On distributive join-semilattices
Logic
2019-02-06 v1
Abstract
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.
Cite
@article{arxiv.1902.01656,
title = {On distributive join-semilattices},
author = {Rodolfo C. Ertola-Biraben and Francesc Esteva and Lluís Godo},
journal= {arXiv preprint arXiv:1902.01656},
year = {2019}
}