Pervasive applications are involving more and more autonomous computing and communicating devices, augmented with the abilities of sensing and controlling the logical / physical environment. To enable context-awareness for such applications, we are challenged by the intrinsic asynchrony among the context collecting devices. To this end, we introduce the predicate detection theory and propose the Predicate-Detection-based Context-Awareness (PD-CA) framework, in which: a) logical time is used to explicitly cope with the asynchrony; b) specification of predicates enables the applications to express contextual properties of their concerns; c) online and incremental predicate detection algorithms effectively enable context-awareness at runtime. Under the guidance of the PD-CA framework, we present the design and implementation of the MIPA middleware, which shields the applications from the burden of processing the asynchronous contexts. We also demonstrate how PD-CA simplifies the development of context-aware applications. Experimental evaluations show the performance of MIPA in supporting context-aware applications despite of the asynchrony.