Superamalgamation for modal lattices via non-distributive dualities
Logic
2026-03-17 v2
Abstract
We show that the variety of modal lattices has the superamalgamation property. As a consequence, we obtain that the weak positive modal logic has the Craig interpolation property. Our proof employs the recent duality for modal lattices based on modal L-spaces. Moreover, we extend this result to a number of other weak positive modal logics axiomatized by modal axioms corresponding to universal Horn sentences.
Keywords
Cite
@article{arxiv.2602.20380,
title = {Superamalgamation for modal lattices via non-distributive dualities},
author = {Rodrigo Nicolau Almeida and Nick Bezhanishvili and Simon Lemal},
journal= {arXiv preprint arXiv:2602.20380},
year = {2026}
}