- Abstract:
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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.
- Copyright:
- 2002 by The University of Edinburgh. All Rights Reserved
- Links To Paper
- No links available
- Bibtex format
- @Article{EDI-INF-RR-0150,
- 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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