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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References found in this work BETA
Rule Separation and Embedding Theorems for Logics Without Weakening.J. Van Alten Clint & G. Raftery James - 2004 - Studia Logica 76 (2):241-274.
The Finite Model Property for Various Fragments of Intuitionistic Linear Logic.Mitsuhiro Okada & Kazushige Terui - 1999 - Journal of Symbolic Logic 64 (2):790-802.
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.
Citations of this work BETA
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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