Skip Navigation


Logic Journal of IGPL Advance Access originally published online on September 26, 2007
Logic Journal of IGPL 2007 15(5-6):475-501; doi:10.1093/jigpal/jzm036
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Fernández, V. L.
Right arrow Articles by Coniglio, M. E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Fibring in the Leibniz Hierarchy

Víctor L. Fernández

Basic Sciences Institute (Mathematical Area), Philosophy College, National University of San Juan (UNSJ), San Juan, Argentina. E-mail: vlfernan{at}ffha.unsj.edu.ar

Marcelo E. Coniglio

Institute of Philosophy and Human Sciences (IFCH) and Centre for Logic, Epistemology and The History of Science (CLE), State University of Campinas (UNICAMP), Campinas, SP, Brazil. Security and Quantum Information Group (SQIG), Instituto de Telecomunicações (IT), Lisbon, Portugal. E-mail: coniglio{at}cle.unicamp.br

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.

Key Words: abstract algebraic logic • fibring of logics • categorial combination of logics.

Received for publication 20 October 2006.

References

  1. Blok W, Pigozzi. Abstract algebraic logic and the deduction theorem. The Bulletin of Symbolic Logic. To appear.

  2. Blok W, Pigozzi D. Protoalgebraic logics. Studia Logica (1986) 45:337–369.[CrossRef]

  3. Blok W, Pigozzi D. Algebraizable Logics, volume 77 (396) of Memoirs of the American Mathematical Society. (1989) AMS, Providence, Rhode Island.

  4. Bueno J. Semântica Algébrica de Traduções Possíveis (Possible – Translations Algebraic Semantics, in Portuguese). In: Masters Thesis (2004) Brazil: IFCH – State University of Campinas.

  5. Bueno-Soler J, Coniglio ME, Carnielli W. Possible-translations algebraizability. In: Handbook of Paraconsistency—Béziau J-Y, Carnielli W, Gabbay D, eds. (2008) Elsevier. To appear.

  6. Caleiro C. Combining Logics. In: PhD thesis (2000) Lisbon: IST.

  7. Caleiro C, Carnielli WA, Rasga J, Sernadas C. Fibring of logics as a universal construction. In: Volume 13 of Handbook of Philosophical Logic, 2nd Edition (2005) Springer. 123–187.

  8. Carnielli W. Many–valued logics and plausible reasoning. In: Proceedings of the XX International Congress on Many–Valued Logics, University of Charlotte, USA (1990) IEEE Computer Society. 328–335.

  9. Carnielli WA, Coniglio ME, Gabbay D, Gouveia P, Sernadas C. Analysis and Synthesis of Logics. In: Volume 35 of Applied Logic Series (2008) Springer. In print.

  10. Coniglio ME. Recovering a logic from its fragments by meta-fibring. (2007) 1(2). Logica Universalis. 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.htm.

  11. Coniglio ME, Fernández VL. Plain fibring and direct union of logics with matrix semantics. Prasad B, ed. (2005) Proceedings of the 2nd Indian International Conference on Artificial Intelligence (IICAI 2005), Pune, India. IICAI. Preliminary version available at CLE e-Prints, Vol. 5(10), 2005. URL = http://www.cle.unicamp.br/e-prints/vol_5,n_10,2005.html.

  12. Czelakowski J. Equivalential logics (I) and (II). Studia Logica (1981) 40:227–236. 335–372.[CrossRef]

  13. Czelakowski J. Protoalgebraic Logics (2001) Dordrecht: Kluwer Academic Publishers.

  14. D'Ottaviano IML, da Costa NCA. Sur un probléme de Jaskowski. Comptes Rendus de l'Academie de Sciences de Paris (A-B) (1970) 270:1349–1353.

  15. Fernández VL. Fibrilaçáo de Lógicas na Hierarquia de Leibniz (Fibring Logics within the Leibniz Hierarchy, in Portuguese). In: PhD thesis (2005) Brazil: IFCH – State University of Campinas.

  16. Fernández VL, Coniglio ME. Fibring algebraizable consequence systems, 2004. Proceedings of CombLog'04 - Workshop on Combination of Logics: Theory and Applications. 93–98. (W. A. Carnielli, F. M. Dioní sio, P. Mateus eds.);.

  17. Font JM, Jansana R, Pigozzi D. A survey of abstract algebraic logic. Studia Logica (Special Issue on Abstract Algebraic Logic II) (2003) 74(1–2):13–97. A preliminary version appeared as Preprint 329, Mathematics Preprint Series, Universitat de Barcelona.

  18. Gabbay D. Fibred semantics and the weaving of logics: Part 1. Journal of Symbolic Logic (1996) 61(4):1057–1120.[CrossRef][ISI]

  19. Gabbay D. Fibring Logics (1999) Oxford: Clarendon Press.

  20. Herrmann B. Characterizing equivalential and algebraizable logics by the Leibniz operator. Studia Logica (1997) 58:305–323.[CrossRef]

  21. Jánossy A, Kurucz A, Eiben Á. Combining algebraizable logics. The Notre Dame Journal of Formal Logic (1996) 37(2):366–380.[CrossRef]

  22. Lewin R, Mikenberg I, Schwarze MG. Algebraization of paraconsistent logic P1. The Journal of Non-Classical Logics (1990) 7(1/2):79–88.

  23. Los J, Suszko R. Remarks on sentential logics. Indagationes Mathematicae (1958) 20:177–183.

  24. Prucnal T, Wrónski A. An algebraic characterization of the notion of structural completeness. Bulletin of the Section of Logic (1974) 3:30–33.

  25. Sernadas A, Sernadas C, Caleiro C. Fibring of logics as a categorial construction. Journal of Logic and Computation (1999) 9(2):149–179.[Abstract/Free Full Text]

  26. Sette A. On the propositional calculus P1. Mathematica Japonicae (1973) 18:173–180.

  27. van Benthem J, Pearce D. A mathematical characterization of interpretation between theories. Studia Logica (1984) 43:295–303.[CrossRef]

  28. Voutsadakis G. Categorical Abstract Algebraic Logic: Categorical Algebraization of Equational Logic. Logic Journal of the IGPL (2004) 12(4):313–333.

  29. Voutsadakis G. Categorical Abstract Algebraic Logic: Protoalgebricity and Leibniz Theory Systems. Scientiae Mathematicae Japonicae (2004) 62(1):109–117.

  30. Wójcicki R. Theory of Logical Calculi (1988) Synthese Library. Kluwer Academic Publishers.

  31. Zanardo A, Sernadas A, Sernadas C. Fibring: Completeness preservation. The Journal of Symbolic Logic (2001) 66(1):414–439.[CrossRef]


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Fernández, V. L.
Right arrow Articles by Coniglio, M. E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?