Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-23T12:48:09.962Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly algebraizable logics

Published online by Cambridge University Press:  12 March 2014

Janusz Czelakowski  and
Ramon Jansana
Janusz Czelakowski
Affiliation:
Department of Mathematics, Opole University, Poland, E-mail: jczel@sparc-1.uni.opole.pl
Ramon Jansana
Affiliation:
Department of Logic, History and Philosophy of Science, Universität de Barcelona, E-mail: jansana@mat.ub.es
Get access Rights & Permissions [Opens in a new window]

Abstract

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

Keywords

Weakly algebraizable logicsprotoalgebraic logicsalgebraizable logicsLeibniz congruence
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 641 - 668
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Agliano, P. and Ursini, A., On subtractive varieties II: general properties, Algebra Universalis, vol. 36 (1996), pp. 222–259.CrossRefGoogle Scholar
[2]Agliano, P. and Ursini, A., On subtractive varieties III: from ideals to congruences, preprint, 1997.CrossRefGoogle Scholar
[3]Beran, L., Orthomodular lattices, an algebraic approach, Academia, Prague, 1984.Google Scholar
[4]Blok, W. and Pigozzi, D., Protoalgebraic logics, Studia Logica, vol. 45 (1986), pp. 337–369.CrossRefGoogle Scholar
[5]Blok, W. and Pigozzi, D., Algebraic semantics for Universal Horn Logic without equality, Universal algebra and quasigroup theory (Romanowska, A. and Smith, J.D.H., editors), Heldermann, Berlin, 1992.Google Scholar
[6]Blok, W. and Pigozzi, D., Algebraizable logics, Memoirs of the American Mathematical Society, vol. 396, January 1989.Google Scholar
[7]Blok, W. and Raftery, J.G., Ideals in quasivarieties of algebras, Models, algebras, and proofs (Caicedo, X. and Montenegro, C.H., editors), Lecture Notes in Pure and Applied Mathematics, vol. 203, Marcel Dekker, New York, 1999, pp. 167–186.Google Scholar
[8]Czelakowski, J., Reduced products of logical matrices, Studia Logica, vol. 39 (1980), pp. 19–43.CrossRefGoogle Scholar
[9]Czelakowski, J., Consequence operations, foundational studies, (Report of the research project “Theories, Models, Cognitive Schemas”), Institute of Philosophy and Sociology, Polish Academy of Sciences, Warszawa, 1992.Google Scholar
[10]Czelakowski, J., Protoalgebraic logics, manuscript, 1994.Google Scholar
[11]Font, J.M. and Jansana, R., A general algebraic semantics for sentential logics, Lecture Notes in Logic, vol. 7, Springer, Berlin, 1996.CrossRefGoogle Scholar
[12]Herrmann, B., Equivalential logics and definability of truth, Ph.D. thesis, Freie Universität Berlin, 1993.Google Scholar
[13]Herrmann, B., Equivalential and algebraizable logics, Studia Logica, vol. 57 (1996), pp. 419–436.CrossRefGoogle Scholar
[14]Herrmann, B., Characterizing equivalential and algebraizable logics by the Leibniz operator, Studia Logica, vol. 58 (1997), pp. 305–323.CrossRefGoogle Scholar
[15]Malinowski, J., The deduction theorem for quantum logic, some negative results, this Journal, vol. 55 (1990), pp. 615–625.Google Scholar
[16]Prucnal, T. and Wroński, A., An algebraic characterization of the notion of structural completeness, Bulletin of the Section of Logic, Polish Academy of Sciences, vol. 3 (1974), pp. 30–33.Google Scholar
[17]Rasiowa, H., An algebraic approach to non-classical logics, North-Holland, Amsterdam, 1974.Google Scholar
[18]Ursini, A., Sulle varietà di algebre con una buona teoria degli ideale, Bolletino U.M.I., vol. 6 (4) (1972), pp. 90–95.Google Scholar
[19]Ursini, A., On subtractive varieties I, Algebra Universalis, vol. 31 (1994), pp. 204–222.CrossRefGoogle Scholar