Interpolation for intermediate logics via injective nested sequents

Interpolation for intermediate logics via injective nested sequents

Abstract We introduce a novel, semantically inspired method of constructing nested sequent calculi for propositional intermediate logics. Applying recently developed methods for proving Craig interpolation to these nested sequent calculi, we obtain constructive proofs of the interpolation property f...

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Veröffentlicht in:Journal of logic and computation 2021-04, Vol.31 (3), p.797-831
Hauptverfasser: Kuznets, Roman, Lellmann, Björn
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Lellmann, Björn
description Abstract We introduce a novel, semantically inspired method of constructing nested sequent calculi for propositional intermediate logics. Applying recently developed methods for proving Craig interpolation to these nested sequent calculi, we obtain constructive proofs of the interpolation property for most non-trivial interpolable intermediate logics, as well as Lyndon interpolation for Gödel logic. Finally, we provide a prototype implementation combining proof search and countermodel construction.
doi_str_mv 10.1093/logcom/exab015
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title Interpolation for intermediate logics via injective nested sequents
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