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
M3 - Conference contribution
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 -