Proceedings ArticleDOI
On Strong Maximality of Paraconsistent Finite-Valued Logics
Arnon Avron,Ofer Arieli,Anna Zamansky +2 more
- pp 304-313
TLDR
This paper introduces a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic, and investigates this notion in the framework of finite-valued paraconsistent logics.Abstract:
Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain as much as possible from classical logic. In this paper we introduce a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic. We investigate this notion in the framework of finite-valued paraconsistent logics, and show that for every $n>2$ there exists an extensive family of $n$-valued logics, each of which is maximally paraconsistent in our sense, is partial to classical logic, and is not equivalent to any $k$-valued logic with $kread more
Citations
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Journal ArticleDOI
Ideal Paraconsistent Logics
TL;DR: It is shown that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal, and for every n > 2 there exists an extensive family of ideal n-valued logics.
Proceedings ArticleDOI
What is an ideal logic for reasoning with inconsistency
TL;DR: A list of desirable properties of "ideal" logics for reasoning with inconsistency is formulated, a variety of logics that have these properties are identified, and a systematic way of constructing a family of such n-valued logics is provided.
Journal ArticleDOI
Revisiting $\mathbb{Z}$
Journal ArticleDOI
Revisiting da Costa logic
TL;DR: It is proved that a restricted Hilbert system for daC, named DC, satisfies certain properties that help to show that this logic is not a maximal paraconsistent system.
Proceedings Article
A paraconsistent view on B and S5.
Arnon Avron,Anna Zamansky +1 more
TL;DR: This paper shows that the famous modal logics B and S5, can be viewed as paraconsistent logics with several particularly useful properties.
References
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Book ChapterDOI
A Useful Four-Valued Logic
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Journal ArticleDOI
On the theory of inconsistent formal systems.
Book ChapterDOI
Logics of Formal Inconsistency
TL;DR: The Logicas da Inconsistencia Formal (LIFs) as mentioned in this paper form a classe of logicas paraconsistentes particularmente expressivas, in which a nocao meta-teonca de consistencia pode ser internalizada ao nivel da linguagem obje[c]to.