Labelled Non-Classical Logics

✍ Scribed by Luca Viganò (auth.)

• Publisher: Springer US
• Year: 2000
• Tongue: English
• Leaves: 294
• Edition: 1
• Category: Library

✦ Synopsis

I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof­ theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys­ tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-14
Front Matter....Pages 15-15
Labelled Natural Deduction Systems for Propositional Modal Logics....Pages 17-52
Labelled Natural Deduction Systems for Propositional Non-Classical Logics....Pages 53-89
Labelled Natural Deduction Systems for Quantified Modal Logics....Pages 91-113
Encoding Labelled Non-Classical Logics in Isabelle....Pages 115-135
Labelled Sequent Systems for Non-Classical Logics....Pages 137-156
Discussion....Pages 157-164
Front Matter....Pages 165-165
Introduction and Preliminaries....Pages 167-185
Substructural Analysis of S(K)....Pages 187-200
Substructural Analysis of S(T)....Pages 201-222
Substructural Analysis of S(K4) and S(S4)....Pages 223-246
Complexity of Proof Search in K, T, K4 and S4....Pages 247-252
Discussion....Pages 253-262
Conclusions and Further Research....Pages 263-265
Back Matter....Pages 267-291

✦ Subjects

Logic; Computer Science, general; Mathematical Logic and Foundations