Varieties of De Morgan bisemilattices
Logic
2026-03-13 v1
Abstract
De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain generalisation of the P{\l}onka sum construction (De Morgan- P{\l}onka sums). In this paper, we provide a complete description of the lattice of subvarieties of the variety DMBL of De Morgan bisemilattices. For each subvariety in the lattice, we identify a finite set of finite generators, a characterisation of the De Morgan-P{\l}onka representations of its members, and a syntactic description of its valid identities. In many cases, we also give an axiomatisation relative to DMBL.
Keywords
Cite
@article{arxiv.2603.12175,
title = {Varieties of De Morgan bisemilattices},
author = {Francesco Paoli and Damian Szmuc and Agustina Borzi and Martina Zirattu},
journal= {arXiv preprint arXiv:2603.12175},
year = {2026}
}