A Theory for Convex Interval Relations including Unbounded Intervals.
Diana Cukierman, James P. Delgrande · 2004
fdiana,jimgcs.sfu.ca We extend the basic axiomatization of interval convex rela-tions by Allen and Hayes with unbounded intervals. Un-bounded intervals include since intervals with a finite begin-ning point and infinite ending point, until intervals with an in-finite 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 in-tervals are proven to contain unbounded sequences of meet-ing intervals extending towards the past and/or the future. Im-portantly, the theory is proven to be consistent.