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.

Nested Sequents for Quantified Modal Logics

Orlandelli, Eugenio
Co-primo
2023

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.
2023
Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2023
449
467
Lyon, Tim S.; Orlandelli, Eugenio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/942053
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