7 research outputs found

    A Global Glance On Categories In Logic

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    We explore the possibility and some potential payoffs of using the theory of accessible categories in the study of categories of logics. We illustrate this by two case studies focusing on the category of finitary structural logics and its subcategory of algebraizable logics. © Birkhäuser Verlag Basel/Switzerland 2007.11339Adámek, J., Rosicḱy, J., Locally Presentable and Accessible Categories (1994) Lecture Notes Series of the LMS, 189. , Cambridge University Press, CambridgeAgeron, P., Limites projectives conditionnelles dans les catégories accessibles (1997) Diagrammes, 38, pp. 3-18Ageron, P., Sur les catégories accessibles multicomplétes (2002) Journal of Pure and Applied Algebra, 170, pp. 109-114Arndt, P., Freire, R.A., Luciano, O.O., Mariano, H.L., Fibring and Sheaves (2005) Proceedings of IICAI-05, Special Session at the 2nd Indian International Conference on Arti.cial Intelligence, , PuneP. Arndt, R.A.Freire, O.O. Luciano, H.L. Mariano, On the category of algebraizable logics, CLE e-Prints 6 n. 1, (2006), available at: http://www.cle.-nicamp.br/e-prints/vol_6,n_1,2006.htmlBaez, J., Dolan, J., Higherdimensional algebra III: N-categories and the algebra of opetopes (1998) Adv. Math, 135 (2), pp. 145-206. , http://math.ucr.edu/home/baez, also available atJ.-Y. Béziau, From Consequence Operator to Universal Logic: A Survey of General Abstract Logic in Logica Universalis: Towards a General Theory of Logic (J.-Y. Beziau, ed.), Birkhaeuser, Basel, 2005Blok, W.J., Pigozzi, D., (1989) Algebraizable Logics, , Memoirs of the AMS 396, American Mathematical Society, ProvidenceBorceux, F., (1994) Handbook of Categorical Algebra 2 - Categories and Structures, , Encyclopedia of Mathematics and its Applications 51, Cambridge University Press, CambridgeBueno, J., (2004) Semântica Algébrica de Traduçcoes Possíveis, , Dissertation in Portuguese, Universidade de Campinas, CampinasBueno, J., Coniglio, M.E., Carnielli, W.A., Finite Algebraizability via Possible- Translations Semantics (2004) Proceedings of CombLog'04 - Workshop on Combination of Logics: Theory and Applications, Departamento de Matemática, , Instituto Superior Técnico, LisboaJ. Bueno-Soler, W.A. Carnielli, Possible-translations algebraization for paraconsistent logics, Bulletin of the Section of Logic, University of Lodz, Poland, 34, n. 2, 2005, pp. 77-92. CLE e-Prints 5 n. 6, (2005). available at: http://www.cle.unicamp.br/e-prints/ vol_5,n_6,2005.htmlBueno-Soler, J., Coniglio, M.E., Carnielli, W.A., (2006) Possible-Translations Algebraizability, Handbook of Paraconsistency, , J.-Y. Beziau and W.A. Carnielli, and D.M. Gabbay eds, North-Holland, AmsterdamBurroni, E., Burroni, A., (1992) Structures Algébriques: Theme et Variations, , Cahiers de Topologie et Geometrie Di.erentielle Categoriques, XXXIII:207-216Coniglio, M., (2005) The Meta-Fibring environment: Preservation of meta-properties by fibring, CLE e-Prints, 5 (4). , http://www.cle.unicamp.br/e-prints, available atV. L. Fernández, M. E. Coniglio, Fibring algebraizable consequence systems, Proceedings of CombLog'04 - Workshop on Combination of Logics: Theory and Applications, pp. 79-86 (W.A. Carnielli, F. M. Dionísio, and P. Mateus, eds.), Departamento de Matemática, Instituto Superior Técnico, Lisboa 2004Gabbay, D., Fibred semantics and the weaving of logics: Part 1 (1996) Journal of Symbolic Logic, 61 (4), pp. 1057-1120P. Gabriel, F. Ulmer, Lokal präsentierbare Kategorien, Springer Lecture Notes in Mathematics 221, Springer, Berlin 1971Jacobs, B., (1999) Categorical Logic and Type Theory, , North Holland, AmsterdamLoś, J., Suszko, R., Remarks on sentential logics (1958) Series A, 61, pp. 177-183. , Proceedings Koninkliske Nederlandse Akademie van WetenschappenMakkai, M., Paré, R., Accessible Categories: The Foundations of Categorical Model Theory (1989) Contemporary Mathematics, 104. , American Mathematical Society, ProvidenceMariano, H.L., (1997) Categorias Modeláveis, , Dissertation in Portuguese, Universidade de São Paulo, São PauloSernadas, C., Rasga, J., Carnielli, W.A., Modulated fibring and the collapsing problem (2002) Journal of Symbolic Logic, 67 (4), pp. 1541-1569Sernadas, A., Sernadas, C., Caleiro, C., Fibring of logics a categorial construction (1999) Journal of logic and computation, 9 (2), pp. 149-17

    A Global Glance on Categories in Logic

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