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.

翻译：我们引入了一种基于偏序集乘积的关系语义，并给出了保证其对于多种子结构逻辑具有可靠性和完备性的充分条件。我们还证明，我们的关系语义统一并推广了文献中已有的两种语义：Aguzzoli、Bianchi和Marra为Hájek基本逻辑提出的时间流语义，以及Lewis-Smith、Oliva和Robinson为直觉主义Lukasiewicz逻辑提出的语义。作为我们一般理论的结果，我们以统一的方式恢复了这些先前研究的可靠性和完备性结论，并将其推广到无限多种其他子结构逻辑中。