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Natural Deduction for Non-Classical Logics

MPG-Autoren
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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Zitation

Basin, D. A., Matthews, S., & Viganò, L. (1998). Natural Deduction for Non-Classical Logics. Studia Logica, 60(1), 119-160.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-385E-6
Zusammenfassung
We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. 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. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of soundness, completeness and proof normalization. We have implemented our work in the Isabelle Logical Framework.