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
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
Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although...Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.展开更多
People unavoidably provide reasons for their words and deeds when reasoning in a language-game. Wittgenstein thinks that when people in different language-games argue with one other, they insist on adopting a doubtful...People unavoidably provide reasons for their words and deeds when reasoning in a language-game. Wittgenstein thinks that when people in different language-games argue with one other, they insist on adopting a doubtful attitude toward the reasons provided by the other side. His use of the term ＂language-game＂ here is a metaphor, and implies＇that people in different cultures can scarcely reason with one another. Indeed, according to Wittgenstein＇s consideration of concepts of logic in On Certainty, language-games are incompatible with one another because their internal logic and reasons are different from each other. However, in his discussion of empiricalpropositions Wittgenstein has also shown us the possibility that the internal reasons of one language-game can transmit beyond its own borders and be valid in another language-game.展开更多
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.
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.
文摘Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.
基金This work was supposed by the National Fundamental Research 973 Program of China(Grand No．2002CB312103)； the National Natural Science Foundation of China(Grant Nos．60033020，70371052)．
文摘People unavoidably provide reasons for their words and deeds when reasoning in a language-game. Wittgenstein thinks that when people in different language-games argue with one other, they insist on adopting a doubtful attitude toward the reasons provided by the other side. His use of the term ＂language-game＂ here is a metaphor, and implies＇that people in different cultures can scarcely reason with one another. Indeed, according to Wittgenstein＇s consideration of concepts of logic in On Certainty, language-games are incompatible with one another because their internal logic and reasons are different from each other. However, in his discussion of empiricalpropositions Wittgenstein has also shown us the possibility that the internal reasons of one language-game can transmit beyond its own borders and be valid in another language-game.
