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arXiv · 2601.15905

Pregroup representable expansions of residuated lattices

Andrew Craig·Claudette Robinson
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Abstract

Group representable relation algebras play an important role in the study of representable relation algebras. The class of distributive involutive FL-algebras (DInFL-algebras) generalises relation algebras, as well as Sugihara monoids and MV-algebras. We construct DInFL-algebras from pregroups and show that they can be represented as algebras of binary relations. Even for finite pregroups we obtain relational representations of DInFL-algebras with non-Boolean lattice reducts. If the pregroup is enriched with a particular unary order-reversing operation, then our construction yields representation results for distributive quasi relation algebras.

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Andrew Craig, Claudette Robinson. 2026-01-22. Pregroup representable expansions of residuated lattices. https://arxiv.org/abs/2601.15905

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