Complexity Results for First-Order Theories of Temporal Constraints

We study the complexity of quantiier elimination and decision in rst-order theories of temporal constraints. With the exception of Ladkin, AI researchers have largely ignored this problem. We consider the rst-order theories of point and interval constraints over two time structures: the integers and the ra-tionals. We show that in all cases quantiier-elimination can be done in PSPACE. We also show that the decision problem for arbitrarily quantiied sentences is PSPACE-complete while for 9 k sentences it is p k-complete. Our results must be of interest to researchers working on temporal constraints, computational complexity of logical theories, constraint databases and constraint logic programming .