Decremental Consistency Checking Of Temporal Constraints: Algorithms For The Point Algebra And The Ord-Horn Class

Deciding consistency of a set of temporal constraints (CSP) over either the Point Algebra (PA) or the Interval Algebra (IA) is a fundamental problem in qualitative temporal reasoning. Given an inconsistent temporal CSP and a sequence of constraint relaxations to perform, incrementally decided by the user or an application, decremental consistency checking is the problem of determining if the revised CSP becomes consistent after each relaxation. We propose new algorithms for decremental consistency checking of a CSP over either PA or the ORD-Horn subalgebra of IA. These techniques exploit a graph representation of the CSP and some data structures that are maintained at each relaxation. An experimental analysis shows that solving decremental consistency checking using our algorithms can be significantly faster than using existing static algorithms.