Towards a general temporal theory
The research work presented herein addresses time representation and temporal reasoning in the domain of artificial intelligence. A general temporal theory, as an extension of Alien and Hayes', Gallon's and Vilain's theories, is proposed which treats both time intervals and time points on an equal footing; that is, both intervals and points are taken as primitive time elements in the theory. This means that neither do intervals have to be constructed out of points, nor do points have to be created as some limiting construction of intervals. This approach is different from that of Ladkin, of Van Beek, of Dechter, Meiri and Pearl, and of Maiocchi, which is either to construct intervals out of points, or to treat points and intervals separately. The theory is presented in terms of a series of axioms which characterise a single temporal relation, "meets", over time elements. The axiomatisation allows non-linear time structures such as branching time and parallel time, and additional axioms specifying the linearity and density of time are specially presented. A formal characterisation for the open and closed nature of primitive intervals, which has been a problematic question of time representation in artificial intelligence, is provided in terms of the "meets" relation. It is shown to be consistent with the conventional definitions of open/closed intervals which are constructed out of points. It is also shown that this general theory is powerful enough to subsume some representative temporal theories, such as Alien and Hayes's interval based theory, Bruce's and McDermott's point based theories, and the interval and point based theory of Vilain, and of Gallon. A finite time network based on the theory is specially addressed, where a consistency checker in two different forms is provided for cases with, and without, duration reasoning, respectively. Utilising the time axiomatisation, the syntax and semantics of a temporal logic for reasoning about propositions whose truth values are associated with particular intervals/points are explicitly defined. It is shown that the logic is more expressive than that of some existing systems, such as Alien's interval-based logic, the revised theory proposed by Gallon, Shoham's point-based interval logic, and Haugh's MTA based logic; and the corresponding problems with these systems are satisfactorily solved. Finally, as an application of the temporal theory, a new architecture for a temporal database system which allows the expression of relative temporal knowledge of data transaction and data validity times is proposed. A general retrieval mechanism is presented for a database with a purely qualitative temporal component which allows queries with temporal constraints in terms of any logical combination of Alien's temporal relations. To reduce the computational complexity of the consistency checking algorithm when quantitative time duration knowledge is added, a class of databases, termed time-limited databases, is introduced. This class allows absolute-time-stamped and relative time information in a form which is suitable for many practical applications, where qualitative temporal information is only occasionally needed, and the efficient retrieval mechanisms for absolute-time-stamped databases may be adopted.