  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.
