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BL-algebras of basic fuzzy logic.

Esko Turunen (1999)

Mathware and Soft Computing

BL-algebras [Hajek] rise as Lindenbaum algebras from certain logical axioms familiar in fuzzy logic framework. BL-algebras are studied by means of deductive systems and co-annihilators. Duals of many theorems known to hold in MV-algebra theory remain valid for BL-algebras, too.

Boolean differential operators

Jorge Catumba, Rafael Díaz (2014)

Commentationes Mathematicae Universitatis Carolinae

We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.

Boolean matrices ... neither Boolean nor matrices

Gabriele Ricci (2000)

Discussiones Mathematicae - General Algebra and Applications

Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.

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