David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
|Buy the book||$195.28 new (28% off) $255.55 direct from Amazon (5% off) $287.17 used Amazon page|
|Call number||QA9.V54 2000|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
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.
Similar books and articles
Irving H. Anellis (2009). Russell and His Sources for Non-Classical Logics. Logica Universalis 3 (2):153-218.
David Basin, Seán Matthews & Luca Viganò (1998). Labelled Modal Logics: Quantifiers. [REVIEW] Journal of Logic, Language and Information 7 (3):237-263.
D. M. Gabbay & U. Reyle (1997). Labelled Resolution for Classical and Non-Classical Logics. Studia Logica 59 (2):179-216.
Marcello D'agostino, Dov M. Gabbay & Alessandra Russo (1997). Grafting Modalities Onto Substructural Implication Systems. Studia Logica 59 (1):65-102.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
Dov M. Gabbay & Nicola Olivetti (1998). Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication. Studia Logica 61 (2):237-280.
Dov M. Gabbay (2000). Goal-Directed Proof Theory. Kluwer Academic.
Greg Restall (1998). Displaying and Deciding Substructural Logics 1: Logics with Contraposition. [REVIEW] Journal of Philosophical Logic 27 (2):179-216.
David Basin, Seán Matthews & Luca Viganò (1998). Natural Deduction for Non-Classical Logics. Studia Logica 60 (1):119-160.
Added to index2009-01-28
Total downloads3 ( #283,452 of 1,096,707 )
Recent downloads (6 months)1 ( #271,187 of 1,096,707 )
How can I increase my downloads?