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About the unification type of fusions of modal logics

Abstract : In a modal logic L, a unifier of a formula ϕ is a substitution σ such that σ(ϕ) is in L. When unifiable formulas have no minimal complete sets of unifiers, they are nullary. Otherwise, they are either infinitary, or finitary, or unitary depending on the cardinality of their minimal complete sets of unifiers. In this paper, we prove that if the fusion L 1 ⊗ L 2 is unitary then L 1 and L 2 are unitary and if the fusion L 1 ⊗ L 2 is finitary then L 1 and L 2 are either unitary, or finitary. We also prove that the fusion of arbitrary consistent extensions of S5 is nullary when these extensions are different from Triv.
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Submitted on : Friday, September 11, 2020 - 12:12:53 PM
Last modification on : Tuesday, October 19, 2021 - 2:23:37 PM
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  • HAL Id : hal-02936464, version 1

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Philippe Balbiani, Cigdem Gencer, Maryam Rostamigiv. About the unification type of fusions of modal logics. Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications, College Publications, In press. ⟨hal-02936464⟩

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