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Journal Article

Labelled Modal Logics: quantifiers

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44075

Basin,  David A.
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45002

Matthews,  Seán
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45670

Viganò,  Luca
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Basin, D. A., Matthews, S., & Viganò, L. (1998). Labelled Modal Logics: quantifiers. Journal of Logic, Language and Information, 7(3), 237-263.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-384D-C
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.