Теорема представления Пристли и метод резолюций в многозначных логиках.
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04.11.2003
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Abstract
In this paper we study proof theory o f many-valued logics from the algebraic point o f view. We solve the problem posed in [7] and formulate a criterion o f correctness o f the many-valued resolution based on the Priestley representation theorem with respect to an arbitrary many-valued logic.
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How to Cite
Komendantsky V. Теорема представления Пристли и метод резолюций в многозначных логиках. // Logicheskie Issledovaniya / Logical Investigations. 2003. VOL. 10. C. 109-116.
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References
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Комендантский В.Е. Метод резолюций в смешанной логике Поста // Труды XVI научно-исследовательского семинара логического центра ИФРАН. М.: ИФРАН, 2002 С. 64-74.
Чень Ч, Ли Р. Математическая логика и автоматическое доказательство теорем. М.: Мир, 1983
Anshakov О., Rychkov S. On Finite-Valued Propositional Logical Calculi // Notre Dame Journal o f Formal Logic. 1994. Vol. 36, № 4. P. 606-629.
Chang C.C. Algebraic analysis of many valued logics // Trans. Amer. Math. Soc. 1958. Vol. 88. P. 467-490.
Gehrke M., Priestley H.A. Non-canonicity o f MV-algebras // Houston Jounal o f Mathematics, 2002
Komendantsky V. On automated theorem proving by means o f representation theory in Lukasiewicz logics // Smirnov’s Readings. 4 international conference. Moscow: IPhRAS, 2003. P. 78-79.
Sofronie-Stokkermans V. Duality and canonical extensions o f bounded distributive lattices with opeiators, and applications to the semantics o f nonclassical logics I. // Studia Logica. 2000. Vol 64, № 1. P. 151-172.
Sofronie-Stokkermans V. Representation Theorems and the Semantics o f Non-classical Logics, and Applications to Automated Theorem Proving // Beyond Two: Theory' and Applications o f Multiple Valued Logic. Springer, 2003. P. 59-100. 10 .Vasyukov V.L. The Completeness o f the Factor Semantics for Lukasiewicz's Infinite-valued Logics // Studia Logica. 1993. Vol. 52. P 143-167.
Комендантский В.Е. Метод резолюций в смешанной логике Поста // Труды XVI научно-исследовательского семинара логического центра ИФРАН. М.: ИФРАН, 2002 С. 64-74.
Чень Ч, Ли Р. Математическая логика и автоматическое доказательство теорем. М.: Мир, 1983
Anshakov О., Rychkov S. On Finite-Valued Propositional Logical Calculi // Notre Dame Journal o f Formal Logic. 1994. Vol. 36, № 4. P. 606-629.
Chang C.C. Algebraic analysis of many valued logics // Trans. Amer. Math. Soc. 1958. Vol. 88. P. 467-490.
Gehrke M., Priestley H.A. Non-canonicity o f MV-algebras // Houston Jounal o f Mathematics, 2002
Komendantsky V. On automated theorem proving by means o f representation theory in Lukasiewicz logics // Smirnov’s Readings. 4 international conference. Moscow: IPhRAS, 2003. P. 78-79.
Sofronie-Stokkermans V. Duality and canonical extensions o f bounded distributive lattices with opeiators, and applications to the semantics o f nonclassical logics I. // Studia Logica. 2000. Vol 64, № 1. P. 151-172.
Sofronie-Stokkermans V. Representation Theorems and the Semantics o f Non-classical Logics, and Applications to Automated Theorem Proving // Beyond Two: Theory' and Applications o f Multiple Valued Logic. Springer, 2003. P. 59-100. 10 .Vasyukov V.L. The Completeness o f the Factor Semantics for Lukasiewicz's Infinite-valued Logics // Studia Logica. 1993. Vol. 52. P 143-167.