The Shortest Axioms of Łukasiewicz’s Modal Logic

  • Zdzisław Dywan The John Paul II Catholic University of Lublin, Faculty of Philosophy
DOI: https://doi.org/10.18290/rf.2016.64.2-1
Keywords: axiomatization; modal logic

Abstract

We show that the formula CLpEqLq axiomatizes Łukasiewicz’s modal logic and that there exists no shorter axiom for it.

References

Lemmon, E[dward] J. „Algebraic semantics for modal logics II”. The Journal of Symbolic Logic 31 (1996), 2:191–218.

Łukasiewicz, Jan. „A system of modal logic”. The Journal of Computing Systems 1 (1953), 3: 111–149.

Tkaczyk, Marcin. „On axiomatization of Łukasiewicz’s four-valued modal logic”. Logic and Logical Philosophy 20 (2011), 3: 215–232.

Published
2020-06-15
Issue
Vol 64 No 2 (2016)
Section
Articles

Copyright (c) 2016 Roczniki Filozoficzne

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