In this paper, we show how well-known graph-theoretic techniques can be successfully explotied to efficiently reason about partially ordered events in Kowalski and Sergot's Event Calculus and in its skeptical and credulous modal variants. We replace the traditional generate-and-test strategy of (Modal) Event Calculus by a generate-only strategy that operates on the transitive closure and reduction of the underlying directed acyclic graph a events. we prove the soundness and completeness of the proposed strategy, and thoroughly analyze its computational complexity.
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