Incremental Tractable Reasoning about Qualitative Temporal Constraints

In many applications of temporal reasoning we are in­ terested in reasoning incrementally In particular, given a CSP of temporal constrains and a new constraint, we want to maintain certain properties in the extended CSP (e.g., a solution), rather than recomputing them from scratch. The Point Algebra (PA) and the Interval Algebra (IA) are two well-known frameworks for qualitative tem­ poral reasoning. Most of the existing algorithms for PA and the known tractable fragments of IA, such as ORDHorn, has been designed for "static" reasoning. In this paper we study the incremental version of some funda­ mental problems of temporal reasoning, proposing new algorithms that amortize their complexity when process­ ing a sequence of input constraints. After analyzing the role of path-consistency for incremental satisfiability, we propose algorithms for maintaining a solution of a CSP over either PA or ORD-Horn, and the minimal labels of a CSP over PA. Our algorithms improve the complexity of using existing techniques by a factor of where n is the number of variables involved in the CSP.