  In this paper, we propose a generalization of Continuous Logic ([BBHU08])
where the distances take values in suitable co-quantales (in the way as it was
proposed in [Fla97]). By assuming suitable conditions (e.g., being
co-divisible, co-Girard and a V-domain), we provide, as test questions, a proof
of a version of the Tarski-Vaught test (Proposition 3.35) and Los Theorem
(Theorem 3.62) in our setting.
