Labelled modal logics: Quantifiers [Book Review]
Journal of Logic, Language and Information 7 (3):237-263 (1998)
Abstract |
In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework
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Keywords | Quantified modal logics free logic natural deduction labelled deductive systems |
Categories | (categorize this paper) |
Reprint years | 2004 |
DOI | 10.1023/A:1008278803780 |
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References found in this work BETA
Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Mathematical Logic.Joseph Robert Shoenfield - 1967 - Reading, MA, USA: Reading, Mass., Addison-Wesley Pub. Co..
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1975 - Journal of Symbolic Logic 40 (2):232-234.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Labelled Deductive Systems: Volume 1.Dov M. Gabbay - 1996 - Oxford, England: Oxford University Press.
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Citations of this work BETA
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
An Approach to Infinitary Temporal Proof Theory.Stefano Baratella & Andrea Masini - 2004 - Archive for Mathematical Logic 43 (8):965-990.
Ontology of Sentential Moods.Berislav Žarnić - 2016 - In Myśli o języku, nauce i wartościach. Seria druga. Profesorowi Jackowi Juliuszowi Jadackiemu w siedemdziesiątą rocznicę urodzin. pp. 323-339.
Harmony and Modality.Read Stephen - 2008 - In C. Dégremont, L. Kieff & H. Rückert (eds.), Dialogues, Logics and Other Strange Things: Essays in Honour of Shahid Rahman. London: College Publications. pp. 285-303.
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