A More Efficient Knowledge Representation for Allen’s Algebra and Point Algebra

Abstract

In many AI applications, one has incomplete qualitative knowledge about the order of occurring events. A common way to express knowledge about this temporal reasoning problem is Allen’s interval algebra. Unfortunately, its main interesting reasoning tasks, consistency check and minimal labeling, are intractable (assuming P ≠ NP). Mostly, reasoning tasks in tractable subclasses of Allen’s algebra are performed with constraint propagation techniques. This paper presents a new reasoning approach that performs the main reasoning tasks much more efficient than traditional constraint propagation methods. In particular, we present a sound and complete O(n ²)-time algorithm for minimal labeling computation that can be used for the pointisable subclass of Allen’s algebra.