We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV alge- bras and √′ quasi-MV algebras - first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √′ quasi- MV algebras; we give a representation of semisimple √′ quasi-MV algebras in terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties
On some properties of quasi-Mv algebras and square root quasi-Mv algebras
PAOLI, FRANCESCO;GIUNTINI, ROBERTO;FREYTES, HECTOR CARLOS
2009-01-01
Abstract
We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV alge- bras and √′ quasi-MV algebras - first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √′ quasi- MV algebras; we give a representation of semisimple √′ quasi-MV algebras in terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties
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