Filters, Ideals and Congruences on Double Boolean Algebras

Yannick Léa, Tenkeu Jeufack; Alomo Temgoua, Etienne Romuald; Kwuida, Léonard (2021). Filters, Ideals and Congruences on Double Boolean Algebras In: Braud, Agnès; Buzmakov, Aleksey; Hanika, Tom; Le Ber, Florence (eds.) Formal Concept Analysis. Proceedings of the16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021. Lecture Notes in Computer Science: Vol. 12733 (pp. 270-280). Springer Professional

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Double Boolean algebras (dBas) are algebras D––:=(D;⊓, ⊔,¬,┘,⊥,⊤) of type (2, 2, 1, 1, 0, 0), introduced by R. Wille to capture the equational theory of the algebra of protoconcepts. Boolean algebras form a subclass of dBas. Our goal is an algebraic investigation of dBas, based on similar results on Boolean algebras. In these notes, we describe filters, ideals and congruences, and show that principal filters as well as principal ideals of dBas form (non necessary isomorphic) Boolean algebras.

Item Type:	Book Section (Book Chapter)
Division/Institute:	Business School > Institute for Applied Data Science & Finance Business School
Name:	Yannick Léa, Tenkeu Jeufack; Alomo Temgoua, Etienne Romuald; Kwuida, Léonard0000-0002-9811-0747; Braud, Agnès; Buzmakov, Aleksey; Hanika, Tom and Le Ber, Florence
ISBN:	978-3-030-77866-8
Series:	Lecture Notes in Computer Science
Publisher:	Springer Professional
Language:	English
Submitter:	Léonard Kwuida
Date Deposited:	15 Sep 2021 09:15
Last Modified:	10 Oct 2021 02:18
URI:	https://arbor.bfh.ch/id/eprint/15213