Proof theory for quantified monotone modal logics

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Negri , S & Orlandelli , E 2019 , ' Proof theory for quantified monotone modal logics ' , Logic journal of the IGPL , vol. 27 , no. 4 , pp. 478–506 .

Title: Proof theory for quantified monotone modal logics
Author: Negri, Sara; Orlandelli, Eugenio
Contributor: University of Helsinki, Theoretical Philosophy
Date: 2019-08
Language: eng
Number of pages: 29
Belongs to series: Logic journal of the IGPL
ISSN: 1367-0751
Abstract: This paper provides a proof-theoretic study of quantified non-normal modal logics (NNML). It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced is sound and complete with respect to the appropriate class of neighbourhood frames. In particular, the completeness proof constructs a formal derivation for derivable sequents and a countermodel for non-derivable ones, and gives a semantic proof of the admissibility of cut.
Subject: 611 Philosophy
non-normal modal logics
quantified modal logics
labelled sequent calculus
neighbourhood semantics
Barcan formulas

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