David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Kluwer Academic Publishers (2000)
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|
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Citations of this work BETA
Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.
Roy Dyckhoff & Sara Negri (2012). Proof Analysis in Intermediate Logics. Archive for Mathematical Logic 51 (1-2):71-92.
Pierluigi Minari (2013). Labeled Sequent Calculi for Modal Logics and Implicit Contractions. Archive for Mathematical Logic 52 (7-8):881-907.
Torben Braüner (2007). Why Does the Proof-Theory of Hybrid Logic Work so Well? Journal of Applied Non-Classical Logics 17 (4):521-543.
Nicola Olivetti & Gian Luca Pozzato (2008). Theorem Proving for Conditional Logics: CondLean and GOALD U CK. Journal of Applied Non-Classical Logics 18 (4):427-473.
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