In this paper, we establish an analogue of Craig Interpolation Property for a many-sorted variant of first-order hybrid logic. We develop a forcing technique that dynamically adds new constants to the underlying signature in a way that preserves consistency, even in the presence of models with possibly empty domains. Using this forcing method, we derive general criteria that are sufficient for a signature square to satisfy both Robinson's consistency and Craig interpolation properties.

翻译：本文针对一阶混合逻辑的多类变体，建立了克雷格插值性质的类似结果。我们发展了一种强制技术，该技术能动态地向基础签名添加新常量，即使在可能包含空域的模型存在的情况下，仍能保持一致性。利用这一强制方法，我们推导出足以使签名方块同时满足罗宾逊一致性与克雷格插值性质的一般性判据。