Abstract

Many practical problems including planning and scheduling involve representation of, and reasoning with, temporal constraints that in general specify a relation between a pair of temporal primitives.

In many practical application domains temporal constraints can not be specified precisely. To make the results more realistic, it is important to introduce uncertainty into the problem specification by providing inexact temporal constraints. A set of results derived by a scheduling system with different grades of certainty enriches the representative quality of the derived solution and presents more practical value than a set of results that are equally plausible. The mechanism of temporal constraint propagation, as an integral part of planning and scheduling systems, must have special reasoning capabilities and mechanisms in order to be able to process uncertainty in the temporal constraints.

This work presents an approach, in which possibility theory is applied to represent temporal properties of systems (such as dates, times, and durations of operations). While probability theory is the most explored way of modeling of uncertainty, it is computationally complex for practical applications. Possibilistic representation is used for modeling probabilistic distributions by approximation. This work provides necessary algorithms and describes how Petri net framework can be extended to handle temporal properties of systems with uncertain representation. An alternative approach is to extend temporal constraint networks by providing means for handling synchronization and for representing time in form of possibilistic distributions. Both of these approaches are studied to find how they can be used to model systems, in which recurrent events can occur. As a result, this work provides a framework for studying the problem of possibilistic propagation of temporal constraints and its application in temporal reasoning with recurrent events.

About the Speaker