Work

Twist-structures isomorphic to modal Nelson lattices

Year: 2025

Type: preprint

Abstract: In this paper, we introduce a new variety of Heyting algebras with two unary modal operators that are not interdefinable but satisfy the weakest condition necessary to define modal operators on Nelson lattices. To achieve this, we utilize the representation of Nelson lattices as twist structures over Heyting algebras and establish a categorical equivalence. Finally, we develop a topological duality for this new variety and apply it to derive a topological duality for modal Nelson lattices.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2504.08109

Authors: Menchón, Paula, Rodriguez, Ricardo O.

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Nicolaus Copernicus University, Universidad Nacional del Centro de la Provincia de Buenos Aires, Universidad de Buenos Aires, Institute of Astronomy and Space Physics

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción Científica y Tecnológica

Awards: G1501505563, G2124491608, G3348288316, G4359570771, Modalities in Substructural Logics: Theory, Methods and Applications, G7849308659

OpenAlex ID: W4414827424

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