Foundations of a Formal Theory of Time Travel

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. 1. Motivation and Overview The phenomenon of time travel is common in fiction, film, television, and video games. Examples include A Connecticut Yankee in King Arthur’s Court, , Slaughterhouse-Five, Harry Potter and the Prisoner of Azkaban Back to the Future, Bill and Ted’s Excellent Adventure; Star Trek, Lost, and Chrono Trigger. This paper explores the development of a formal theory of time travel, in which one would be able to represent and reason with time travel stories. There are two motivations for this work. First, the growing field of AI and Entertainment has in recent years included research on tools for analysis and generation of video games (see, e.g., (Nelson & Mateas 2008; Whitehead & Young 2009)). A formal analysis of what makes a time-travel story work—that is, what makes a time-travel narrative coherent, and what inferences in a time-travel scenario are reasonable—could be useful for this line of work. Second, this is part of a long-term research program in formal models of narrative, and in particular, in de∗This paper reports on research done in 2009 and 2010 while the author was visiting research scientist at Courant Institute, and was originally written between June 2009 and January 2010. The author’s current address is SAIC, 4001 N. Fairfax Drive, Arlington, VA 22203. She can be reached by email at NYU (leora@cs.nyu.edu) or SAIC (leora.morgenstern@saic.com). veloping formal theories that can support determining when narrative structures are coherent. We believe that this is part of the general story-understanding problem, which remains a challenging problem for AI(Louchart, Mehta, & Roberts 2009). Intelligent beings understand time-travel stories (and other science fiction) in much the same way that they understand other works of fiction, which would seem to indicate that it is possible to develop some formal model in which to represent and reason with these stories. In fact, time-travel stories that involve going back to an earlier time in the life of the protagonist may speak to an important theme of literature, used frequently in the works of authors such as Jane Austen (e.g., Pride and Prejudice, Emma, and Persuasion): the reparation of an error made during one’s (relative) youth. The desire to correct one’s mistakes, to recreate a world in which one can still achieve at least part of one’s goals, in which one’s missteps are not permanent, is perhaps one of the reasons that timetravel stories have such a hold on our imagination. Scope: The goal is to develop a representation in which one can represent and reason with time-travel stories. The aim is to develop a formal object-level theory that first, enables representation of a story as a formal timetravel narrative, and second, supports the inference that a time-travel narrative is motivated with respect to an agent and his goals. We do not claim that this model explains how time travel might actually happen. That is the focus of physicists’ approach to time travel: see Related Work. In this initial work, the bulk of the effort lies in constructing a representation that addresses several conceptual difficulties and showing by example that a timetravel narrative of reasonable complexity can be represented and reasoned with using this structure. This work focuses on backward time travel and restricts time travel to one agent at a time. Overview and Structure: We first present the working example (adapted from Star Trek). Next we discuss an extension to a branching-time temporal ontology that allows representation of paths that correspond to time travel. 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 a model can be constructed using this ontology that allows the representation of the working example. Next, we give the formal specification of the ontology and model, give a formal characterization of motivated time-travel narratives, and discuss the inferences that this model supports. We discuss whether time-travel paradoxes arise within the model. We conclude with a discussion of related work, evaluation, and future work.