Note of the full generalized models of the extensions of a logic

• Autorzy: Albuquerque H. , Font J. M. , Jansana R.

Identyfikatory

DOI

10.4467/20842589RM.17.003.7141

• Języki publikacji: EN

Abstrakty

EN

In this short note we show that the full generalized models of any extension of a logic can be determined from the full generalized models of the base logic in a simple way. The result is a consequence of two central theorems of the theory of full generalized models of sentential logics. As applications we investigate when the full generalized models of an extension can also be full generalized models of the base logic, and we prove that each Suszko lter of a logic determines a Suszko lter of each of its extensions, also in a simple way.

Słowa kluczowe

EN

abstract algebraic logic; generalized model; full model; Suszko filter; strong version; truth-equational logic

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2017
• Tom: Vol. 52
• Strony: 57--68
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Albuquerque H.

• Departament de Filosofia, Universitat de Barcelona (UB) Montalegre 7, E-08001 Barcelona, Spain

autor

Font J. M.

• Josep Maria Font Departament de Matemátiques i Informática, Universitat de Barcelona (UB) Gran Via de les Corts Catalanes 585, E-08007 Barcelona, Spain

autor

Jansana R.

• Departament de Filosofia, Universitat de Barcelona (UB) Montalegre 7, E-08001 Barcelona, Spain

Bibliografia

• [1] H. Albuquerque, Operators and strong versions in abstract algebraic logic, Ph.D. Dissertation, University of Barcelona, March 2016. Available at http://hdl.handle.net/10803/394003.
• [2] H. Albuquerque, J.M. Font, and R. Jansana, Compatibility operators in abstract algebraic logic, The Journal of Symbolic Logic 81 (2016), 417-462.
• [3] H. Albuquerque, J.M. Font, and R. Jansana, The strong version of a sentential logic, Studia Logica 105 (2017), 703-760.
• [4] W.J. Blok and D. Pigozzi, Protoalgebraic logics, Studia Logica 45 (1986), 337-369.
• [5] W.J. Blok and D. Pigozzi, Algebraizable logics, vol. 396 of Memoirs of the American Mathematical Society. A.M.S., Providence, January 1989. Reprinted in the Classic Reprints series, Advanced Reasoning Forum, 2014.
• [6] J. Czelakowski, Protoalgebraic logics, vol. 10 of Trends in Logic - Studia Logica Library. Kluwer Academic Publishers, Dordrecht, 2001.
• [7] J.M. Font, Abstract Algebraic Logic - An Introductory Textbook, vol. 60 of Studies in Logic. College Publications, London, 2016.
• [8] J.M. Font and R. Jansana, Leibniz filters and the strong version of a protoalgebraic logic, Archive for Mathematical Logic 40 (2001), 437-465.
• [9] J.M. Font and R. Jansana, A general algebraic semantics for sentential logics. Second revised edition, vol. 7 of Lecture Notes in Logic. Association for Symbolic Logic, 2009. Cambridge University Press, 2017. Electronic version freely available through Project Euclid at http://projecteuclid.org/euclid.lnl/1235416965. First edition published by Springer-Verlag, 1996.
• [10] J.M. Font and R. Jansana, and D. Pigozzi, Fully adequate Gentzen systems and the deduction theorem, Reports on Mathematical Logic 35 (2001), 115-165.
• [11] J.M. Font and R. Jansana, and D. Pigozzi, On the closure properties of the class of full g-models of a deductive system, Studia Logica (Special issue in memory of Willem Blok) 83 (2006), 215-278.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).