Abstract
We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all \({\square}\)-free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula \({\phi}\) and a sublanguage L of the language of the formula, we can decide whether \({\phi}\) has a uniform interpolant with respect to L in K4. The \({\square}\)-free case is proved using a reduction to the Gödel Löb Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the μ-calculus.
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D’Agostino, G., Lenzi, G. Deciding the existence of uniform interpolants over transitive models. Arch. Math. Logic 50, 185–196 (2011). https://doi.org/10.1007/s00153-010-0208-5
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DOI: https://doi.org/10.1007/s00153-010-0208-5