A unifying approach to temporal constraint reasoning

Abstract

We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomial-time satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORD-Horn algebra by Nebel and Bürckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable unifying formalism for reasoning about temporal constraints.