On varieties of biresiduation algebras

Studia Logica 83 (1-3):425-445 (2006)
A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters and use this to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1007/s11225-006-8312-6
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References found in this work BETA
The Bottom of the Lattice of BCK-Varieties.Tomasz Kowalski - 1995 - Reports on Mathematical Logic:87-93.
Komori Identities In Algebraic Logic.Willem Blok & Silvia La Falce - 2000 - Reports on Mathematical Logic:79-106.

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Multi-Posets in Algebraic Logic, Group Theory, and Non-Commutative Topology.Wolfgang Rump - 2016 - Annals of Pure and Applied Logic 167 (11):1139-1160.
Non-Commutative Logical Algebras and Algebraic Quantales.Wolfgang Rump & Yi Chuan Yang - 2014 - Annals of Pure and Applied Logic 165 (2):759-785.

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