Finding a Solution, all Solutions, or the Most Probable Solution to a Temporal Interval Algebra Network

the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks. I. INTRODUCTION LLEN [1] defines a temporal reasoning approach based on intervals and the 13 possible binary relations between them. The relations are before (b), meets (m), overlaps (o), during (d), starts (s), finishes (f), and equals (=). Each relation has an inverse. The inverse symbol for b is bi and similarly for the others: mi, oi, di, si, and fi. The inverse of equals is equals. A relation between two intervals is restricted to a disjunction of the basic relations, which is represented as a set. For example, (A m B) V (A o B) is written as A {m,o} B. The relation between two intervals is allowed to be any subset of I An IA (interval algebra) network is a graph where each node represents an interval. Directed edges in the network are labeled with subsets of I. By convention, edges labeled with I are not shown. An IA network is consistent (or satisfiable) if each interval in the network can be mapped to a real interval such that all the constraints on the edges hold (i.e., one disjunct on each edge is true).