Maehara-style modal nested calculi - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Archive for Mathematical Logic Year : 2019

Maehara-style modal nested calculi

Abstract

We develop multi-conclusion nested sequent calculi for the fifteen logics of the intuitionistic modal cube between IK and IS5. The proof of cut-free completeness for all logics is provided both syntactically via a Maehara-style translation and semantically by constructing an infinite birelational countermodel from a failed proof search. Interestingly, the Maehara-style translation for proving soundness syntactically fails due to the hierarchical structure of nested sequents. Consequently, we only provide the semantic proof of soundness. The countermodel construction used to prove completeness required a completely novel approach to deal with two independent sources of non-termination in the proof search present in the case of transitive and Euclidean logics.
Fichier principal
Vignette du fichier
10.1007%2Fs00153-018-0636-1.pdf (899.25 Ko) Télécharger le fichier
Origin : Publication funded by an institution

Dates and versions

hal-01942240 , version 1 (03-12-2018)

Identifiers

Cite

Roman Kuznets, Lutz Strassburger. Maehara-style modal nested calculi. Archive for Mathematical Logic, 2019, 58 (3-4), pp.359-385. ⟨10.1007/s00153-018-0636-1⟩. ⟨hal-01942240⟩
51 View
218 Download

Altmetric

Share

Gmail Facebook X LinkedIn More