An extended temporal system based on points and intervals

摘要

This paper proposes axioms for temporal systems based on a discrete set of intervals and points which are treated equally as primitive elements. Temporal ordering is specified by means of the primitive relation “meets”. The axioms, and a graphical representation of temporal knowledge, are specified formally by using the Z language. A consistency condition for a temporal database is given in terms of the cyclic properties of the graphical representation, and an algorithm for consistency checking is provided. Formal proofs of Allen's transitivity table for interval relations are given. The paper addresses some hitherto unresolved issues in the use of interval based systems for temporal databases and proposes a solution. These issues are the problems involved in modelling “open” and “closed” intervals.