## 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

### Citations:

Zbl 1034.03029; Zbl 1047.03050; Zbl 1161.03014
Full Text:

### References:

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