The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some prop...The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some properties is discussed. Formulas of the extended calculus can be expressed in the extension multi-layer perceptron. Naturally, semantic deduction of prop ositional knowledge base can be implement by the extension multi-layer perceptr on, and by learning, an unknown formula set can be found.展开更多
＂In this paper, we construct a six-element intuitionistic linguistic truth-valued fuzzy propositional logic （6LTV-IP） based on the framework of linguistic truth-valued propoitional logic, which can express bath the...＂In this paper, we construct a six-element intuitionistic linguistic truth-valued fuzzy propositional logic （6LTV-IP） based on the framework of linguistic truth-valued propoitional logic, which can express bath the comparable and incomparable truth values. Truth degree and falsity degree of intuitionistic fuzzy proposition are two truth values with linguistic hedge. With the concrete logic operation of 6LTV-IP, some special properties are obtained. Then based on （α, β）-complementary literals and （a, β）-similar literals, we propose a soft-resolution method of 6LTV-IP.展开更多
Previous studies interpreting the meanings of the sentence-final particle“LE”displayed two trends:either excessively complicated or excessively general.Since some scholars established a theoretical foundation of pro...Previous studies interpreting the meanings of the sentence-final particle“LE”displayed two trends:either excessively complicated or excessively general.Since some scholars established a theoretical foundation of propositional domain,epistemic domain and dialogic domain for the sentence-final particle“LE”,the nature or orientation of its semantic property has become more clear.However,there are also defects in the current“Three Domains”research model.In the first place,this model defines the meanings of the sentence-final particle“LE”as“emergence of new propositional content”,“emergence of new epistemic content”,and“emergence of new dialogic content”.But,the definition is excessively abstract and extensive.As many sentences not concluded with the particle“LE”can also express the three mentioned meanings,it fails to explain the difference between sentences ended with particle“LE”and ones without it.Secondly,the model fails to explore and discuss the nature or generation mechanism of relevant meanings of the particle“LE”.This study attempts to find a practical solution to those defects.展开更多
The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as...The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as“classical calculus of predicates”or“first-order logic”),which is necessary to construct the classical functional calculus.This last one is being used for formalization of the Arithmetic System.At the beginning of this paper,we introduce a notation and we repeat certain well-known notions(among others,the notions of operation of consequence,a system,consistency in the traditional sense,consistency in the absolute sense)and certain well-known theorems.Next,we establish that classical propositional calculus is an inconsistent theory.展开更多
For the problem of propositional satisfiability a polynomial algorithm of limited propositional deduction is proposed which can be viewed as a sort of boolean constraint propagation mechanism. It can be embodied in a ...For the problem of propositional satisfiability a polynomial algorithm of limited propositional deduction is proposed which can be viewed as a sort of boolean constraint propagation mechanism. It can be embodied in a backtracking search program for propositional satisfiability problems to make search efficient. The efficiency is gained in two ways:One is to use the algorithm to derive literals so as to overcome the ambiguities in search. The other is to exploit the consequence sets of unbound atoms generated during limited deduction as a heuristic measure for possible choices. The experiments have shown remarkable improvement in reducing search space.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
Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high scho...Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.展开更多
The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integ...The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.展开更多
Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typ...Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typical ones are default logic[2,3],R-calculus[4],autoepistemic logic[5],circumscription[5],etc.展开更多
This paper gives an outline of knowledge base revision and some recently presented complexity results about propositional knowledge base revision. Different methods for revising propositional knowledge baize have been...This paper gives an outline of knowledge base revision and some recently presented complexity results about propositional knowledge base revision. Different methods for revising propositional knowledge baize have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a revision method for special case, and gives its corresponding polynomial algorithm.展开更多
On April 26,the first event of CIIS Dialogue was held under the theme of“An Equal and Orderly Multipolar World&A Universally Beneficial and Inclusive Economic Globalization:Implications and the Way Forward.”Offi...On April 26,the first event of CIIS Dialogue was held under the theme of“An Equal and Orderly Multipolar World&A Universally Beneficial and Inclusive Economic Globalization:Implications and the Way Forward.”Officials of international organizations in China and renowned scholars at home and abroad had in-depth discussions on the two major Chinese propositions.展开更多
Objective:This paper aims to evaluate the implementation effect of the diversified course assessment method reform.Methods:A diversified assessment method was implemented for 196 undergraduate nursing students.Student...Objective:This paper aims to evaluate the implementation effect of the diversified course assessment method reform.Methods:A diversified assessment method was implemented for 196 undergraduate nursing students.Students’mastery of key knowledge in“Nursing Research”was assessed through group reports on topic selection and literature retrieval,as well as the proposition level of the final examination.Results:81.6%of the students agreed with the course assessment method,and 97.9%believed studying“Nursing Research”would be helpful for future scientific research applications.Conclusion:Diversified assessment methods can help improve undergraduate nursing students’scientific research skills and comprehensive quality.展开更多
Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership de...Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R0 n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.展开更多
To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variab...To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variables and some generalized literals of L14P（X）, which is a lattice-valued propositional logic system with truth-values in L14, were discussed. There are 4 filters in L14. For any constant a not belonging to J, a and g （generalized literal of L14P（X）） form a J-resolution pair. For a propositional variable x, if x belongs to J and g does not belong to J, then x and g form a J-resolution pair.展开更多
Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a del...Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.展开更多
Truth-functionality is the most important concept in propositional logic.Some compound propositions are truth-functional and some are not.In this essay,I explain the difference between truth-functional compound propos...Truth-functionality is the most important concept in propositional logic.Some compound propositions are truth-functional and some are not.In this essay,I explain the difference between truth-functional compound propositions and non-truth-functional compound propositions,using what I call“belief statements”as an example of the latter.My explanation of why belief statements are not truth-functional is both more thorough and(I submit)more illuminating than the explanations provided by the leading logic textbooks.The authors of these textbooks may wish to incorporate some of my suggestions into future editions.Alternatively,they may direct their students to this essay for edification.展开更多
文摘The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some properties is discussed. Formulas of the extended calculus can be expressed in the extension multi-layer perceptron. Naturally, semantic deduction of prop ositional knowledge base can be implement by the extension multi-layer perceptr on, and by learning, an unknown formula set can be found.
