2019/02/05 by Rodolfo C. Ertola-Biraben, Ertola-Biraben, Rodolfo C., Francesc Esteva +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1902.01656
openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a notion present in the literature. In the way, we prove that those notions are linearly ordered. We finally consider the notion of distributivity in join-semilattices with arrow, that is, the algebraic structure corresponding to the disjunction-conditional fragment of intuitionistic logic.