On the consistency problem for the INDU calculus

In this paper, we further investigate the consistency problem for the qualitative temporal calculus INDU introduced by Pujari et al. [A.K. Pujari, G.V. Kumari, A. Sattar, INDU: An interval and duration network, in: Australian Joint Conference on Artificial Intelligence, 1999, pp. 291-303]. We prove the intractability of the consistency problem for the subset of pre-convex relations, and the tractability of strongly pre-convex relations. Furthermore, we also define another interesting set of relations for which the consistency problem can be decided by the ⋄-closure method, a method similar to the usual path-consistency method. Finally, we prove that the ⋄-closure method is also complete for the set of atomic relations of INDU implying that the intervals have the same duration.