Artículos de revistas
Modal Extensions Of Sub-classical Logics For Recovering Classical Logic
Registro en:
Logica Universalis. , v. 7, n. 1, p. 71 - 86, 2013.
16618297
10.1007/s11787-012-0076-3
2-s2.0-84874662369
Autor
Coniglio M.E.
Peron N.M.
Institución
Resumen
In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0. 50 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as "is provable in classical logic". This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems. © 2013 Springer Basel. 7 1 71 86 Batens, D., Paraconsistent extensional propositional logics (1980) Logique et Analyse 90/91, pp. 195-234 Batens, D., de Clercq, K., Kurtonina, N., Embedding and interpolation for some paralogics (1999) The Propositional Case. Rep. Math. Log., 33, pp. 29-44 Boolos, G., (1993) The Logic of Provability, , Cambridge: Cambridge University Press Carnielli, W.A., Coniglio, M.E., Marcos, J., Logics of Formal Inconsistency (2007) Handbook of Philosophical Logic, 14, pp. 1-93. , In: Gabbay, D., Guenthner, F. (eds.), 2nd edn., Springer, Berlin Carnielli, W.A., Pizzi, C., (2008) Modalities and Multimodalities, Vol. 12 of Logic, Epistemology, and the Unity of Science, , Berlin: Springer Coniglio, M.E., Logics of deontic inconsistency (2009) Revista Brasileira de Filosofia, 233, pp. 162-186. , http://www.cle.unicamp.br/e-prints/vol_7,n_4,2007.html, A preliminary version was published in CLE e-Prints 7(4), 2007 Available at Creswell, M.J., The completeness of S0. 5 (1966) Logique et Analyse, 34, pp. 262-266 Creswell, M.J., Hughes, G.E., (1968) An Introduction to Modal Logic, , Routledge, London and New York Glivenko, V., Sur quelques points de la logique de M. Brouwer. Academie Royale de Belgique (1929) Bulletins de la Classe des Sciences, 5 (15), pp. 183-188 Gödel, K., Eine Intepretation des intionistischen Aussagenkalk̈ul (1933) Ergebnisse eines Mathematischen Kolloquiums, 4, pp. 6-7. , English translation in Gödel (1986) pp. 300-303 Gödel, K., (1986) Kurt Gödel, Collected Works: Publications 1929-1936, , Cary: Oxford University Press Kripke, S., Semantical Analysis of Modal Logic I (1963) Normal Proposicional Calculi. Zeitschrift Fur Mathematische Logik Und Grundlagen Der Mathematik, 9, pp. 67-96 Kripke, S., Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi (1965) The Theory of Models (Proceedings of the 1963 International Symposium at Berkeley), pp. 206-220. , In: Addison, J. W., Henkin, L., Tarski, A. (eds.), Amsterdam, North-Holland Lemmon, E.J., New Foundations for Lewis Modal Systems (1957) J. Symb. Logic, 22 (2), pp. 176-186 Lemmon, E.J., Algebraic semantics for modal logics I (1966) J. Symb. Logic, 31 (1), pp. 44-65 Lewis, C.I., Langford, C.H., (1932) Symbolic Logic, , Century Segerberg, K.K., (1971) An Essay in Classical Modal Logic, , PhD thesis, Stanford University Shoenfield, J.R., (1967) Mathematical Logic, , Addison-Wesley, Reading Wójcicki, R., (1984) Lectures on Propositional Calculi, , http://www.ifispan.waw.pl/studialogica/wojcicki/papers.html, Ossolineum, Wroclaw, Available at