Filters, Ideals and Congruences on Double Boolean Algebras
Version
Published
Date Issued
2021-06
Author(s)
Editor(s)
Braud, Agnès
Buzmakov, Aleksey
Hanika, Tom
Le Ber, Florence
Type
Book Chapter
Language
English
Abstract
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.
ISBN
978-3-030-77866-8
Series/Report No.
Lecture Notes in Computer Science
Organization
Volume
12733
Conference
International Conference on Formal Concept Analysis ICFCA 2021
Publisher
Springer Professional
Submitter
Kwuida, Léonard
Citation apa
Kwuida, L., Yannick Léa, T. J., & Alomo Temgoua, E. R. (2021). Filters, Ideals and Congruences on Double Boolean Algebras (A. Braud, A. Buzmakov, T. Hanika, & F. Le Ber, Eds.; Vol. 12733). Springer Professional. https://arbor.bfh.ch/handle/arbor/43881