Some Additional Axioms for T-normal Logics. Defining K45, KB4, KD45 and S5 without Using Modal Rules
DOI:
https://doi.org/10.18778/0138-0680.2024.12Keywords:
modal logic, t-normal logics, Kripke-style semanticsAbstract
The paper studies extensions of t-normal logics S0.5o and S0.5 obtained by means of some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.
References
B. F. Chellas, Modal Logic: An Introduction, Cambridge University Press, Cambridge (1980), DOI: https://doi.org/10.1017/CBO9780511621192 DOI: https://doi.org/10.1017/CBO9780511621192
G. E. Hughes, M. J. Cresswell, A New Introduction to Modal Logic, Routledge, London and New York (1966).
E. J. Lemmon, New foundations for Lewis modal systems, The Journal of Symbolic Logic, vol. 22(2) (1957), pp. 176–186, DOI: https://doi.org/10.2307/29641792 DOI: https://doi.org/10.2307/2964179
A. Pietruszczak, Simplified Kripke style semantics for modal logics K45, KB4 and KD45, Bulletin of the Section of Logic, vol. 38(3/4) (2009), pp. 163–171.
A. Pietruszczak, Simplified Kripke style semantics for some very weak modal logics, Logic and Logical Philosophy, vol. 18(3–4) (2009), pp. 271–296, DOI: https://doi.org/10.12775/LLP.2009.013 DOI: https://doi.org/10.12775/LLP.2009.013
A. Pietruszczak, Semantical investigations on some weak modal logics. Part I, Bulletin of the Section of Logic, vol. 41(1/2) (2012), pp. 33–50.
A. Pietruszczak, Semantical investigations on some weak modal logics. Part II, Bulletin of the Section of Logic, vol. 41(3/4) (2012), pp. 109–130.
R. Routley, Decision procedure and semantics for C1, E1 and S0.5º, Logique et Analyse, vol. 11(44) (1968), pp. 468–471.
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