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
By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the s...By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.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
By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introdu...By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.展开更多
The theory of （n） truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the （n） truth degree of a modality-free formula equals the truth degree ...The theory of （n） truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the （n） truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of （n） truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of （n） similarity degrees among modal formulas is proposed and the （n） modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.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.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 19831040 and 69831040).
文摘By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.
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the National Natural Science Foundation of China （Grant No. 10331010）, and the Innovation Foundation for Doctors of Shaanxi Normal University.
文摘By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10331010 and 10771129)the Foundation of 211 Constructionof Shaanxi Normal University
文摘The theory of （n） truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the （n） truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of （n） truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of （n） similarity degrees among modal formulas is proposed and the （n） modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
