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Logic and Logical Philosophy

Logics and operators
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Logics and operators

Authors

  • Janusz Czelakowski University of Opole

DOI:

https://doi.org/10.12775/LLP.1995.005

Abstract

Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of a logic C defines a class of abstract algebras. The members of the class are called Lindenbaum-Tarski algebras of the logic C. One may abstract from the origin of these algebras and examine them by means of purely algebraic methods.

Author Biography

Janusz Czelakowski, University of Opole

Institute of Mathematics

References

Blok, W. J. and Pigozzi, D. [1986] „Protoalgebraic logics”, Studia Logica 45, 337–369.

Blok, W. J. and Pigozzi, D. [1989] Algebraizable Logics, Memoirs of the Amer. Math. Soc. No. 396, Amer. Math. Soc., Providence.

Blok, W. J. and Pigozzi, D. [1992] „Algebraic semantics for universal Horn logic without quality”, [in:] Universal Algebra and Quasigroups, (eds. A. Romanowska and J. D. H. Smith), Heldermann Verlag, Berlin.

Czelakowski, J. [1981] „Equivalential logics: (I), (II)”, Studia Logica 40, 227–236, 335–372.

Czelakowski, J. [l992] Consequence Operations. Foundational Studies, Polish Academy of Sciences, Warsaw.

Czelakowski, J. [a] „Protoalgebraic logics”, to appear.

Czelakowski, J. and Dziobiak, W. [1991] „A deduction theorem scheme for deductive systems of propositional logics”, Studia Logica 50, Special Issue on Algebraic Logic (eds. W. J. Blok and Don Pigozzi), 385–390.

Herrmann, B. [1993] Equivalential Logics and Definability of Truth, Ph. Dissertation, Freie Universität Berlin.

Łoś, J. [1949] On Logical Matrices (Polish), Travaux de la Soci´ ete les Sciences et des Lettres de Wrocław, Seria B, Nr 19, Wrocław.

Pigozzi, D. [1991] „Fregean algebraic logic”, [in:] Algebraic Logic (Proc. Conf. Budapest, 8–14 August 1988), (eds. H. Andr´ eka, J. Monk and I. N´ emeti) , Colloq. Math. Soc. J. Bolyai, Vol. 54, North-Holland, Amsterdam, 473–502.

Prucnal, T. and Wroński, A. [1974] „An algebraic characterization of the notion of structural completeness”, Bulletin of the Section of Logic 3, Polish Academy of Sciences, 30–33.

Rasiowa H. [1974] An Algebraic Approach to Non-Classical Logics, PWN and North-Holland, Warsaw – Amsterdam.

Suszko, R. [1968] „Ontology in the Tractatus of L. Wittgenstein”, Notre Dame Journal of Formal Logic 9, 7–33.

Suszko, R. [1975] „Abolition of the Fregean axiom”, [in:] Logic Colloquium (Boston, Mass, 1972–1973), (ed. R. Parikh), Lecture Notes in Mathematics 453, Springer Verlag, Berlin, 169–236.

Wójcicki, R. [1973] „Matrix approach in sentential calculi”, Studia Logica 32, 7–37.

Wójcicki, R. [1988] Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer, Dordrecht.

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Published

2003-01-27

How to Cite

1.
CZELAKOWSKI, Janusz. Logics and operators. Logic and Logical Philosophy. Online. 27 January 2003. No. 3, pp. 87-100. [Accessed 1 July 2025]. DOI 10.12775/LLP.1995.005.
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No. 3 (1995)

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