On Complete Residuated Many-Valued Logics with t-Norm Conjunction

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Venue:
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Year:
2001

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Abstract

In this paper we summarize recent results, both logical and algebraic, about [0; 1]-valued logical systems having a t-norm and its residuum as truth functions for conjunction and implication. We describe their axiomatic systems and their algebraic varieties, and we stress that the most general variety generated by residuated structures in [0, 1] defined by (left-continuous) t-norms is the variety of pre-linear residuated lattices.