基金National Natural Science Foundations of China(No.60875034, No.60873042)
文摘＂In this paper, we construct a six-element intuitionistic linguistic truth-valued fuzzy propositional logic （6LTV-IP） based on the framework of linguistic truth-valued propoitional logic, which can express bath the comparable and incomparable truth values. Truth degree and falsity degree of intuitionistic fuzzy proposition are two truth values with linguistic hedge. With the concrete logic operation of 6LTV-IP, some special properties are obtained. Then based on （α, β）-complementary literals and （a, β）-similar literals, we propose a soft-resolution method of 6LTV-IP.
文摘Previous studies interpreting the meanings of the sentence-final particle“LE”displayed two trends:either excessively complicated or excessively general.Since some scholars established a theoretical foundation of propositional domain,epistemic domain and dialogic domain for the sentence-final particle“LE”,the nature or orientation of its semantic property has become more clear.However,there are also defects in the current“Three Domains”research model.In the first place,this model defines the meanings of the sentence-final particle“LE”as“emergence of new propositional content”,“emergence of new epistemic content”,and“emergence of new dialogic content”.But,the definition is excessively abstract and extensive.As many sentences not concluded with the particle“LE”can also express the three mentioned meanings,it fails to explain the difference between sentences ended with particle“LE”and ones without it.Secondly,the model fails to explore and discuss the nature or generation mechanism of relevant meanings of the particle“LE”.This study attempts to find a practical solution to those defects.
文摘The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as“classical calculus of predicates”or“first-order logic”),which is necessary to construct the classical functional calculus.This last one is being used for formalization of the Arithmetic System.At the beginning of this paper,we introduce a notation and we repeat certain well-known notions(among others,the notions of operation of consequence,a system,consistency in the traditional sense,consistency in the absolute sense)and certain well-known theorems.Next,we establish that classical propositional calculus is an inconsistent theory.
基金Project supported by the "863" High-Tech Program of China.
文摘For the problem of propositional satisfiability a polynomial algorithm of limited propositional deduction is proposed which can be viewed as a sort of boolean constraint propagation mechanism. It can be embodied in a backtracking search program for propositional satisfiability problems to make search efficient. The efficiency is gained in two ways:One is to use the algorithm to derive literals so as to overcome the ambiguities in search. The other is to exploit the consequence sets of unbound atoms generated during limited deduction as a heuristic measure for possible choices. The experiments have shown remarkable improvement in reducing search space.
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Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.
基金This work was supported by the National Natural Science Foundation of China(Grant No．10331010)
文摘The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.
基金supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2010KF-06)Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901)。
文摘Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typical ones are default logic[2,3],R-calculus[4],autoepistemic logic[5],circumscription[5],etc.
文摘This paper gives an outline of knowledge base revision and some recently presented complexity results about propositional knowledge base revision. Different methods for revising propositional knowledge baize have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a revision method for special case, and gives its corresponding polynomial algorithm.
文摘On April 26,the first event of CIIS Dialogue was held under the theme of“An Equal and Orderly Multipolar World&A Universally Beneficial and Inclusive Economic Globalization:Implications and the Way Forward.”Officials of international organizations in China and renowned scholars at home and abroad had in-depth discussions on the two major Chinese propositions.
基金Nursing Research Outcome of the Pilot Project for Course Assessment Reform in Sanya University(Project number:SYJGKH2022138)。
文摘Objective:This paper aims to evaluate the implementation effect of the diversified course assessment method reform.Methods:A diversified assessment method was implemented for 196 undergraduate nursing students.Students’mastery of key knowledge in“Nursing Research”was assessed through group reports on topic selection and literature retrieval,as well as the proposition level of the final examination.Results:81.6%of the students agreed with the course assessment method,and 97.9%believed studying“Nursing Research”would be helpful for future scientific research applications.Conclusion:Diversified assessment methods can help improve undergraduate nursing students’scientific research skills and comprehensive quality.
文摘Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R0 n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.
基金The Nationl Natural Science Foundation of China (No.60474022)
文摘To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variables and some generalized literals of L14P（X）, which is a lattice-valued propositional logic system with truth-values in L14, were discussed. There are 4 filters in L14. For any constant a not belonging to J, a and g （generalized literal of L14P（X）） form a J-resolution pair. For a propositional variable x, if x belongs to J and g does not belong to J, then x and g form a J-resolution pair.
文摘Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.
文摘Truth-functionality is the most important concept in propositional logic.Some compound propositions are truth-functional and some are not.In this essay,I explain the difference between truth-functional compound propositions and non-truth-functional compound propositions,using what I call“belief statements”as an example of the latter.My explanation of why belief statements are not truth-functional is both more thorough and(I submit)more illuminating than the explanations provided by the leading logic textbooks.The authors of these textbooks may wish to incorporate some of my suggestions into future editions.Alternatively,they may direct their students to this essay for edification.
