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2010
IEEE

On Strong Maximality of Paraconsistent Finite-Valued Logics

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On Strong Maximality of Paraconsistent Finite-Valued 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 k < n. On the other hand, we specify a natural condition that guarantees that a paraconsistent logic is contained in a logic in the class of three-valued paraconsistent logics, and show that all reasonably expressive logics in this class are maximal.
Arnon Avron, Ofer Arieli, Anna Zamansky
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where LICS
Authors Arnon Avron, Ofer Arieli, Anna Zamansky
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