TY - JOUR
T1 - Fuzzy logics based on [0,1)-continuous uninorms
AU - Gabbay, Dov
AU - Metcalfe, George
PY - 2007/7
Y1 - 2007/7
N2 - Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics.
AB - Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics.
KW - Cross ratio
KW - Fuzzy logic
KW - Uninorm
KW - t-Norm
UR - http://www.scopus.com/inward/record.url?scp=34249051984&partnerID=8YFLogxK
U2 - 10.1007/s00153-007-0047-1
DO - 10.1007/s00153-007-0047-1
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AN - SCOPUS:34249051984
SN - 0933-5846
VL - 46
SP - 425
EP - 449
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
IS - 5-6
ER -