Non-distributive positive logic as a fragment of first-order logic over semilattices

08/24/2022

∙

by   Jim de Groot, et al.

∙

0

∙

share

We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs of states from one model to single states from another. En route to this result we use a more traditional notion of simulations and prove a Hennessy-Milner style theorem for it, using an analogue of modal saturation called meet-compactness.