Runtime verification is an important method for improving software reliability of pervasive computing applications. Some properties of these applications consider both temporal and spatial relationships. Such spatio-temporal properties bring some specific challenges for runtime verification. On one hand, traditional temporal logic cannot describe spatial properties. On the other hand, while ambient logic is suitable for spatial properties, it does not properly support the description of temporal properties in finite traces, especially when the truth values cannot be decided. In order to support the runtime verification of spatio-temporal properties for pervasive computing applications, this paper firstly imports 3-valued semantics and proposes AL₃ (3-valued ambient logic). On the basis of AL₃, it designs and implements an algorithm for properties checking and a runtime monitor. Moreover, the paper uses a case study and a performance measurement to clarify the usability and feasibility of the proposed approach.