A Theory for Convex Interval Relations including Unbounded Intervals

We extend the basic axiomatization of interval convex relations by Allen and Hayes with unbounded intervals. Unbounded intervals include since intervals with a finite beginning point and infinite ending point, until intervals with an infinite beginning point and finite ending point and the constant alltime representing the whole time line, with both extreme points being infinite. A number of results show the adequacy of the axiomatization proposed; in particular, unbounded intervals are proven to contain unbounded sequences of meeting intervals extending towards the past and/or the future. Importantly, the theory is proven to be consistent.