TY - GEN

T1 - On strong maximality of paraconsistent finite-valued logics

AU - Avron, Arnon

AU - Arieli, Ofer

AU - Zamansky, Anna

PY - 2010

Y1 - 2010

N2 - 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 > 2there 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.

AB - 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 > 2there 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.

UR - http://www.scopus.com/inward/record.url?scp=78449305843&partnerID=8YFLogxK

U2 - 10.1109/LICS.2010.20

DO - 10.1109/LICS.2010.20

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AN - SCOPUS:78449305843

SN - 9780769541143

T3 - Proceedings - Symposium on Logic in Computer Science

SP - 304

EP - 313

BT - Proceedings - 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010

Y2 - 11 July 2010 through 14 July 2010

ER -