We exploit graph-theoretic techniques to efficiently reason about partially ordered events in the Event Calculus. We replace the traditional generate-and-test reasoning strategy by a more efficient generate-only one that operates on the underlying directed acyclic graph of events representing ordering information by pairing breadth-first and depth-first visits in a suitable way. We prove the soundness and completeness of the proposed strategy, and thoroughly analyze its computational complexity. Furthermore, we show how it can be generalized to deal with the Modal Event Calculus, that provides a uniform modal framework for the basic Event Calculus and its skeptical and credulous variants.
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