Based on the intuitionistic first order predicate calculusH given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a...Based on the intuitionistic first order predicate calculusH given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zorn lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason's result.展开更多
In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper ...In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper would be prepared to discuss the same connexion for quantifications of all the modal systems considered therein. Unfortunately, owing to his untimely death, this Paper did not come out. In this note we discuss the展开更多
It was A. N. Prior who introduced the system MIPC in his monograph Time and Modality in 1957, which is of type S5 in the sense of R. A. Bull, i. e. adding the law of excluded middle to it yields S5. Many different mod...It was A. N. Prior who introduced the system MIPC in his monograph Time and Modality in 1957, which is of type S5 in the sense of R. A. Bull, i. e. adding the law of excluded middle to it yields S5. Many different modal intuitionistic calculi of type S5 (also in the same sense of Bull )were given by several logicians in recent years. One of the basic prob-展开更多
Let S be a propositional modal system and S~* be the quantification of S, then we can prove the algebraic semantic completeness theorem of the kind of Rasiowa-Sikorski for S~* by showing that S has the property (E)giv...Let S be a propositional modal system and S~* be the quantification of S, then we can prove the algebraic semantic completeness theorem of the kind of Rasiowa-Sikorski for S~* by showing that S has the property (E)given in [1]. But except for a few cases, it is very difficult to show thara system S has the property (E). So for most quantified modal systems,展开更多
文摘Based on the intuitionistic first order predicate calculusH given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zorn lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason's result.
文摘In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper would be prepared to discuss the same connexion for quantifications of all the modal systems considered therein. Unfortunately, owing to his untimely death, this Paper did not come out. In this note we discuss the
文摘It was A. N. Prior who introduced the system MIPC in his monograph Time and Modality in 1957, which is of type S5 in the sense of R. A. Bull, i. e. adding the law of excluded middle to it yields S5. Many different modal intuitionistic calculi of type S5 (also in the same sense of Bull )were given by several logicians in recent years. One of the basic prob-
文摘Let S be a propositional modal system and S~* be the quantification of S, then we can prove the algebraic semantic completeness theorem of the kind of Rasiowa-Sikorski for S~* by showing that S has the property (E)given in [1]. But except for a few cases, it is very difficult to show thara system S has the property (E). So for most quantified modal systems,
