Work

Double Boolean algebras: Constructions, sub-structures and morphisms

Year: 2025

Type: article

Abstract: Double Boolean algebras are algebras D _ : = ( D ; ⊓ , ⊔ , ¬ , ⌟ , ⊥ , ⊤ ) of type ( 2 , 2 , 1 , 1 , 0 , 0 ) introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Every double Boolean algebra D _ contains two Boolean algebras: D _ ⊓ and D _ ⊔ . Three main goals are achieved in this paper. First we characterize sub-algebras of a double Boolean algebra D _ as join sets of sub-algebras of the Boolean algebras D _ ⊓ and D _ ⊔ and a subset of D ﹨ D p (where D p = D ⊓ ∪ D ⊔ ) satisfying certain conditions. Second, we characterize homomorphisms between two double Boolean algebras D _ and E _ by homomorphisms between the Boolean algebras D _ ⊓ and E _ ⊓ , D _ ⊔ and E _ ⊔ and maps between D ﹨ D p and E satisfying certain conditions. Third, we give some tools to construct some classes of pure double Boolean algebras.

Source: International Journal of Approximate Reasoning

DOI: 10.1016/j.ijar.2025.109519

Authors: Gael Tenkeu Kembang, Yannick Léa Tenkeu Jeufack, Etienne Romuald Temgoua Alomo, Leonard Kwuida

Institutions: Université de Yaoundé I, Bern University of Applied Sciences

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,050

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung