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Conference Paper

A Modular Presentation of Modal Logics in a Logical Framework

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

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

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

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Citation

Basin, D. A., Matthews, S., & Viganò, L. (1998). A Modular Presentation of Modal Logics in a Logical Framework. In J. Ginzburg, Z. Khasidashvili, C. Vogel, J.-J. Levy, & E. Vallduvi (Eds.), Proceedings of the 1st Tbilisi Symposium on Language, Logic and Computation: Selected Papers (pp. 293-307). Stanford, USA: CSLI.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-3811-0
Abstract
We present a theoretical and practical approach to the modular natural deduction presentation of modal logics and their implementation in a logical framework. Our work treats a large and well-known class of modal logics (including $K$, $KD$, $T$, $B$, $S4$, $S4.2$, $S5$) in a uniform way with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. Moreover, it results in a pleasingly simple and usable implementation of these logics.