Labelled Non-Classical Logics

Kluwer Academic Publishers (2000)

Abstract
The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics.
Keywords Nonclassical mathematical logic
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Call number QA9.V54 2000
ISBN(s) 0792377494   9780792377498  
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Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Proof Analysis in Intermediate Logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1-2):71-92.
Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
Labeled Sequent Calculi for Modal Logics and Implicit Contractions.Pierluigi Minari - 2013 - Archive for Mathematical Logic 52 (7-8):881-907.

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