Proof Theory of N4-Paraconsistent Logics

Anglický jazyk

Proof Theory of N4-Paraconsistent Logics

Vydavateľstvo: College Publications
Rok vydania: 2015
Formát: Paperback
Rozmer: 234 x 156 mm
Jazyk: Anglický jazyk
ISBN: 9781848901674

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O knihe

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.