Проблема структуры универсальной логики
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16.01.2007
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Аннотация
Предметом исследования является природа и структура общего универсума возможных комбинаций логических систем. Введены некоторые категориальные конструкции, которые наряду с копроизведениями, лежащими в основе расслоения логик, описывают внутреннюю структуру категории логических систем. Показано, что с точки зрения категорий универсум универсальной логики оказывается паранепротиворечивым дополняющим топосом.
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Как цитировать
Васюков В. Проблема структуры универсальной логики // Логические исследования / Logical Investigations. 2007. Т. 13. C. 95-113.
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Статьи
Литература
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Расева Е., Сикорский Р. Математика метаматематики. М.: 1972.
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Baader F. and Schulz K. U. (eds.). Frontiers of combining systems, Applied Logic Series. V. 3. Dordrecht, 1996 (Papers from the First International Workshop (FroCoS’96) held in Munich, March 26-29, 1996)
Beziau J.-Y., de Freitas R.P., VianaJ.P. What is Classical Propositional Logic? (A Study in Universal Logic) // Logical Investigations, V. 8, 2001. P. 266-277.
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., Gonsalves R. Equipollent Logical Systems // Logica Universalis. J.-Y. Beziau (ed.). Basel, 2005. P. 99-111.
Caleiro C., Carnielli W.A., Coniglio _. E., Semadas A., and Semadas C. Fibring non-truth-functional logics: Completeness preservation // Journal of Logic, Language and Information. V. 12 № 2. 2003. P. 183-211.
Camielli W. Possible-Translations Semantics for Paraconsistent Logics // Frontiers of Paraconsistent Logic / D. Batens et al (eds.). Baldock, Herfordshire, 2000. P.149- 163.
Coniglio M.E., Sernadas A., and SemadasC. Fibring logics with topos semantics // Journal of Logic and Computation. V. 13. № 4. 2003. P. 595-624.
Font J.M., Jansana R., Pigozzi D. A Survey of Abstract Algebraic Logic // Studia Logica. Vol. 74, No 1/2, 2003. P. 13-97.
Gabbay D. Fibred semantics and the weaving of logics: part 1 // Journal of Symbolic Logic. V. 61. Л* 4. 1996. P. 1057-1120.
Gabbay D. and Pirri F. (eds.). Special issue on combining logics // Studia Logica, V. 59. № 1,2. 1997.
Kirchner H. and Ringeissen C. (eds.). Frontiers of combining systems. Lecture Notes in Computer Science. V. 1794. Berlin, 2000.
Mortensen C. Inconsistent Mathematics. Dordrecht, 1995.
Pratt V.R. Rational Mechanics and Natural Mathematics // Proc. TAPSOFT’95, LNCS V. 915. Aarhus, Denmark, May 1995. P. 108-122.
Rasga J., Sernadas A., Sernadas C. and Vigano L. Fibring labelled deduction systems // Journal of Logic and Computation. V. 12. № 3. 2002. P. 443-473.
Rauszer C. A Formalization of the Propositional Calculus of H-B-logic // Studia Logica. V. 33. № 1. 1973. P. 23-34.
de Rijke M. and Blackburn P. (eds.). Special issue on combining logics // Notre Dame Journal of Formal Logic, V. 37. № 2. 1996.
Sernadas A., Sernadas C., Caleiro C. Fibring of Logics as a Categorial Construction // Journal of Logic and Computation. V. 9. № 2. 1999. P. 149-179.
Sernadas C., Rasga J. and Carnielli W.A. Modulated fibring and the collapsing problem // Journal of Symbolic Logic. V. 67. № 4. 2002. P. 1541-1569.
Sernadas C., Vigano L., Rasga J., and Sernadas A. Truth-values as labels: A general recipe for labelled deduction // Journal of Applied Non-Classical Logics. V. 13. № 3-4. 2003. P. 277-315.
Wojcicki R. Theory of Logical Calculi. Synthese Library. VI. 199. Dordrecht, 1988.
Расева Е., Сикорский Р. Математика метаматематики. М.: 1972.
Armando A. (ed.). Frontiers of combining systems. Lecture Notes in Computer Science, V. 2309 Berlin, 2002.
Baader F. and Schulz K. U. (eds.). Frontiers of combining systems, Applied Logic Series. V. 3. Dordrecht, 1996 (Papers from the First International Workshop (FroCoS’96) held in Munich, March 26-29, 1996)
Beziau J.-Y., de Freitas R.P., VianaJ.P. What is Classical Propositional Logic? (A Study in Universal Logic) // Logical Investigations, V. 8, 2001. P. 266-277.
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., Gonsalves R. Equipollent Logical Systems // Logica Universalis. J.-Y. Beziau (ed.). Basel, 2005. P. 99-111.
Caleiro C., Carnielli W.A., Coniglio _. E., Semadas A., and Semadas C. Fibring non-truth-functional logics: Completeness preservation // Journal of Logic, Language and Information. V. 12 № 2. 2003. P. 183-211.
Camielli W. Possible-Translations Semantics for Paraconsistent Logics // Frontiers of Paraconsistent Logic / D. Batens et al (eds.). Baldock, Herfordshire, 2000. P.149- 163.
Coniglio M.E., Sernadas A., and SemadasC. Fibring logics with topos semantics // Journal of Logic and Computation. V. 13. № 4. 2003. P. 595-624.
Font J.M., Jansana R., Pigozzi D. A Survey of Abstract Algebraic Logic // Studia Logica. Vol. 74, No 1/2, 2003. P. 13-97.
Gabbay D. Fibred semantics and the weaving of logics: part 1 // Journal of Symbolic Logic. V. 61. Л* 4. 1996. P. 1057-1120.
Gabbay D. and Pirri F. (eds.). Special issue on combining logics // Studia Logica, V. 59. № 1,2. 1997.
Kirchner H. and Ringeissen C. (eds.). Frontiers of combining systems. Lecture Notes in Computer Science. V. 1794. Berlin, 2000.
Mortensen C. Inconsistent Mathematics. Dordrecht, 1995.
Pratt V.R. Rational Mechanics and Natural Mathematics // Proc. TAPSOFT’95, LNCS V. 915. Aarhus, Denmark, May 1995. P. 108-122.
Rasga J., Sernadas A., Sernadas C. and Vigano L. Fibring labelled deduction systems // Journal of Logic and Computation. V. 12. № 3. 2002. P. 443-473.
Rauszer C. A Formalization of the Propositional Calculus of H-B-logic // Studia Logica. V. 33. № 1. 1973. P. 23-34.
de Rijke M. and Blackburn P. (eds.). Special issue on combining logics // Notre Dame Journal of Formal Logic, V. 37. № 2. 1996.
Sernadas A., Sernadas C., Caleiro C. Fibring of Logics as a Categorial Construction // Journal of Logic and Computation. V. 9. № 2. 1999. P. 149-179.
Sernadas C., Rasga J. and Carnielli W.A. Modulated fibring and the collapsing problem // Journal of Symbolic Logic. V. 67. № 4. 2002. P. 1541-1569.
Sernadas C., Vigano L., Rasga J., and Sernadas A. Truth-values as labels: A general recipe for labelled deduction // Journal of Applied Non-Classical Logics. V. 13. № 3-4. 2003. P. 277-315.
Wojcicki R. Theory of Logical Calculi. Synthese Library. VI. 199. Dordrecht, 1988.