Overview

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.

Full Product Details

Author:   Luca Viganò
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 2000
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.474kg
ISBN:  

9781441949622

ISBN 10:   1441949623
Pages:   292
Publication Date:   03 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Introduction.- I Labelled deduction for non-classical logics.- 2. Labelled Natural Deduction Systems for Propositional Modal Logics.- 3. Labelled Natural Deduction Systems for Propositional Non-Classical Logics.- 4. Labelled Natural Deduction Systems for Quantified Modal Logics.- 5. Encoding Labelled Non-Classical Logics in Isabelle.- 6. Labelled Sequent Systems for Non-Classical Logics.- 7. Discussion.- II Substructural and complexity analysis of modal sequent systems.- 8. Introduction and Preliminaries.- 9. Substructural Analysis of S(K).- 10. Substructural Analysis of S(T).- 11. Substructural Analysis of S(K4) and S(S4).- 12. Complexity of Proof Search in K, T, K4 and S4.- 13. Discussion.- 14. Conclusions and Further Research.- References.

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Author Information

Luca Viganò is an assistant professor at the Institute for Computer Science of the University of Freiburg (Germany). His research focuses on the theory and applications of non-classical logics, of proof development systems, of logical frameworks, and of logics for security.

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