A solution of the word problem for free Double Boolean algebras

Authors:
Björn Vormbrock
Affiliations:
Technische Universität Darmstadt, Fachbereich Mathematik, Darmstadt
Venue:
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
Year:
2007

Citing 3
Cited 0

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Semiconcept and protoconcept algebras: the basic theorems

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Abstract

Double Boolean algebras were introduced in [Wi00a] as a variety fundamental for Boolean Concept Logic, an extension of Formal Concept Analysis allowing negations of formal concepts. In this paper, the free double Boolean algebra generated by the constants is described. Moreover, we show that every free double Boolean algebra with at least one generator is infinite. A measure of the complexity of terms specific for double Boolean algebras is introduced. This, together with a modification of the algorithm for protoconcept exploration (cf. [Vo04]) yields double Boolean algebras containing a counterexample to every term identity up to a given complexity if the identity does not hold in general. These algebras can be constructed automatically, thus the word problem for free double Boolean algebras is solved.