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Title:A Systematic Presentation of Quantified Modal Logics
Authors: Claudio Castellini ; Alan Smaill
Date:Sep 2002
Publication Title:Logic Journal of the IGPL
Publication Type:Journal Article Publication Status:Published
Volume No:11 Page Nos:571-599
This paper provides a systematic presentation of Quantified Modal Logics (with constant domains and rigid designators). We therefore present a set of modular, uniform, normalising, sound and complete labelled sequent calculi for all QMLs whose frame properties can be expressed as a finite set of first-order sentences with equality. We first present C-QK, a calculus for the logic QK, and then we extend it to any such logic QL. Each calculus, called C-QL, is modular (obtained by adding rules to C-QK), uniform (each added rule clearly relates to a property of the frame), normalising (frame reasoning only happens at the top of the proof tree) and Kripke-sound and complete for QL. We improve on the existing literature on the subject (mainly, Vigano`, "Labelled non-classical logics", 2000) by extending the class of logics for which such a presentation is given, and by giving a new proof of soundness and completeness.
2002 by The University of Edinburgh. All Rights Reserved
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Bibtex format
author = { Claudio Castellini and Alan Smaill },
title = {A Systematic Presentation of Quantified Modal Logics},
journal = {Logic Journal of the IGPL},
publisher = {OUP},
year = 2002,
month = {Sep},
volume = {11},
pages = {571-599},
doi = {10.1093/jigpal/10.6.571},

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