Abstract
The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.
Similar content being viewed by others
References
Blok, W.J., and D. Pigozzi, ‘Protoalgebraic logics’, Studia Logica 45 (1986), 337-369.
Blok, W. J., and D. Pigozzi, Algebraizable Logics, Memoirs of the American Mathematical Society, No. 396, Amer. Math. Soc., Providence, 1989.
Blok, W. J., and D. Pigozzi, ‘Algebraic semantics for universal Horn logic without equality’, in A. Romanowska and J.D.H. Smith, (eds.), Universal Algebra and Quasigroups, Heldermann Verlag, Berlin, 1992, pp 1-56.
Brown, D. J. and R. Suszko, ‘Abstract Logics’, Dissertationes Mathematicae 102, Polish Scientific Publishers (PWN), Warsaw, 1973.
Czelakowski, J., Model-Theoretic Methods in the Methodology of Propositional Calculi, Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw, 1980.
Czelakowski, J., Consequence Operations. Foundational Studies, Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw, 1992.
Czelakowski, J., Protoalgebraic Logics, vol. 10 of Trends in Logic, Studia Logica Library, Kluwer, Dordrecht, 2001.
Czelakowski, J., and W. Dziobiak, ‘A deduction theorem schema for deductive systems of propositional logics’, in W. Blok and D. Pigozzi, (eds.), Special Issue on Algebraic Logic, Studia Logica 50 (1991), 385-390.
Czelakowski, J., and R. Jansana, ‘Weakly algebraizable logics’, Journal of Symbolic Logic 64 (2000), 641-668.
Czelakowski, J., and D. Pigozzi, ‘Amalgamation and interpolation in abstract algebraic logic’, in X. Caicedo and C. H. Montenegro, (eds.), Models, algebras and proofs, no. 203, in Lecture Notes in Pure and Applied Mathematics Series, Marcel Dekker, Inc., New York and Basel, 1999, pp. 187-265.
Dyrda, K., and T. Prucnal, ‘On finitely based consequence determined by a distributive lattice’, Bulletin of the Section of Logic, Polish Academy of Sciences, 9 (1980), 60-66.
Font, J. M., F. GuzmÁn, and V. VerdÚ, ‘Characterization of the reduced matrices for the {⋀, ⋁}-fragment of classical logic’, Bulletin of the Section of Logic, Polish Academy of Sciences, 20 (1991), 124-128.
Font, J. M., and V. VerdÚ, ‘Algebraic logic for classical conjunct ion and disjunction’, in W. J. Blok and D. Pigozzi, (eds.), Special Issue on Algebraic Logic, Studia Logica 50 (1991), 391-419.
Font, J. M. and V. VerdÚ, ‘Algebraic logic for some non-protoalgebraizable logics’, in H. Andréka, J. D. Monk, and I. Németi, (eds.), Algebraic logic, vol. 54 of Colloquia Math. Soc. János Bolyai. North-Holland, Amsterdam, 1991, pp. 183-188.
Font, J. M. and R. Jansana, A General Algebraic Semantics for Sentential Logics, Lecture Notes in Logic 7, Springer Verlag, Berlin-Heidelberg, 1996.
Frege, G., ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und philosophische Kritik, 1892, 25-50. English translation by M. Black as On sense and reference in: P. T. Geach and M. Black, (eds.), “Translations from the Philosophical Writings of Gottlob Frege”, Oxford 1952, pp 56–78.
Font, J. M. and G. RodrÍguez, ‘Algebraic study of two deductive systems of relevance logic’, Notre Dame Journal of Formal Logic 35 (1994), 369-397.
Herrmann, B., ‘Algebraizability and Beth's Theorem for equivalential logics’, Bulletin of the Section of Logic, University of Łódź, 22 (1993), 85-88.
Herrmann, B., Equivalential Logics and Definability of Truth, Ph. D. Dissertation, Freie Universität Berlin, 1993.
ŁoŚ, J., ‘On logical matrices’ (in Polish), Travaux de la Sociéte des Sciences et des Lettres de Wrocław, Seria B, Nr 19, Wrocław, 1949.
ŁoŚ, J. and R. Suszko, ‘Remarks on sentential logics’, Indagationes Mathematicae 20 (1958), 177-83.
Malinowski, G., Topics in the Theory of Strengthenings of Sentential Calculi, Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw, 1979.
Rautenberg, W., ‘2-element matrices’, Studia Logica 40 (1981), 315-353.
Rautenberg, W., ‘Consequence relations of 2-element algebras’, in: Foundations of Logic and Linguistics (eds. G. Dorn and P. Weingartner), Plenum Press, New York-London, 1985, pp. 3-22.
Rebagliato, J. and V. VerdÚ, ‘On the algebraization of some Gentzen systems’, Fundamenta Informaticae, Special Issue on Algebra and Logic in Computer Science 18 (1993), 319-338.
Shoesmith, D. J. and T. J. Smiley, ‘Deducibility and many-valuedness’, Journal of Symbolic Logic 36 (1971), 610-622.
Suszko, R., ‘Ontology in the Tractatus of L. Wittgenstein’, Notre Dame Journal of Formal Logic 9 (1968), 7-33.
Suszko, R., ‘Abolition of the Fregean axiom’, in: Logic Colloquium (Boston, Mass., 1972–73)”, (ed. R. Parikh), Lecture Notes in Mathematics 453, Springer Verlag, Berlin, 1975, pp 169-236.
Suszko, R., ‘Congruences in sentential calculi’ (Polish), in: A Report from the Autumn School of Logic, Miedzygórze, November 21–29, 1977, Poland, mimeographed notes edited and compiled by J. Zygmunt and G. Malinowski. Restricted distribution.
Tarski, A., Logic, Semantics, Metamathematics. Papers from 1923 to 1938, Clarendon Press, Oxford, 1956.
WÓjcicki, R., ‘Referential matrix semantics for propositional calculi’, Bulletin of the Section of Logic, Polish Academy of Sciences, 8 (1979), 170-176.
WÓjcicki, R., Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer Academic Publishers, Dordrecht-Boston-London, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Czelakowski, J. The Suszko Operator. Part I.. Studia Logica 74, 181–231 (2003). https://doi.org/10.1023/A:1024678007488
Issue Date:
DOI: https://doi.org/10.1023/A:1024678007488