Efficient Algorithms for Fuzzy Qualitative Temporal Reasoning

Fuzzy qualitative temporal relations have been proposed to reason about events whose temporal boundaries are ill defined. Although the corresponding reasoning tasks are in the same complexity class as their crisp counterparts, in practice, the scalability of fuzzy temporal reasoners may be insufficient for applications that require a high expressivity and deal with a large number of events. On the other hand, transitivity rules can be used to make sound but incomplete inferences in polynomial time, utilizing a variant of Allen´s path-consistency algorithm. The aim of this paper is to investigate how this polynomial time algorithm can be improved without altering its time complexity. To this end, we establish a characterization of 2-consistency of fuzzy temporal relations and provide transitivity rules that are significantly stronger than those resulting from straightforwardly generalizing transitivity rules for crisp temporal relations. We furthermore provide experimental evidence for the effectiveness of our improved algorithm.