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Conference Paper

Implementing Modal and Relevance Logics in a Logical Framework

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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. (1996). Implementing Modal and Relevance Logics in a Logical Framework. In L. Carlucci-Aiello, J. Doyle, & S. Shapiro (Eds.), Proceedings of the 5th International Conference on Principles of Knowledge Representation and Reasoning (KR'96) (pp. 386-397). San Francisco, USA: Morgan Kaufmann.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-ABE0-2
Abstract
We present a framework for machine implementation of both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. Our approach is modular and supports uniform proofs of correctness and proof normalization. We have implemented our work in the Isabelle Logical Framework.