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The subvariety lattice for representable idempotent commutative residuated lattices
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In this article, it was shown that the subvariety lattice of RICRL is countable, despite its complexity and in contrast to several varieties of closely related algebras.Abstract:
RICRL denotes the variety of commutative residuated lattices which have an idempotent monoid operation and are representable in the sense that they are subdirect products of linearly ordered algebras. It is shown that the subvariety lattice of RICRL is countable, despite its complexity and in contrast to several varieties of closely related algebras.read more
Citations
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Craig interpolation for semilinear substructural logics
Enrico Marchioni,George Metcalfe +1 more
TL;DR: The first author was supported by the Spanish projects TASSAT (TIN2010-20967-C04-01) and Agree- ment Technologies (CONSOLIDER CSD2007-0022, INGENIO 2010).
Journal ArticleDOI
Structure theorems for idempotent residuated lattices
TL;DR: In this article, structural properties of residuated lattices that are idempotent as monoids are studied, and the authors provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras.
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Structure theorems for idempotent residuated lattices
TL;DR: In this article, structural properties of residuated lattices that are idempotent as monoids are studied, and the authors provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras.
Journal ArticleDOI
Variety generated by conical residuated lattice-ordered idempotent monoids
Wei Chen,Yizhi Chen +1 more
TL;DR: In this article, the authors studied the variety generated by conical idempotent residuated lattices and established a chain decomposition theorem for the variety, which is proved to have the finite embeddability property.
Semilinear idempotent distributive l-monoids
TL;DR: In this article , a representation theorem for totally ordered idempotent monoids via a nested sum construction is presented, and a characterization of the subdirectly irreducible members of the variety of semilinear IDM-monoids and a proof that its subvariety lattice is countably infinite.
References
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Book
Residuated Lattices: An Algebraic Glimpse at Substructural Logics
TL;DR: Algebra and Substructural Logics as mentioned in this paper is a good introduction to algebraic logic and its connections to algebra and logic, where the connections between logic and algebra are shown in every level.
Journal ArticleDOI
The structure of commutative residuated lattices
TL;DR: It is proved that the congruence lattice of each member of is an algebraic, distributive lattice whose meet-prime elements form a root-system (dual tree) of commutative residuated lattices.
Journal ArticleDOI
The finite embeddability property for residuated lattices, pocrims and BCK-algebras
W. J. Blok,C. J. Van Alten +1 more
TL;DR: In this paper, the relationship of the FEP with the FMP and strong finite model property (SFMP) was investigated, and for quasivarieties with equationally definable principal relative congruences the three notions FEP, FMP, and SFMP are equivalent.
Journal ArticleDOI
Super-Ł ukasiewicz propositional logics
TL;DR: In this paper, the authors introduced a 3-valued propositional calculus with one designated truth-value and generalized it to an m -valued calculus (where m is a natural number or ) with a designated truth value.