Path Predicate Modal Logic (PPML) is a generalization of Basic Modal Logic, where atoms are relational predicates instead of propositional symbols. The study of PPML is motivated as a way to abstractly investigate data-aware formalisms, such as XPath or DataGL. In this paper, we investigate some basic model theoretical aspects of PPML to better characterize its expressive power. More concretely, we investigate different ways of defining Hennessy-Milner classes, and a van Benthem characterization theorem. In doing so, we discuss the main challenges of dealing with the novel features of PPML, and what are the similarities with the standard approaches.

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