Simplified Kripke style semantics for some very weak modal logics

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dc.contributor.author Pietruszczak, Andrzej
dc.date.accessioned 2013-10-17T17:05:59Z
dc.date.available 2013-10-17T17:05:59Z
dc.date.issued 2010-03-30
dc.identifier.citation Logic and Logical Philosophy, No. 3-4, Vol. 18, 2010, pp. 271-296
dc.identifier.issn 1425-3305
dc.identifier.other doi:10.12775/LLP.2009.013
dc.identifier.uri http://repozytorium.umk.pl/handle/item/725
dc.description.abstract In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form <w,A,V>, where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (i) for all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form <w,V> in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models.
dc.language.iso eng
dc.rights Attribution-NoDerivs 3.0 Poland
dc.rights info:eu-repo/semantics/openAccess
dc.rights.uri http://creativecommons.org/licenses/by-nd/3.0/pl/
dc.subject simplified Kripke style semantics
dc.subject very weak modal logics
dc.title Simplified Kripke style semantics for some very weak modal logics
dc.type info:eu-repo/semantics/article

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