Allen’s interval algebra and smart-type environments

Abstract

Allen’s interval algebra is a calculus for temporal reasoning that was introduced in 1983. Reasoning with qualitative time in Allen’s full interval algebra is nondeterministic polynomial time (NP) complete. Research since 1995 identified maximal tractable subclasses of this algebra via exhaustive computer search and also other ad-hoc methods. In 2003, the full classification of complexity for satisfiability problems over constraints in Allen’s interval algebra was established algebraically. Recent research proposed scheduling based on the Fishburn-Shepp correlation inequality for posets. This article first reviews Allen’s calculus and surrounding computational issues in temporal reasoning. We then go on to describe three potential temporal-related application areas as candidates for scheduling using the Fishburn-Shepp inequality. We also illustrate through concrete examples, and conclude the importance of Fishburn-Shepp inequality for the suggested application areas that are the development of smart homes, intelligent conversational agents and in physiology with emphasis during time-trial physical exercise. The Fishburn-Shepp inequality will enable the development of smart type devices, which will in turn help us to have a better standard of living.