# Towards Feasible Approach to Plan Checking under Probabilistic Uncertainty: Interval Methods

Raúl Trejo and Vladik Kreinovich, University of Texas at El Paso; Chitta Baral, Arizona State University

The main problem of {\it planning} is to find a sequence of actions that an agent must perform to achieve a given objective. An important part of planning is checking whether a given plan achieves the desired objective. Historically, in AI, the planning and plan checking problems were mainly formulated and solved in a {\it deterministic} environment, when the initial state is known precisely and when the results of each action in each state is known (and uniquely determined). In this deterministic case, planning is difficult, but plan checking is straightforward. In many real-life situations, we only know the probabilities of different fluents; in such situations, even plan checking becomes computationally difficult. {\em In this paper, we describe how methods of interval computations can be used to get a feasible approximation to plan checking under probabilistic uncertainty.} The resulting method is a natural generalization of 0-approximation proposed earlier to describe planning in the case of partial knowledge. It turns out that some of the resulting probabilistic techniques coincides with heuristically proposed fuzzy methods. Thus, we justify these fuzzy heuristics as a reasonable feasible approximation to the (NP-hard) probabilistic problem.