-12)the Shanghai Sailing Program(23YF1402200,23YF1402400)Funded by Basic Research Program of Jiangsu(BK20240424)Taishan Scholar Foundation of Shandong Province(tsqn202408006)Young Talent of Lifting engineering for Science and Technology in Shandong,China(SDAST2024QTB002)the Qilu Young Scholar Program of Shandong University.
文摘As an emerging memory device,memristor shows great potential in neuromorphic computing applications due to its advantage of low power consumption.This review paper focuses on the application of low-power-based memristors in various aspects.The concept and structure of memristor devices are introduced.The selection of functional materials for low-power memristors is discussed,including ion transport materials,phase change materials,magnetoresistive materials,and ferroelectric materials.Two common types of memristor arrays,1T1R and 1S1R crossbar arrays are introduced,and physical diagrams of edge computing memristor chips are discussed in detail.Potential applications of low-power memristors in advanced multi-value storage,digital logic gates,and analogue neuromorphic computing are summarized.Furthermore,the future challenges and outlook of neuromorphic computing based on memristor are deeply discussed.
文摘To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.
