Some remarks on axiomatizing logical consequence operations

Jacek Malinowski



In this paper we investigate the relation between the axiomatization of a given logical consequence operation and axiom systems defining the class of algebras related to that consequence operation. We show examples which prove that, in general there are no natural relation between both ways of axiomatization.

Full Text:



Brown, D.J., and R. Suszko (1973), “Abstract logics”, Dissertationes Mathematica, vol. CII, PWN, Warszawa.

Burris, S., and R. Shankapanavar (1981), A Course in Universal Algebra, SpringerVerlag, New York—Heidelberg–Berlin.

Czelakowski, J. (1981), “Equivalential Logics. Part I”, Studia Logica 40 (3), 227–236; Part II Studia Logica 40 (4), 353–370.

Czelakowski, J. (2001), Protoalgebraic Logics, Trends in Logic, Studia Logica Library, Kluwer, Dordrecht.

Kalmbach, G. (1974), “Orthomodular logics”, Zeitschrift für Math. Logik 20, 395–406.

Kalmbach, G. (1983), Orthomodular Lattices, Academic Press, London.

Kotas, J. (1967), “An axiom system for modular logic”, Studia Logica 21, 17–38.

Malinowski, J. (1989), Equivalence in Intensional Logics, IFiS PAN, Warszawa.

Malinowski, J. (1990a), “Deduction theorem in quantum logic. Some negative results”, The Journal of Symbolic Logic 55 (2), 615–625.

Malinowski, J., (1990b), “Quasivarieties of modular ortholattices”, Bulletin of the Section of Logic 20 (3–4), 138–142.

Malinowski, J. (1992), “Strong versus weak quantum consequence operations”, Studia Logica 51 (1), 113–123.

Malinowski, J. (1999a), “Quantum experiments and the lattice of orthomodular logics”, Logique et Analyse 195–166, 35–47.

Malinowski, J. (1999b), “On the lattice of orthomodular logics”, Bulletin of the Section of Logic 28 (1), 11–16.

Porte, J. (1965), Recherches sur la théorie générale des systemes formels et sur les systemes connectives, Gauthier-Villars, Paris.

Rasiowa, H. (1974), An Algebraic approach to Non-Classical Logic, PWN-North-Holland, Warszawa-Amsterdam.

Shoesmith, D.J., and T.J. Smiley (1978), Multiple-Conclusion Logic, Cambridge University Press, Cambridge.

Wójcicki, R. (1984), Lectures on Propositional Calculi, Ossolineum, Łódź.

Wójcicki, R. (1987), Theory of Sentential Calculi. An Introduction, Reidel, Dordrecht.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism