Simplified Kripke style semantics for modal logics K45, KB4 and KD45

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dc.contributor.author Pietruszczak, Andrzej
dc.date.accessioned 2024-02-16T12:44:49Z
dc.date.available 2024-02-16T12:44:49Z
dc.date.issued 2009
dc.identifier.citation Bulletin of the Section of Logic, vol. 38 (3/4), 2009, pp. 163–172.
dc.identifier.issn 0138-0680
dc.identifier.uri http://repozytorium.umk.pl/handle/item/6988
dc.description.abstract In this paper, we show that logics K45, KB4 (= KB5) and KD45 are determined by some classes of simplified Kripke frames without binary accessibility relations between possible worlds. These frames are ordered pairs of sets <W,A>, where W is a non-empty set of worlds and A\subseteq W (a~set of common alternatives to all worlds in W). From a frame <W,A> we can construct models of the form <W,A,V>, where V is a standard valuation which to formulae and words assigns truth-values with respect to the set A. For K45 we use the class of all simplified frames; for KB4 we have the case that A=0 or A=W; and for KD45 we use frames with A\ne 0. Moreover, to each of these logics we also assign a suitable class of finite Euclidean relational frames which satisfy conditions for normal extensions of K5 presented by Nagle.
dc.description.sponsorship Uniwersytet Mikołaja Kopernika w Toruniu
dc.language.iso eng
dc.publisher Lodz University Press
dc.rights Attribution-NonCommercial-NoDerivs 3.0 Poland
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/pl/
dc.subject simplified Kripke style semantics
dc.subject normal modal logics K45, KB4 and KD45
dc.title Simplified Kripke style semantics for modal logics K45, KB4 and KD45
dc.type info:eu-repo/semantics/article

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