Time Representation and Temporal Reasoning from the Perspective of Non-Standard Analysis

This paper proceeds to develop models for representing time and reasoning about time from the perspective of nonstandard analysis. It sets out a non-standard first-order theory and a non-standard qualitative approach for hyperreals. This first-order theory and this qualitative approach are based on the fact that any hyperreal is either infinitesimal, unlimited or appreciable. Within the first-order theory for hyperreal time presented in this paper, we establish a complete axiomatization and we prove that the associated membership problem is PSPACE-complete. Within the qualitative approach for hyperreal time presented in this paper, we establish qualitative constraint satisfaction problems and we prove that the associated consistency problem is in P .