Fibring In The Leibniz Hierarchy

This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.155-6 SPEC. ISS.475501Blok, W., Pigozzi, D., Abstract algebraic logic and the deduction theorem The Bulletin of Symbolic Logic, , To appearBlok, W., Pigozzi, D., Protoalgebraic logics (1986) Studia Logica, 45, pp. 337-369Blok, W., Pigozzi, D., (1989) Algebraizable Logics, volume 77 (396) of Memoirs of the American Mathematical Society, , AMS, Providence, Rhode IslandJ. Bueno. Semântica Algébrica de Traduções Possíveis (Possible - Translations Algebraic Semantics, in Portuguese). Masters Thesis, IFCH - State University of Campinas, Brazil, 2004Bueno-Soler, J., Coniglio, M.E., Carnielli, W., Possible-translations algebraizability (2008) Handbook of Paraconsistency, , J.-Y. Béziau, W. Carnielli and D. Gabbay, editors, Elsevier, To appearCaleiro, C., (2000) Combining Logics, , PhD thesis, IST, LisbonC. Caleiro, W. A. Carnielli, J. Rasga, and C. Sernadas. Fibring of logics as a universal construction. 13 of Handbook of Philosophical Logic, 2nd Edition, pages 123-187. Springer, 2005Carnielli, W., Many-valued logics and plausible reasoning (1990) Proceedings of the XX International Congress on Many-Valued Logics, University of Charlotte, pp. 328-335. , USA, IEEE Computer SocietyCarnielli, W.A., Coniglio, M.E., Gabbay, D., Gouveia, P., Sernadas, C., Analysis and Synthesis of Logics (2008) Applied Logic Series, 35. , of, Springer, In printM. E. Coniglio. Recovering a logic from its fragments by meta-fibring. Logica Universalis, 1(2), 2007. In print. Preliminary version available as: The meta-fibring environment: Preservation of meta-properties by fibring. CLE e-Prints, 5(4), 2005. URL = http://www.cle.unicamp.br/ e-prints/vol_5,n_4,2005.htmM. E. Coniglio and V. L. Fernández. Plain fibring and direct union of logics with matrix semantics. In B. Prasad, editor, Proceedings of the 2nd Indian International Conference on Artificial Intelligence (HCAI 2005), Pune, India. IICAI, 2005. Preliminary version available at CLE e-Prints, 5(10), 2005. URL = http://www.cle.unicamp.br/e-prints/vol_5,n_10,2005.htmlCzelakowski, J., Equivalential logics (I) and (II) (1981) Studia Logica, 40, pp. 227-236,335-372Czelakowski, J., (2001) Protoalgebraic Logics, , Kluwer Academic Publishers, DordrechtD'Ottaviano, I.M.L., da Costa, N.C.A., Sur un problème de Jaśkowski. (1970) Comptes Rendus de l'Academie de Sciences de Paris (A-B), 270, pp. 1349-1353V. L. Fernández. Fibrilação de Lógicas na Hierarquia de Leibniz (Fibring Logics within the Leibniz Hierarchy, in Portuguese). PhD thesis, IFCH - State University of Campinas, Brazil, 2005Fernández, V.L., Coniglio, M.E., Fibring algebraizable consequence systems (2004) Proceedings of CombLog'04 - Workshop on Combination of Logics: Theory and Applications, pp. 93-98. , W. A. Carnielli, F. M. Dionísio, P. Mateus edsJ. M. Font, R. Jansana, and D. Pigozzi. A survey of abstract algebraic logic. Studia Logica (Special Issue on Abstract Algebraic Logic II 74(1-2):13-97, 2003. 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Kluwer Academic PublishersZanardo, A., Sernadas, A., Sernadas, C., Fibring: Completeness preservation (2001) The Journal of Symbolic Logic, 66 (1), pp. 414-43