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The subvariety of commutative residuated lattices represented by twist-products. (English) Zbl 1303.03092

The authors study the subvariety \(K\) of integral commutative residuated lattices \(L\) that can be represented by twist-products, that is, the product \(L \times L\) can be endowed with the structure of a commutative residuated lattice with involution. They give an equational characterization of this subvariety and analyze the subvariety of representable algebras in \(K\). For the case of bounded integral commutative residuated lattices, the authors generalize a result by S. P. Odintsov [J. Log. Comput. 13, No. 4, 453–468 (2003; Zbl 1034.03029); Stud. Log. 76, No. 3, 385–405 (2004; Zbl 1047.03050); Constructive negations and paraconsistency. Dordrecht: Springer (2008; Zbl 1161.03014)] for generalized Heyting algebras.

MSC:

03G10 Logical aspects of lattices and related structures
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03G25 Other algebras related to logic
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