Проблема структуры универсальной логики


V.L. Vasyukov


The subject of the inquiry is the nature and the structure of the general universe of possible combinations of logical systems. Some categorical constructions are introduced which along with the coproducts underlying the fibring of logics describe the inner structure of the category of logical systems. It is shown that categorically the universe of universal logic turns out to be a paraconsistent complement topos.






Голдблатт Р. Топосы. Категорный анализ логики. М.: 1983.
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.