2017/08/31 by Antonio Ledda · 7 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Category theory #Distributive property #Duality (order theory) #Focus (optics) #Representation (politics) #Rough Sets and Fuzzy Logic #Variety (cybernetics) #math.LO #semigroups and automata theory
paper · pdf · doi:10.1007/s11225-017-9745-9
published in Studia Logica 106(2), 417-448 (Springer Science+Business Media)
openalex publication_date 2017/08/31 · openalex created_date 2017/09/15 · arxiv created 2018/03/18 · arxiv updated 2018/03/20 · openalex updated_date 2026/08/05
In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes' representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn duality and introduce the categories of 2spaces and 2spaces⋆. The categories of 2spaces and 2spaces⋆ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent.