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
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
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
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
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
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.
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
Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively ...Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.展开更多
a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncerta...a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.展开更多
This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basi...This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basis of [2—5] Morley categoricity theorem for finite valued lattice is deduced.展开更多
This paper praidrs a theurvtheal hasts for establishing the congergente of paraled interative and itratiee techaigues,for computing nmtrfied solution of Ar three A is a singal M-matrix,These results do not assuine A t...This paper praidrs a theurvtheal hasts for establishing the congergente of paraled interative and itratiee techaigues,for computing nmtrfied solution of Ar three A is a singal M-matrix,These results do not assuine A to irreducihle,A concrete relaxed parallet multixpla ting algorithin culled the parallel multispliting AOR algarithm is showed Findly,numericales amples are givep,arhleh show effertielve of parallel iterurise methods for singalar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
Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analy...Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analytically characterize the completely distributive law? Moreover, can we characterize the completely distributive law in terms of fuzzy topology? The purpose of this note is to answer affirmatively these questions for the infinitely distributive lattices. This study connecting algebra with analysis and topology seems to be rather interesting.展开更多
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.
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.
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.
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 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The Project Supported by National Natural Science Foundation of China.
文摘Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.
基金National Natural Science Foundations of China (No. 60875034,No. 61175055)
文摘a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.
文摘This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basis of [2—5] Morley categoricity theorem for finite valued lattice is deduced.
文摘This paper praidrs a theurvtheal hasts for establishing the congergente of paraled interative and itratiee techaigues,for computing nmtrfied solution of Ar three A is a singal M-matrix,These results do not assuine A to irreducihle,A concrete relaxed parallet multixpla ting algorithin culled the parallel multispliting AOR algarithm is showed Findly,numericales amples are givep,arhleh show effertielve of parallel iterurise methods for singalar
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.
基金Project supported by the National Natural Science Foundation of China
文摘Using an algebraic property, the completely distributive law, we have ever given out a characterization of the semicontinuity of lattice-valued mappings. How about the inverse implication? That is to say, can we analytically characterize the completely distributive law? Moreover, can we characterize the completely distributive law in terms of fuzzy topology? The purpose of this note is to answer affirmatively these questions for the infinitely distributive lattices. This study connecting algebra with analysis and topology seems to be rather interesting.
