A Divide-and-Conquer Approach for Solving Interval Algebra Networks

Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding consistency. We identify a key theoretical property of a qualitative calculus that ensures the soundness and completeness of this method, and show that it is satisfied by the Interval Algebra (IA) and the Point Algebra (PA). We develop a new encoding scheme for IA networks based on a combination of our divide-and-conquer method with an existing encoding of IA networks into SAT. We empirically show that our new encoding scheme scales to much larger problems and exhibits a consistent and significant improvement in efficiency over state-of-the-art solvers on the most difficult instances

Qualitative Spatial and Temporal Reasoning with Answer Set Programming

Representing and reasoning spatial and temporal information is a key research issue in Computer Science and Artificial Intelligence. In this paper, we introduce tools that produce three novel encodings which translate problems in qualitative spatial and temporal reasoning into logic programs for answer set programming solvers. Each encoding reflects a different type of modeling abstraction. We evaluate our approach with two of the most well known qualitative spatial and temporal reasoning formalisms, the Interval Algebra and Region Connection Calculus. Our results show some surprising findings, including the strong performance of the solver for disjunctive logic programs over the non-disjunctive ones on our benchmark problems

Automated complexity proofs for qualitative spatial and temporal calculi

Identifying complexity results for qualitative spatial or temporal calculi has been an important research topic in the past 15 years. Most interesting calculi have been shown to be at least NP-complete, but if tractable fragments of the calculi can be found then efficient reasoning with these calculi is possible. In order to get the most efficient reasoning algorithms, we are interested in identifying maximal tractable fragments of a calculus (tractable fragments such that any extension of the fragment leads to NP-hardness). All required complexity proofs are usually made manually, sometimes using computer assisted enumerations. In a recent paper by Renz (2007), a procedure was presented that automatically identifies tractable fragments of a calculus. In this paper we present an efficient procedure for automatically generating NP-hardness proofs. In order to prove correctness of our procedure, we develop a novel proof method that can be checked automatically and that can be applied to arbitrary spatial and temporal calculi. Up to now, this was believed to be impossible. By combining the two procedures, it is now possible to identify maximal tractable fragments of qualitative spatial and temporal calculi fully automatically