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Poset Products as Relational Models

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Abstract

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform fashion, and extend them to infinitely-many other substructural logics.

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Acknowledgements

This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 670624).

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  1. Laboratoire J.A Dieudonné, Université Côte d’Azur, Parc Valrose, 06108, Nice Cedex 2, France

    Wesley Fussner

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Correspondence to Wesley Fussner.

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Fussner, W. Poset Products as Relational Models. Stud Logica 110, 95–120 (2022). https://doi.org/10.1007/s11225-021-09956-z

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