We introduce a novel framework to describe dynamic interactive reasoning in presence of unawareness. We extend the notion of conditional probability systems for this setting and we perform the construction of the corresponding canonical hierarchical structure, that is, the structure that contains all coherent infinite hierarchies of beliefs in presence of unawareness and conditioning events, which is an extension of the one constructed in Battigalli and Siniscalchi (1999a). Relying on the existence of this object, we provide an epistemic characterization of Strong Rationalizability of Pearce (1984) as defined in Heifetz et al. (2013) to address the case of dynamic games with unawareness. The characterization is based on the notion of Strong Belief, introduced in the literature by Battigalli and Siniscalchi (2002).
