Logic and Logical Philosophy 18 (3-4):271-296 (2009)

Authors
Andrzej Pietruszczak
Nicolaus Copernicus University
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 , 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 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
Keywords very weak modal logics  simplified Kripke style semantics
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Reprint years 2010
DOI 10.12775/LLP.2009.013
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References found in this work BETA

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Citations of this work BETA

Semantical Investigations on Some Weak Modal Logics. Part II.Andrzej Pietruszczak - 2012 - Bulletin of the Section of Logic 41 (3/4):109-130.

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