Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra

Bernhard Nebel, Hans-Jürgen Bürckert

DFKI DFKI Research Reports (RR) 93-11 1993.


We introduce a new subclass of Allen's interval algebra we call "ORD-Horn subclass", which is a strict superset of the "pointisable subclass". We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming P≠NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations.

RR-93-11.pdf (pdf, 253 KB )

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence