 Proof Theory of N4related Paraconsistent Logics
Norihiro Kamide and Heinrich Wansing
The present book is the first monograph ever with a central focus on the proof theory of paraconsistent logics in the vicinity of the fourvalued, 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 inconsistencytolerant logic. The material covers the structural proof theory of
* N4,
* its fragments, including firstdegree entailment logic,
* related logics, such as trilattice logics, connexive systems, systems of symmetric and dual paraconsistent logic, and variations of biintuitionistic 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 prooftheory of N4 and N4related logics is the central theme of the present monograph, models and modeltheoretic semantics also play an important role in the presentation. The relational, Kripkestyle 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 Gentzenstyle proof systems  in particular sequent calculi of a standard and less standard kind  for paraconsistent logics, and cutelimination 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.
19 January 2015
9781848901674
