论文标题
Poset产品作为关系模型
Poset Products as Relational Models
论文作者
论文摘要
我们介绍了基于Poset产品的关系语义，并提供了足够的条件，可以保证其对各种子结构逻辑的合理性和完整性。我们还证明，我们的关系语义统一并概括了文献中已经出现的两种语义：Aguzzoli，Bianchi和Marra的Hájek基本逻辑的时间流语义学以及Lewis-Smith，Oliva和Robinson的直觉Lukasiewistic Lukasiewics logic。由于我们的一般理论，我们以统一的方式恢复了这些先前研究的健全性和完整性结果，并将其扩展到无限的其他下部结构逻辑。
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 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.
