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arXiv · 2603.12175

Varieties of De Morgan bisemilattices

Francesco Paoli·Damian Szmuc·Agustina Borzi·Martina Zirattu
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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.

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Francesco Paoli, Damian Szmuc, Agustina Borzi, Martina Zirattu. 2026-03-12. Varieties of De Morgan bisemilattices. https://arxiv.org/abs/2603.12175

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