Nested Sequents for Quantified Modal Logics

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Contributors

Abstract

This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains. Each calculus is proved to have good structural properties: weakening and contraction are height-preserving admissible and cut is (syntactically) admissible. Each calculus is shown to be equivalent to the corresponding axiomatic system and, thus, to be sound and complete. Finally, it is argued that the calculi are internal -- i.e., each sequent has a formula interpretation -- whenever the existence predicate is expressible in the language.

Details

Original languageEnglish
Title of host publicationAutomated Reasoning with Analytic Tableaux and Related Methods
EditorsRevantha Ramanayake, Josef Urban
PublisherSpringer, Cham
Pages449–467
Number of pages19
ISBN (electronic)978-3-031-43513-3
ISBN (print)978-3-031-43512-6
Publication statusPublished - 2023
Peer-reviewedYes

Publication series

SeriesLecture Notes in Computer Science
Volume14278
ISSN0302-9743

External IDs

Scopus 85172418810

Keywords

Keywords

  • Cut elimination, Nested sequent, Quantified modal logic