Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the ...Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.展开更多
A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a ...A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a Petri net with predicated transition. All components of the net are expressed by annotation which is defined on rational set Q. The analysis method for the plant is interval temporal logic represented by Petri nets. This paper combines the above two methods to synthesize the hybrid system, gives a simple and clear expression of the expected action of the studied plant.展开更多
This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable...This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable information.This method can also deal with the uncertain problem which has both positive evidence and negative evidence at the same time.10-elements linguistic truthvalued intuitionistic fuzzy first-order logic system has been established in the intuitionistic fuzzy algebra.展开更多
Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-va...Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-valued first-order logic, we discussed the satisfiable problem of 6-elements linguistic truth-valued first-order logic and proposed a resolution method of 6-elements linguistic truth-valued firstorder logic. Then the resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.展开更多
In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about...In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about uniform co-identical truthand uniform co-satisfiability.Thus some theorems in the book“A Course inMathematical Logic”,written by J.L.Bell and M.Machover,are corrected.展开更多
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main r...The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.展开更多
I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself o...I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself of the functional and logic paradigms. The purpose of this note, proceeding from the algebraic oersoective, is to formulize the first-order mathematical展开更多
A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The ...A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.展开更多
Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for qua...Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for quantifiers;and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.展开更多
基金National Natural Science Foundation of China (No. 60875034)Spanish Ministry of Education and Science Fund,Spain (No.TIN-2009-0828)Spanish Regional Government (Junta de Andalucia) Fund,Spain (No. P08-TIC-3548)
文摘Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.
文摘A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a Petri net with predicated transition. All components of the net are expressed by annotation which is defined on rational set Q. The analysis method for the plant is interval temporal logic represented by Petri nets. This paper combines the above two methods to synthesize the hybrid system, gives a simple and clear expression of the expected action of the studied plant.
基金This work is partly supported by National Nature Science Foundation of China (Grant No.61105059,61175055,61173100), International Cooperation and Exchangeof the National Natural Science Foundation of China (Grant No.61210306079),Sichuan Key Technology Research and Development Program (Grant No.2011FZ0051),Radio Administration Bureau of MIIT of China (Grant No.[2011]146), China Institution of Communications (Grant No.[2011]051), and Sichuan Key Laboratory of Intelligent Network Information Processing (Grant No.SGXZD1002-10),Liaoning Excellent Talents in University (LJQ2011116).
文摘This paper presents 10-elements linguistic truth-valued intuitionistic fuzzy algebra and the properties based on the linguistic truth-valued implication algebra which is fit to express both comparable and incomparable information.This method can also deal with the uncertain problem which has both positive evidence and negative evidence at the same time.10-elements linguistic truthvalued intuitionistic fuzzy first-order logic system has been established in the intuitionistic fuzzy algebra.
基金This work is partly supported by National Nature Science Foundation of China (Grant No.61105059,61175055,61173100), International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No.61210306079), Sichuan Key Technology Research and Development Program (Grant No.2011FZ0051), Radio Administration Bureau of MIIT of China (Grant No.[2011]146), China Institution of Communications (Grant No.[2011]051), and Sichuan Key Laboratory of Intelligent Network Information Processing (Grant No.SGXZD1002-10),Liaoning Excellent Talents in University (LJQ2011116).
文摘Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-valued first-order logic, we discussed the satisfiable problem of 6-elements linguistic truth-valued first-order logic and proposed a resolution method of 6-elements linguistic truth-valued firstorder logic. Then the resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.
文摘In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about uniform co-identical truthand uniform co-satisfiability.Thus some theorems in the book“A Course inMathematical Logic”,written by J.L.Bell and M.Machover,are corrected.
基金Supported by the National Science Foundation of China under Grant Nos.11235003 and 11475023National Social Sciences Foundation of China under Grant No.14BZX078+1 种基金the Research Fund for the Doctoral Program of Higher Education of Chinathe Undergraduate Training Program of Beijing
文摘The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.
基金Project supported by the National High Technique Planning Foundation
文摘I. INTRODUCTION The exploration for a unified basis of the combinatory logic and the predicate calculus will promote laying a strict and thorough mathematical foundation of the programming language possessing itself of the functional and logic paradigms. The purpose of this note, proceeding from the algebraic oersoective, is to formulize the first-order mathematical
文摘A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.
基金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Traditional first-order logic has four definitions for quantifiers,which are defined by universal and existential quantifiers.In L_(3)-valued(three-valued)first-order logic,there are eight kinds of definitions for quantifiers;and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.
