Qualitative Simulation as a Temporally-extended Constraint Satisfaction Problem

Traditionally, constraint satisfaction problems (CSPs) are characterized using a finite set of constraints expressed within a common, shared constraint language. When reasoning across time, however, it is possible to express both temporal and state-based constraints represented within multiple constraint languages. Qualitative simulation provides an instance of this class of CSP in which, traditionally, all solutions to the CSP are computed. In this paper, we formally describe this class of temporally-extended CSPs and situate qualitative simulation within this description. This is followed by a description of the DecSIM algorithm which is used to incrementally generate all possible solutions to a temporally-extended CSP. DecSIM combines problem decomposition, a tree-clustering algorithm and ideas similar to directed arc--consistency to exploit structure and causality within a qualitative model resulting in an exponential speed-up in simulation time when compared to existing techniques.