Proof theory for quantified monotone modal logics

Logic Journal of the IGPL 27 (4):478-506 (2019)

Authors
Sara Negri
University of Helsinki
Abstract
This paper provides a proof-theoretic study of quantified non-normal modal logics. 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.
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DOI 10.1093/jigpal/jzz015
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References found in this work BETA

Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Structural Proof Theory.Jan von Plato & Sara Negri - 2006 - Philosophical Review 115 (2):255-258.
Geometrisation of First-Order Logic.Roy Dyckhoff & Sara Negri - 2015 - Bulletin of Symbolic Logic 21 (2):123-163.
First-Order Classical Modal Logic.Horacio Arló-Costa & Eric Pacuit - 2006 - Studia Logica 84 (2):171 - 210.

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