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On the hierarchy of t-norm based rediduated fuzzy logics. (English) Zbl 1038.03026
Fitting, Melvin (ed.) et al., Beyond two: Theory and applications of multiple-valued logic. Heidelberg: Physica-Verlag (ISBN 3-7908-1541-1/pbk). Stud. Fuzziness Soft Comput. 114, 251-272 (2003).
In this publication, the authors give a survey on logical and algebraic results on [0,1]-valued logics having a t-norm as conjunction and its associated residuum as implication operator. Axiomatic systems and algebraic varieties are described and placed into a hierarchy of logics. It is shown that the most general variety generated by residuated structures in [0,1] defined by means of left-continuous t-norms is the variety of pre-linear residuated lattices (MTL-algebras). Relations with substructural logics and with Ono’s hierarchy of extensions of the Full Lambek Calculus are given.
For the entire collection see [Zbl 1015.00007].

MSC:
03B52 Fuzzy logic; logic of vagueness
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03G10 Logical aspects of lattices and related structures
06D20 Heyting algebras (lattice-theoretic aspects)
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