A survey on categories of logics and algebraizable logics

São Paulo Journal of Mathematical Sciences - Tập 9 - Trang 76-96 - 2015
Darllan C. Pinto1
1São Paulo, Brazil

Tóm tắt

The present work is intended as an overview of issues that surround the study of categories of logics, i.e., motivations to definition of category of logics, the main categories of logics, and the application these categories in a representation theory of logics.

Tài liệu tham khảo

Arndt, P., Freire, R.A., Luciano, O.O., Mariano, H.L.: Fibring and sheaves. In: Proceedings of IICAI-05, Special Session at the 2nd Indian International Conference on Artificial Intelligence, Pune, India, pp. 1679–1698 (2005) Arndt, P., Freire, R.A., Luciano, O.O., Mariano, H.L.: On the category of algebraizable logics. CLE e-Prints 6(1), 24 (2006) Arndt, P., Freire, R.A., Luciano, O.O., Mariano, H.L.: A global glance on categories in Logic. Logica Universalis 1, 3–39 (2007) Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Lecture Notes Series of the LMS 189. Cambridge University Press, Cambridge (1994) Béziau, J.Y.: From consequence operator to universal logic: a survey of general abstract logic in logica universalis. In: Beziau, J.-Y. (ed.) Towards a General Theory of Logic. Birkhaeuser, Basel (2005) Bueno-Soler, J., Carnielli, W.A.: Possible-translations algebraization for paraconsistent logics. Bull Sect Log 34(2), 77–92, University of Lodz, Polônia; CLE e-Prints 5(6), 13 (2005) Bueno, J., Coniglio, M.E., Carnielli, W.A.: Finite algebraizability via possible-translations semantics, In: Carnielli, W.A., Dionísio, F.M., Mateus, P. (eds.) Proceedings of CombLog 04—Workshop on Combination of Logics: Theory and Applications, pp. 79–86 (2004) Bueno-Soler, J., Coniglio, M.E., Carnielli, W.A.: Possible-translations algebraizability. In: Handbook of Paraconsistency, pp. 321–340. College Publications, London (2007) Blok, W.J., Pigozzi, D.: Algebraizable Logics, Memoirs of the AMS 396. American Mathematical Society, Providence (1989) Carnielli, W.A.: Many-valued logics and plausible reasoning. In: Proceedings of the XX International Congress on Many-Valued Logics, IEEE Computer Society, University of Charlotte, USA, pp. 328–335 (1990) Coniglio, M.E.: The Meta-Fibring Environment: Preservation of Meta-Properties by Fibring. CLE e-Prints 5(4), 36 (2005) Czelakowski, J.: Protoalgebraic logic. In: Trends in Logic, Studia Logica Library, vol. 10. Kluwer Academic Publisher, Dordrecht (2001) Carnielli, W.A., Coniglio, M.E.: A categorial approach to the combination of logics. Manuscript 22, 64–94 (1999) Carnielli, W.A., Coniglio, M.E.: Transfers between logics and their applications. Stud Log 72 (2002); CLE e-Prints 1(4), 31 (2001) Carnielli, W.A., Coniglio, M.E.: Combining Logics, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-combining/ Carnielli, W.A., Coniglio, M., Gabbay, D., Gouveia, P., Sernadas, C.: Analysis and Synthesis of Logics: How to Cut and Paste Reasoning System. Applied Logic Series. Springer, Berlin (2008) Caleiro, C., Carnielli, W., Rasga, J., Sernadas, C.: Fibring of logics as a universal construction. In: Handbook of Philosophical Logic, vol. 13. Kluwer Academic Publishers, Berlin (2005) Caleiro, C., Carnielli, W., Coniglio, M.E., Sernadas, A., Sernadas, C.: Fibring non-truth-functional logics: completeness preservation. J. Log. Lang. Inf 12(2), 183–211 (2003); CLE e-Prints 1(1), 34 (2001) Caleiro, C., Gonçalves, R.: Equipollent logical systems. In: Beziau, J.-Y. (ed.) Logica Universalis. Birkhäuser, Basel (2005) Caleiro, C., Ramos, J.: Cryptofibring. In: Carnielli, W.A., Dionísio, F.M., Mateus, P. (eds.) Proceedings of CombLog 04—Workshop on Combination of Logics: Theory and Applications, Lisboa, Portugal, pp. 87–92 (2004) Coniglio, M.E., Sernadas, A., Sernadas, C.: Fibring logics with topos semantics. J. Log. Comput. 13(4), 595–624 (2003) Fernández, V.L., Coniglio, M.E.: Fibring algebraizable consequence systems. In: Carnielli, W.A., Dionísio F.M., Mateus P. (eds.) Proceedings of CombLog 04—Workshop on Combination of Logics: Theory and Applications, pp. 93–98 (2004) Gabbay, D.: Fibred semantics and the weaving of logics: part 1. J. Symb. Log. 61(4), 1057–1120 (1996) Jánossy, A., Kurucz, Á., Eiben, Á.E.: Combining algebrizable logics. Notre Dame J. Form. Log. 37(2), 366–381 (1996) MacLane, S.: Categories for the Working Mathematician, Graduate Texts in Mathematics 5. Springer, Berlin (1971) Mariano, H.L., Mendes, C.A.: Towards a Good Notion of Categories of Logics. arXiv preprint, http://arxiv.org/abs/1404.3780 (2014) Mariano, H., Pinto, D.: Representation Theory of Logics: A Categorial Approach. arXiv preprint, http://arxiv.org/abs/1405.2429 (2014) Makkai, M., Paré, R.: Accessible Categories: The Foundations of Categorical Model Theory, Contemporary Mathematics 104. American Mathematical Society, Providence (1989) Patrícia, J.: Sistemas Dedutivos n\(\tilde{a}\)o algebriz\(\acute{a}\)veis. http://www2.mat.ua.pt/martins/documentos/didaticos/SistDednAlg (2012) Sernadas, C., Rasga, J., Carnielli, W.A.: Modulated fibring and the collapsing problem. J. Symb. Log. 67, 1541–1569 (2002). CLE e-Prints 1(2), 34 (2001) Sernadas, A., Sernadas, C., Caleiro, C.: Fibring of logics as a categorial construction. J. Log. Comput. 9(2), 149–179 (1999) Zanardo, A., Sernadas, A., Sernadas, C.: Fibring: completeness preservation. J. Symb. Log. 66(1), 414–439 (2001)