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Forthcoming papers


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About the Unification Type of Fusions of Modal Logics

Philippe Balbiani, Çi˘gdem Gencer and Maryam Rostamigiv

In a modal logic {bf L}, a unifier of a formula $varphi$ is a substitution $sigma$ such that $sigm(varphi)$ is in {bf 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. The fusion ${bf L}_1 otimes {bf L}_2$ of modal logics ${bf L}_1$ and ${bf L}_2$ respectively based on the modal connectives $square_1$ and $square_2$ is the least modal logic based on these modal connectives and containing both ${bf L}_1$ and ${bf L}_2$. In this paper, we prove that if $L_1otimes L_2$ is unitary then ${bf L}_1$ and ${bf L}_2$ are unitary and if ${bf L}_1 otimes {bf L}_2$ is finitary then ${bf L}_1$ and ${bf L}_2$ are either unitary, or finitary. We also prove that the fusion<
>of arbitrary consistent extensions of {bf S}5 is nullary when these extensions are different from {bf Triv}.






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