A NOTE ON SUGIHARA ALGEBRAS

In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of...

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Bibliographic Details
Published in:Publicacions matemàtiques 1992-01, Vol.36 (2A), p.591-599
Main Authors: Font, Josep M., Pérez, Gonzalo Rodríguez
Format: Article
Language:English
Subjects:
Abstract algebra
Algebra
Anells (Àlgebra)
Axioms
Logical theorems
Mathematical theorems
Relevance logic
Rings (Algebra)
Semantics
Semigroups
Typographic fonts
Universal algebra
Àlgebra
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Summary:In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same sense to the calculus R of relevance logic, and we determine the totally ordered, the subdirectly irreducible, and the simple members of this variety, by using some consequences of the algebraizability of the logic RM (R-Mingle) with which they are associated.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_362A92_19