On nested sequents for constructive modal logics

Ryuta Arisaka; Anupam Das; Lutz Strassburger

doi:10.2168/LMCS-11(3:7)2015

On nested sequents for constructive modal logics

Ryuta Arisaka
, Anupam Das
, Lutz Strassburger

NRIA, 1 rue Honoré d’Estienne d’Orves

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination.

Original language	English
Article number	7
Journal	Logical Methods in Computer Science
Volume	11
Issue number	3
DOIs	https://doi.org/10.2168/LMCS-11(3:7)2015
Publication status	Published - 3 Sept 2015
Externally published	Yes

Keywords

Cut-elimination
Intuitionistic logic
Modal logic
Nested sequents

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10.2168/LMCS-11(3:7)2015

Cite this

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AB - We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination.

KW - Cut-elimination

KW - Intuitionistic logic

KW - Modal logic

KW - Nested sequents

U2 - 10.2168/LMCS-11(3:7)2015

DO - 10.2168/LMCS-11(3:7)2015

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On nested sequents for constructive modal logics

Abstract

Keywords

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