We prove the completeness of a first-order analogue of the Fischer Servi logic $\mathsf{FS}$ with respect to its expected birelational semantics. To this end we introduce the notion of the $\textit{trace model}$ and, much like in a canonical model argument, prove a truth lemma. We conclude by examining a number of other first-order Fischer Servi logics, including the first-order analogue of $\mathsf{FSS4}$, whose completeness can be similarly proved.

翻译：我们证明了Fischer Servi逻辑$\mathsf{FS}$的一阶类比相对于其预期的双关系语义的完备性。为此，我们引入了$\textit{迹模型}$的概念，并类似于典范模型论证，证明了一个真值引理。最后，我们考察了若干其他一阶Fischer Servi逻辑，包括$\mathsf{FSS4}$的一阶类比，其完备性可类似地证明。