MOIN: A Nested Sequent Theorem Prover for Intuitionistic Modal Logics (System Description)

We present a simple Prolog prover for intuitionistic modal logics based on nested sequent proof systems. We have implemented single-conclusion systems (Gentzen-style) and multi-conclusion systems (Maehara-style) for all logics in the intuitionistic modal IS5-cube. While the single-conclusion system...

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Bibliographic Details
Published inAutomated Reasoning Vol. 12167; pp. 398 - 407
Main Authors Girlando, Marianna, Straßburger, Lutz
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2020
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Intuitionistic modal logic
Nested sequents
Prolog
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Summary:We present a simple Prolog prover for intuitionistic modal logics based on nested sequent proof systems. We have implemented single-conclusion systems (Gentzen-style) and multi-conclusion systems (Maehara-style) for all logics in the intuitionistic modal IS5-cube. While the single-conclusion system are better investigated and have an internal cut-elimination, the multi-conclusion systems can provide a countermodel in case the proof search fails. To our knowledge this is the first automated theorem prover for intuitionistic modal logics. For wider usability, we also implemented classical normal modal logics in the S5-cube.
ISBN:9783030510534
3030510530
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-51054-1_25