Although the phenomenon of time travel is common in popular culture, there has been little work in AI on developing a formal theory of time travel. This paper develops such a theory. The paper introduces a branching-time ontology that maintains the classical restriction of forward movement through a temporal tree structure, but permits the representation of paths in which one can perform inferences about time-travel scenarios. Central to the ontology is the notion of an agent embodiment whose beliefs are equivalent to those of an agent who has time-traveled from the future. We show how to formalize an example scenario and demonstrate what it means for such a scenario to be motivated with respect to an agent embodiment.