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.
High-performance terahertz(THz)logic gate devices are crucial components for signal processing and modulation,playing a significant role in the application of THz communication and imaging.Here,we propose a THz broadb...High-performance terahertz(THz)logic gate devices are crucial components for signal processing and modulation,playing a significant role in the application of THz communication and imaging.Here,we propose a THz broadband NOR logic encoder based on a graphene-metal hybrid metasurface.The unit structure consists of two symmetrical dual-gap metal split-ring resonators(DSRRs)arranged in a staggered configuration,with graphene strips embedded in their gaps.The NOR logic gate metadevice is controlled by the bias voltages independently applied to the two electrodes.Experiments show that when the bias voltages are applied to both electrodes,the metadevice achieves the NOR logic gate within a 0.52 THz bandwidth,with an average modulation depth above 80%.The experimental results match well with theoretical simulations.Additionally,the strong near-field coupling induced by the staggered DSRRs causes redshift at both LC resonance and dipole resonance.This phenomenon was demonstrated by coupled mode theory.Besides,we analyze the surface current distribution at resonances and propose four equivalent circuit models to elucidate the physical mechanisms of modulation under distinct loaded voltage conditions.The results not only advance modulation and logic gate designs for THz communication but also demonstrate significant potential applications in 6G networks,THz imaging,and radar systems.展开更多
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
In-memory computing(IMC)based on spin-logic devices is regarded as an advantageous way to optimize the Von Neumann bottleneck.However,performing complete Boolean logic with spintronic devices typi-cally requires an in...In-memory computing(IMC)based on spin-logic devices is regarded as an advantageous way to optimize the Von Neumann bottleneck.However,performing complete Boolean logic with spintronic devices typi-cally requires an initialization operation,which can reduce processing speed.In this work,we conceptu-alize and experimentally demonstrate a programmable and initialization-free spin-logic gate,leveraging spin-orbit torque(SOT)to effectuate magnetization switching,assisted by in-plane Oersted field gener-ated by an integrated bias-field Au line.This spin-logic gate,fabricated as a Hall bar,allows complete Boolean logic operations without initialization.A current flowing through the bias-field line,which is electrically isolated from the device by a dielectric,generates an in-plane magnetic field that can invert the SOT-induced switching chirality,enabling on-the-fly complete Boolean logic operations.Additionally,the device demonstrated good reliability,repeatability,and reproducibility during logic operations.Our work demonstrates programmable and scalable spin-logic functions in a single device,offering a new approach for spin-logic operations in an IMC architecture.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
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
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 National Natural Science Foundation of China(Grant Nos.62005058 and 62365006)the Natural Science Foundation of Guangxi,China(Grant No.2020GXNSFBA238012)+2 种基金the China Postdoctoral Science Foundation(Grant No.2020M683726)the Innovation Project of Guangxi Graduate Education(Grant Nos.YCSW2024345 and YCBZ2025157)the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(Grant No.YQ24101).
文摘High-performance terahertz(THz)logic gate devices are crucial components for signal processing and modulation,playing a significant role in the application of THz communication and imaging.Here,we propose a THz broadband NOR logic encoder based on a graphene-metal hybrid metasurface.The unit structure consists of two symmetrical dual-gap metal split-ring resonators(DSRRs)arranged in a staggered configuration,with graphene strips embedded in their gaps.The NOR logic gate metadevice is controlled by the bias voltages independently applied to the two electrodes.Experiments show that when the bias voltages are applied to both electrodes,the metadevice achieves the NOR logic gate within a 0.52 THz bandwidth,with an average modulation depth above 80%.The experimental results match well with theoretical simulations.Additionally,the strong near-field coupling induced by the staggered DSRRs causes redshift at both LC resonance and dipole resonance.This phenomenon was demonstrated by coupled mode theory.Besides,we analyze the surface current distribution at resonances and propose four equivalent circuit models to elucidate the physical mechanisms of modulation under distinct loaded voltage conditions.The results not only advance modulation and logic gate designs for THz communication but also demonstrate significant potential applications in 6G networks,THz imaging,and radar systems.
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.
基金supported by the National Science and Technology Major Project(2020AAA0109005)the National Natural Science Foundation of China(62374055,12327806,62304083,62074063,61821003,61904060,61904051,61674062)+4 种基金the Interdisciplinary Program of Wuhan National High Magnetic Field Center(WHMFC202119)the Shenzhen Science and Technology Program Award(JCYJ20220818103410022)the Shenzhen Virtual University Park(2021Szvup091)the Natural Science Foundation of Wuhan(2024040701010049)Shuai Zhang acknowledges support from the China Postdoctoral Science Foundation(2022M721237).
文摘In-memory computing(IMC)based on spin-logic devices is regarded as an advantageous way to optimize the Von Neumann bottleneck.However,performing complete Boolean logic with spintronic devices typi-cally requires an initialization operation,which can reduce processing speed.In this work,we conceptu-alize and experimentally demonstrate a programmable and initialization-free spin-logic gate,leveraging spin-orbit torque(SOT)to effectuate magnetization switching,assisted by in-plane Oersted field gener-ated by an integrated bias-field Au line.This spin-logic gate,fabricated as a Hall bar,allows complete Boolean logic operations without initialization.A current flowing through the bias-field line,which is electrically isolated from the device by a dielectric,generates an in-plane magnetic field that can invert the SOT-induced switching chirality,enabling on-the-fly complete Boolean logic operations.Additionally,the device demonstrated good reliability,repeatability,and reproducibility during logic operations.Our work demonstrates programmable and scalable spin-logic functions in a single device,offering a new approach for spin-logic operations in an IMC architecture.
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 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.
