TY - JOUR
T1 - Paraconsistent fuzzy logic preserving non-falsity
AU - Avron, Arnon
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We introduce proof systems and semantics for two paraconsistent extensions of the system T of Anderson and Belnap, and prove strong soundness, completeness, and decidability for both. The semantics of both systems is based on excluding just one element from the set of designated values. One of the systems has the variable sharing property, and so it is a relevant logic. The other is an extension of the first that may be viewed as a semi-relevant counterpart of Łukasiewicz Logic which preserves non-falsity rather than truth.
AB - We introduce proof systems and semantics for two paraconsistent extensions of the system T of Anderson and Belnap, and prove strong soundness, completeness, and decidability for both. The semantics of both systems is based on excluding just one element from the set of designated values. One of the systems has the variable sharing property, and so it is a relevant logic. The other is an extension of the first that may be viewed as a semi-relevant counterpart of Łukasiewicz Logic which preserves non-falsity rather than truth.
UR - http://www.scopus.com/inward/record.url?scp=84904843452&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2014.07.001
DO - 10.1016/j.fss.2014.07.001
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AN - SCOPUS:84904843452
SN - 0165-0114
VL - 292
SP - 75
EP - 84
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -