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Temporal reasoning with constraints

This dissertation is focused on representing and reasoning about temporal information. We design general temporal languages supported by specialized efficient inference procedures. The contribution is in combining the existing logic-based temporal reasoning languages with the existing temporal constraint models, and in designing new efficient inference algorithms for the combined languages. We explore a specific combination of Datalog, a polynomial fragment of logic programming, with Temporal Constraint Satisfaction Problems (TCSP). To render this combination meaningful, attention is given to the formal syntax, semantics and the inference algorithms employed. We address some historical challenges relevant to the introduction of time and constraints into logic programming. 
The dissertation surveys and develops new and improved temporal constraint processing algorithms. When processing traditional Constraint Satisfaction Problems (CSP), path-consistency (PC) algorithms are polynomial. We demonstrate that when processing temporal constraints, PC is exponential, and thus does not scale up. To remedy this problem, two new polynomial algorithms are introduced: Upper Lower Tightening (ULT) and Loose Path Consistency (LPC). These algorithms are complete for a class of problems, called the STAR class. The empirical evaluation of these algorithms demonstrates a substantial performance improvement (up to six orders of magnitude) relative to other algorithms. We also demonstrate the existence of a phase transition for TCSPs.