Natural deduction for non-classical logics

Studia Logica 60 (1):119-160 (1998)
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
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1005003904639
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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.
Sara Negri (2005). Proof Analysis in Modal Logic. Journal of Philosophical Logic 34 (5/6):507 - 544.

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