Proof Theory of N4-Paraconsistent Logics

Norihiro Kamide

ISBN 10: 1848901674 / ISBN 13: 9781848901674

Published by College Publications, 2015

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - The present book is the first monograph ever with a central focus on the proof theory of paraconsistent logics in the vicinity of the four-valued, constructive paraconsistent logic N4 by David Nelson. The volume brings together a number of papers the authors have written separately or jointly on various systems of inconsistency-tolerant logic. The material covers the structural proof theory of¿ N4¿ its fragments, including first-degree entailment logic¿ related logics, such as trilattice logics, connexive systems, systems of symmetric and dual paraconsistent logic, and variations of bi-intuitionistic logic¿ paraconsistent temporal logics¿ substructural subsystems of N4, such as paraconsistent intuitionistic linear logics, paraconsistent logics based on involutive quantales, and paraconsistent Lambek logics.Although the proof-theory of N4 and N4-related logics is the central theme of the present monograph, models and model-theoretic semantics also play an important role in the presentation. The relational, Kripke-style models that are dealt with provide a motivating and intuitively appealing insight into the logics with respect to which they are shown to be sound and complete. Nevertheless, the emphasis is on Gentzen-style proof systems -in particular sequent calculi of a standard and less standard kind- for paraconsistent logics, and cut-elimination and its consequences are a central topic throughout. A unifying element of the presentation is the repeated application of embedding theorems in order to transfer results from other logics such as intuitionistic logic to the paraconsistent case.

Seller Inventory # 9781848901674

Bibliographic Details

• Title: Proof Theory of N4-Paraconsistent Logics
• Publisher: College Publications
• Publication Date: 2015
• Language: English
• ISBN 10: 1848901674
• ISBN 13: 9781848901674
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 234W x 156H x 23D millimeters 234 millimeters width by 156 millimeters height by 23 millimeters depth
• Weight: 626 grams

About this title

Synopsis

The present book is the first monograph ever with a central focus on the proof theory of paraconsistent logics in the vicinity of the four-valued, constructive paraconsistent logic N4 by David Nelson. The volume brings together a number of papers the authors have written separately or jointly on various systems of inconsistency-tolerant logic. The material covers the structural proof theory of - N4, - its fragments, including first-degree entailment logic, - related logics, such as trilattice logics, connexive systems, systems of symmetric and dual paraconsistent logic, and variations of bi-intuitionistic logic, - paraconsistent temporal logics, - substructural subsystems of N4, such as paraconsistent intuitionistic linear logics, paraconsistent logics based on involutive quantales, and paraconsistent Lambek logics. Although the proof-theory of N4 and N4-related logics is the central theme of the present monograph, models and model-theoretic semantics also play an important role in the presentation. The relational, Kripke-style models that are dealt with provide a motivating and intuitively appealing insight into the logics with respect to which they are shown to be sound and complete. Nevertheless, the emphasis is on Gentzen-style proof systems -in particular sequent calculi of a standard and less standard kind- for paraconsistent logics, and cut-elimination and its consequences are a central topic throughout. A unifying element of the presentation is the repeated application of embedding theorems in order to transfer results from other logics such as intuitionistic logic to the paraconsistent case.