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Pré-Publication, Document De Travail Année : 2021

About the unification type of modal logic K5 and its extensions

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Introduction : We prove that all extensions of K45 have projective unification and K5 and some of its extensions are of unification type 1. The breakdown of the paper is as follows. Firstly, we prove in Proposition 9 that if L contains K45 then every formula has extension property in L. Secondly, generalizing some results obtained in [6], we prove in Proposition 13 that if L contains K5 then every L-unifiable formula is L-filtering. Thirdly, imitating arguments used in [18, 19], we prove in Proposition 20 that if L contains K5 then every formula having extension property in L is L-projective. Fourthly, we prove in Proposition 21 that if L contains K5 and L is global1 then for all substitutions σ, every formula L-unified by σ is implied by an L-projective formula based on the variables of the given formula and having σ as one of its L-unifiers.
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hal-03252589 , version 1 (07-06-2021)

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  • HAL Id : hal-03252589 , version 1

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Majid Alizadeh, Mohammad Ardeshir, Philippe Balbiani, Mojtaba Mojtahedi. About the unification type of modal logic K5 and its extensions. 2021. ⟨hal-03252589⟩
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