Abstract
In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS's). This generalization allows us to define BRS's in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers.
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References
Alchourrón, C., P. Gärdenfors, D. Makinson, 'On the logic of theory change: Partial meet contraction and revision functions', The Journal of Symbolic Logic 50 (1985), 510-530.
Batens, D., 'A survey of inconsistency-adaptive logics', pp. 49-73 in Frontiers of Paraconsistent Logic (Proceedings of the I World Congress on Paraconsistency), D. Batens, C. Mortensen, G. Priest and J. P. Van Bendegem (eds.), Baldock: Research Studies Press, King's College Publications, Logic and Computation Series, 2000.
Batens, D., K. De Clercq, N. Kurtonina, 'Embedding and interpolation for some paralogics. The propositional case', Reports on Mathematical logic 33 (1999), 29-44.
Bell, J. L., A. B. Slomson, Models and Ultraproducts: an introduction, North Holland, 1971.
Béziau, J. Y., Recherches sur la Logique Universelle (Excessivité, Négation, Séquents), Ph.D. Thesis, Paris 7, 1994.
Brown, D. J., R. Suszko, 'Abstract Logics', Dissertationes Mathematicae 102 (1973), 9-41.
Carnielli, W. A., 'Methods of proof for relatedness and dependence logic', Reports on Mathematical Logic 21 (1987), 35-46.
Carnielli, W. A., 'Possible-translations semantics for paraconsistent logics', pp. 159-172 in Frontiers of Paraconsistent Logic (Proceedings of the I World Congress on Paraconsistency), D. Batens, C. Mortensen, G. Priest and J. P. Van Bendegem (eds.), Baldock: Research Studies Press, King's College Publications, Logic and Computation Series, 2000.
Carnielli, W. A., M. E. Coniglio, 'A categorial approach to the combination of logics', Manuscrito 22, vol. 2 (1999), 69-94.
Carnielli, W. A., I. M. L D'Ottaviano, 'Translations between logical systems: a manifesto', Logique et Analyse 157 (1997), 67-81.
Carnielli, W. A., M. Lima-Marques, 'Society semantics for multiple-valued logics', pp. 33-52 in Advances in Contemporary Logic and Computer Science (Proceedings of the XII EBL), W. A. Carnielli and I. M. L. D'Ottaviano (eds.), American Mathematical Society, Series Contemporary Mathematics, Volume 235, 1999.
Carnielli, W. A., J. Marcos, S. de Amo, 'Formal inconsistency and evolutionary databases', Logic and Logical Philosophy 8 (2001), 115-152. (Proceedings of the Stanisław Jaśkowski's Memorial Symposium, Toruń 1998.)
Chang, C. C., H. J. Keisler, Model Theory, North Holland, 1990.
Coniglio, M. E., W. A. Carnielli, 'A model theoretic approach to translations between logics', pp. 55-65 in Proceedings of 7th Workshop on Logic, Language, Information and Computation (WoLLIC 2000), Natal, 2000.
Coniglio, M. E., W. A. Carnielli, 'Holoi and mesoi', forthcoming.
da Silva, J. J., I. M. L. D'Ottaviano, A. M. Sette, 'Translations between logics', pp. 435-448 in Models, Algebras and Proofs, X. Caicedo and C. H. Montenegro (eds.), Marcel Dekker, 1999.
D'Ottaviano, I. M. L., N. C. A. da Costa, 'Sur un probléme de Jaśkowski', Comptes Rendus de l'Académie de Sciences de Paris (A-B) 270 (1970), 1349-1353.
Epstein, R. L., Propositional Logics: The Semantics Foundations of Logic, Wadsworth Thompson Learning, 2nd. edition, 2000.
Feitosa, H., Traduções Conservativas (Conservative Translations; in Portuguese), Ph.D. Thesis, State University of Campinas, Brazil, 1997.
Gabbay, D., 'Fibred semantics and the weaving of logics: Part I', The Journal of Symbolic Logic 61, vol. 4 (1996), 1057-1120.
Gabbay, D., O. Rodrigues, A. Russo, 'Revision by translation', pp. 3-32 in Information, Uncertainty and Fusion, Proceedings of IPMU 98, Bernadette Bouchon-Meunier, Roland R. Yager and Lotfi A. Zadeh (eds.), Kluwer Academic Publishers, 2000.
Gärdenfors, P., Knowledge in Flux: Modeling the Dynamics of Epistemic States, The MIT Press, 1988.
Restall, G., J. Slaney, 'Realistic belief revision', pp. 367-378 in WOCFAI 95, Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence, M. de Glas and Z. Pawlak (eds.), Angkor, 1995.
Schütte, K., Proof Theory, Springer-Verlag, 1977. (Translated from German original version, from 1960.)
Wassermann, R., Resource Bounded Belief Revision, Ph.D. Thesis, University of Amsterdam, ILLC Dissertation Series 2000-01, 1999.
Wójcicki, R., Theory of Logical Calculi, Synthese Library, Kluwer Academic Publishers, 1988.
Zanardo, A., A. Sernadas, C. Sernadas, 'Fibring: Completeness preservation', The Journal of Symbolic Logic 66, vol. 1 (2001), 414-439.
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Coniglio, M., Carnielli, W. Transfers between Logics and their Applications. Studia Logica 72, 367–400 (2002). https://doi.org/10.1023/A:1021845424153
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DOI: https://doi.org/10.1023/A:1021845424153