Poset Products as Relational Models
Logic
2023-07-24 v2 Logic in Computer Science
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 H\'ajek's basic logic, and Lewis-Smith, Oliva, and Robinson's semantics for intuitionistic Lukasiewicz 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.
Keywords
Cite
@article{arxiv.2012.01247,
title = {Poset Products as Relational Models},
author = {Wesley Fussner},
journal= {arXiv preprint arXiv:2012.01247},
year = {2023}
}