The assessment of emergent global behaviors of self-organizing applications is an important task to accomplish before employing such systems in real scenarios, yet their intrinsic complexity make this activity still challenging. In this paper we present a logic language used to verify graph-based global properties of self-organizing systems at run-time. The logic language extends a chemical-based coordination model based on logic inference recently proposed. The logic formulae defined by using the language operators depict the intended global spatial properties arising from local interactions among components. Logic formulae are evaluated in a distributed manner by using an inference procedure which checks them against the current global state of the system, verifying whether the intended emergent global behavior actually appears in the system. As examples of spatial properties we consider color patterns: at first we show how to verify specified patterns of identified colors in sets of nodes directly connected, then we present other formulae verifying the appearance of global patterns of colors without specifying the colors themselves. We conclude the examples with the computation of mathematical functions, like the verification of the existence of a maximum value in a specific node of the system.