Capítulos de libros
Two's Company: The Humbug Of Many Logical Values
Registro en:
3764372591; 9783764372590
Logica Universalis: Towards A General Theory Of Logic. Birkhäuser Verlag Basel • Boston • Berlin, v. , n. , p. 169 - 189, 2005.
10.1007/3-7643-7304-0_10
2-s2.0-84895255290
Autor
Caleiro C.
Carnielli W.
Coniglio M.
Marcos J.
Institución
Resumen
The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, there are but two logical values, true and false. As a matter of fact, a result by Wójcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more than two values? Because, we argue, one has to decide how to deal with bivalence and settle down the trade-off between logical 2-valuedness and truth-functionality, from a pragmatical standpoint. This paper will illustrate the ups and downs of a two-valued reduction of logic. Suszko's reductive result is quite non-constructive. We will exhibit here a way of effectively constructing the two-valued semantics of any logic that has a truth-functional finite-valued semantics and a sufficiently expressive language. From there, as we will indicate, one can easily go on to provide those logics with adequate canonical systems of sequents or tableaux. The algorithmic methods developed here can be generalized so as to apply to many non-finitely valued logics as well- or at least to those that admit of computable quasi tabular two-valued semantics, the so-called dyadic semantics.
169 189 Batens, D., A bridge between two-valued and many-valued semantic systems: N-tuple semantics (1982) Proceedings of the XII International Symposium on Multiple-valued Logic, pp. 318-322. , IEEE Computer Science Press Belnap, N.D., (1977) A Useful Four-valued Logic, pp. 8-37. , Modern Uses of Multiple-Valued Logic J. M. Dunn, ed., D. Reidel Publishing, Boston Beziau, J.-Y., Universal logic (1994) Logica'94, Proceedings of the VIII International Symposium, pp. 73-93. , T. Childers and O. Majers, eds., Czech Academy of Science, Prague, CZ Beziau, J.-Y., Recherches sur la logique abstraite: Les logiques normales (1998) Acta Universitatis Wratislaviensis No. 2023, Logika, 18, pp. 105-114 Beziau, J.-Y., Sequents and bivaluations (2001) Logique et Analyse (N. S.), 44 (176), pp. 373-394 Caleiro, C., Carnielli, W.A., Coniglio, M.E., Marcos, J., Dyadic Semantics for Many-valued Logics, , http://wslc.math.ist.utl.pt/ftp/pub/CaleiroC/03-CCCM-dyadic2.pdf Caleiro, C., Carnielli, W.A., Coniglio, M.E., Marcos, J., How Many Logical Values Are There? Dyadic Semantics for Many-valued Logics, , Preprint Caleiro, C., Carnielli, W.A., Coniglio, M.E., Marcos, J., Suszko's Thesis and Dyadic Semantics, , http://wslc.math.ist.utl.pt/ftp/pub/CaleiroC/03-CCCM-dyadic1.pdf Caleiro, C., Marcos, J., Non-truth-functional fibred semantics (2001) Proceedings of the International Conference on Artificial Intelligence (IC-AI'2001), pp. 841-847. , http://wslc.math.ist.utl.pt/ftp/pub/CaleiroC/01-CM-fiblog10.ps, held in Las Vegas, USA, June 2001 H. R. Arabnia, ed., vol. II, CSREA Press, Athens GA, USA Carnielli, W.A., Systematization of the finite many-valued logics through the method of tableaux (1987) The Journal of Symbolic Logic, 52, pp. 473-493 Carnielli, W.A., Lima-Marques, M., Society semantics for multiple-valued logics (1999) Advances in Contemporary Logic and Computer Science, 235, pp. 33-52. , W. A. Carnielli and I. M. L. D'Ottaviano, eds., Contemporary Mathematics Series, American Mathematical Society Carnielli, W.A., Marcos, J., Tableaux for logics of formal inconsistency (2001) Proceedings of the 2001 International Conference on Artificial Intelligence (IC-AI'2001), 2, pp. 848-852. , http://logica.rug.ac.be/~joao/Publications/Congresses/tableauxLFIs.pdf, held in Las Vegas, USA, June, H. R. Arabnia, ed., CSREA Press, Athens GA, USA, 2001 Carnielli, W.A., Marcos, J., De Amo, S., Formal inconsistency and evolutionary databases (2000) Logic and Logical Philosophy, 8, pp. 115-152. , http://www.cle.unicamp.br/e-prints/abstract6.htm Da Costa, N.C.A., Calculs propositionnels pour les systemes formels inconsistants (1963) Comptes Rendus d'Academie des Sciences de Paris, 257, pp. 3790-3792 Da Costa, N.C.A., Alves, E.H., A semantical analysis of the calculi Cn (1977) Notre Dame Journal of Formal Logic, 18, pp. 621-630 Da Costa, N.C.A., Beziau, J.-Y., Bueno, O.A.S., Malinowski and Suszko on many-valued logics: On the reduction of many-valuedness to two-valuedness (1996) Modern Logic, 3, pp. 272-299 Fernandez, V.L., Coniglio, M.E., Combining valuations with society semantics (2003) Journal of Applied Non-classical Logics, 13 (1), pp. 21-46. , http://www.cle.unicamp.br/e-prints/abstract11.html Malinowski, G., (1993) Many-valued Logics, , Oxford Logic Guides 25, Clarendon Press, Oxford Marcos, J., (1999) Possible-translations Semantics (in Portuguese), , http://www.cle.unicamp.br/students/J.Marcos, Master's thesis, State University of Campinas Brazil Scott, D., (1973) Background to Formalisation, pp. 244-273. , Truth, Syntax and Modality H. Leblanc, ed., North-Holland, Amsterdam Scott, D., Completeness and axiomatizability in many-valued logic (1971) Proceedings of Tarski Symposium (L. Henkin Et. Al., Ed.), Proceedings of Symposia in Pure Mathematics, 25, pp. 411-436. , Berkeley Sette, A.M., On the propositional calculus P1 (1973) Mathematica Japonicae, 18, pp. 173-180 Suszko, R., Abolition of the fregean axiom, logic colloquium: Symposium on logic held at Boston, 1972-73 (1972) Lecture Notes in Mathematics, 453, pp. 169-239. , R. Parikh, ed., Springer-Verlag Suszko, R., Remarks on Lukasiewicz's three-valued logic (1975) Bulletin of the Section of Logic, 4, pp. 87-90 Suszko, R., The Fregean axiom and Polish mathematical logic in the 1920's (1977) Studia Logica, 36, pp. 373-380 Tsuji, M., Many-valued logics and Suszko's Thesis revisited (1998) Studia Logica, 60 (2), pp. 299-309 Wojcicki, R., Logical matrices strongly adequate for structural sentential calculi (1969) Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Mathematiques, Astronomiques et Physiques, 17, pp. 333-335