\(\bigstar\)-autonomous lattices. (English) Zbl 1067.03066
Summary: \(\bigstar\)-autonomous lattices are the algebraic models of linear logic without exponentials and without additive constants. In this paper, we investigate the structure theory of this variety and some of its subvarieties, as well as its relationships with other classes of algebras.
MSC:
| 03G25 | Other algebras related to logic |
| 03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |
| 06B20 | Varieties of lattices |
| 06F15 | Ordered groups |
Keywords:
lattice-ordered group; linear logic; residuated lattice; \(\bigstar\)-autonomous lattice; substructural logicsReferences:
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