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.
Categories: math.LO cs.LO