Paraconsistent logic programming
Theoretical Computer Science
Bilattices and the semantics of logic programming
Journal of Logic Programming
Basic proof theory
Artificial Intelligence
A survey of paraconsistent semantics for logic programs
Handbook of defeasible reasoning and uncertainty management systems
Theoretical Computer Science
Logic of Information Structures
Logic of Information Structures
Paraconsistent Declarative Semantics for Extended Logic Programs
Annals of Mathematics and Artificial Intelligence
Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG '88 Proceedings of the International Conference on Computer Logic
Formulas-as-types for a Hierarchy of Sublogics of Intuitionistic Propositional Logic
Proceedings of the International Workshop on Nonclassical Logics and Information Processing
Reasoning with Negative Information, II: Hard Negation, Strong Negation and Logic Programs
Proceedings of the International Workshop on Nonclassical Logics and Information Processing
Dual Intuitionistic Logic Revisited
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood
Journal of Logic, Language and Information
A Cut-Free Sequent Calculus for Bi-intuitionistic Logic
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Intuitionistic Trilattice Logics
Journal of Logic and Computation
A Paraconsistent Linear-time Temporal Logic
Fundamenta Informaticae
Strong negation in well-founded and partial stable semantics for logic programs
IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
Inconsistency-Tolerant Bunched Implications
International Journal of Approximate Reasoning
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The aim of this paper is to obtain a theoretical foundation of inconsistency-tolerant (or paraconsistent) reasoning by presenting a comprehensive study of the structural proof-theory of David Nelson's paraconsistent logic. Inconsistency handling has a growing importance in Computer Science since inconsistencies may frequently occur in knowledge-based and intelligent information systems. Paraconsistent, inconsistency-tolerant logics have been studied to cope with such inconsistencies. In this paper, proof systems for Nelson's paraconsistent logic N4 are comprehensively studied. The logic N4 is a fundamental system and known to be a common basis for various extended and useful paraconsistent logics. Some basic theorems including cut-elimination, normalization and completeness are uniformly proved using various embedding theorems. A variety of sequent calculi and natural deduction systems for N4 and some closely related systems are presented and compared.