This thesis is a confluence of three problems in constraint reasoning: qualitative temporal reasoning (QTR), incremental reasoning, and explanation generation. We first address a set of algorithms to solve the QTR for point algebra (PA) with explanation. Next, we turn to the tractable form of Allen’s Interval Algebra (IA). For both problems, an incremental version of the problem, where a new temporal object is added to a set of objects committed on the time-line, is being studied. We provide a model or solution space for the new object, if it exists, otherwise, for (PA) and a particular subalgebra of (IA) called ORD-Horn, we provide explanation for inconsistency. Both the problems of incremental reasoning and explanation generation are based on some recent investigation in constraint programming.
Launay, Florent Marie and Mitra, Debasis, "Culprit Detection on Incremental Tractable Qualitative Temporal Reasoning Problems" (2006). Electrical Engineering and Computer Science Student Publications. 13.