TY - GEN
T1 - Maximally paraconsistent three-valued logics
AU - Arieli, Ofer
AU - Avron, Arnon
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 from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM 3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.
AB - Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM 3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.
UR - http://www.scopus.com/inward/record.url?scp=79551550454&partnerID=8YFLogxK
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AN - SCOPUS:79551550454
SN - 9781577354512
T3 - Proceedings of the International Conference on Knowledge Representation and Reasoning
SP - 310
EP - 318
BT - Principles of Knowledge Representation and Reasoning
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 12th International Conference on Principles of Knowledge Representation and Reasoning, KR 2010
Y2 - 9 May 2010 through 13 May 2010
ER -