Extensions of K5: Proof Theory and Uniform Lyndon Interpolation

Extensions of K5: Proof Theory and Uniform Lyndon Interpolation

We introduce a Gentzen-style framework, called layered sequent calculi, for modal logic K5 and its extensions KD5, K45, KD45, KB5, and S5 with the goal to investigate the uniform Lyndon interpolation property (ULIP), which implies both the uniform interpolation property and the Lyndon interpolation...

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Veröffentlicht in:arXiv.org 2023-07
Hauptverfasser: van der Giessen, Iris, Jalali, Raheleh, Kuznets, Roman
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Computer Science - Logic in Computer Science
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Mathematics - Logic
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description We introduce a Gentzen-style framework, called layered sequent calculi, for modal logic K5 and its extensions KD5, K45, KD45, KB5, and S5 with the goal to investigate the uniform Lyndon interpolation property (ULIP), which implies both the uniform interpolation property and the Lyndon interpolation property. We obtain complexity-optimal decision procedures for all logics and present a constructive proof of the ULIP for K5, which to the best of our knowledge, is the first such syntactic proof. To prove that the interpolant is correct, we use model-theoretic methods, especially bisimulation modulo literals.
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subjects Computer Science - Logic in Computer Science
Interpolation
Mathematics - Logic
title Extensions of K5: Proof Theory and Uniform Lyndon Interpolation
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