Abduction in Annotated Probabilistic Temporal Logic

Annotated Probabilistic Temporal (APT) logic programs are a form of logic programs that allow users to state (or systems to automatically learn)rules of the form ``formula G becomes true K time units after formula F became true with L to U% probability.'' In this paper, we develop a theory of abduction for APT logic programs. Specifically, given an APT logic program Pi, a set of formulas H that can be ``added'' to Pi, and a goal G, is there a subset S of H such that Pi \cup S is consistent and entails the goal G? In this paper, we study the complexity of the Basic APT Abduction Problem (BAAP). We then leverage a geometric characterization of BAAP to suggest a set of pruning strategies when solving BAAP and use these intuitions to develop a sound and complete algorithm.