Внутренняя логика универсальной логики


V.L. Vasyukov


Early in [1] some categorical constructions were introduced which describe the inner structure of the category of logical systems. Since this structure both the topos and complemented topos were featured by, then following Benabou-Mitchell's approach the inner language is introduced which is not a standard topos language but an extended one rendering the construction of the language for so-called H-B-logic whose algebraic models are semi-Boolean algebras. McLarty’s sequential version of topos logic is extended to the case of the category of logical systems and the final inner logic formulation is based on the sequential formulation of H-B-logic.






Васюков В.Л. Проблема контекста интерпретации в универсальной логике // Логические исследования. Вып. 14. М., 2007. С.105-130.
Васюков В.Л. Металогика универсальной логики // Современная логика: проблемы теории, истории и применения в науке. Материалы IX Общероссийской научной конференции. Санкт-Петербург, 22-24 июня 2006 г. Спб.ГУ, 2006. С. 45-347.
Джонстон П.Т. Теория топосов. М.: Наука, 1986.
Beziau J.-Y. From Consequence Operator to Universal Logic: A Survey of General Abstract Logic // Logica Universalis / J.-Y. Beziau (ed.). Basel, 2005. P. 3-18.
Caleiro C., Gongalves R. Equipollent Logical Systems // Logica Universalis / J.-Y. Beziau (ed.). Basel, 2005. P. 99-111.
McLarty C. Elementary Categories, Elementary Toposes. Oxford: Clarendon Press.
Rauszer C. A Formalization of the Propositional Calculus of H-B-logic // Studia Logica. 1973. Vol. 33. №1. P. 23-34.
Rauszer C. An algebraic and Kripke-style appraoach to a certain extension of intuionistic logic // Dissertationes Mathematicae, CLXVII. PWN, Warszawa, 1980.
Vasyukov V.L. Structuring the Universe of Universal Logic // Logica Universalis. 2007. Vol. 1-2. P. 277-294.
Wojcicki R. Theory of Logical Calculi // Synthese Library. Vol. 199. Dordrecht, 1988.


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