Convex Relations Between Time Intervals

Abstract

We describe a fragment of Allen’s full algebra of time interval relations (the algebra of convex relations) that is useful for describing the dynamic behavior of technical systems. After an intuitive description of the fragment we give two formal definitions and prove that they are equivalent. This provides the basis for the major result of the paper: in a time net in which all interval relations are convex the test for the global consistency of the edge labelling can be carried out in polynomial time (in the general case it is NP-complete). This result makes convex interval relations an attractive candidate whereever qualitative reasoning about technical systems requires testing for global instead of local consistency.