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arXiv · 2605.21667

From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions

William Zuluaga·Belén Gimenez
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Abstract

We develop a relational duality for semilattices with adjunctions (SLatas) based on binary meet-relations. First, we introduce the category of MoS-spaces and establish a dual equivalence with modal semilattices. Then, by means of A-relations, we define the category RelSP and prove a dual equivalence between SLata and RelSP. To compare this framework with the multirelational semantics previously developed for SLatas, we introduce the notion of normal mS-space and show that, under this condition, the multirelational structure can be canonically recovered from a meet-relation, and conversely. As a consequence, we prove that the categories RelSP and SLataSp are isomorphic.

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William Zuluaga, Belén Gimenez. 2026-05-20. From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions. https://arxiv.org/abs/2605.21667

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