Many-valued non-deterministic semantics for first-order logics of formal (In)consistency

Arnon Avron*, Anna Zamansky

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

19 Scopus citations


A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa's approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved, da Costa's approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide non-deterministic semantics for a very large family of first-order LFIs (which includes da Costa's original system C*1, as well as thousands of other logics). We show that our semantics is effective and modular, and we use this effectiveness to derive some important properties of logics in this family.

Original languageEnglish
Title of host publicationAlgebraic and Proof-Theoretic Aspects of Non-classical Logics
Subtitle of host publicationPapers in Honor of Daniele Mundici on the Occasion of His 60th Birthday
PublisherSpringer Verlag
Number of pages24
ISBN (Print)3540759387, 9783540759386
StatePublished - 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4460 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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