The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science

GQR (Generic Qualitative Reasoner) is a solver for binary qualitative constraint networks. GQR takes a calculus description and one or more constraint networks as input, and tries to solve the networks using the path consistency method and (heuristic) backtracking. In contrast to specialized reasoners, it offers reasoning services for different qualitative calculi, which means that these calculi are not hard-coded into the reasoner. Currently, GQR supports arbitrary binary constraint calculi developed for spatial and temporal reasoning, such as calculi from the RCC family, the intersection calculi, Allen’s interval algebra, cardinal direction calculi, and calculi from the OPRA family. New calculi can be added to the system by specifications in a simple text format or in an XML file format. The tool is designed and implemented with genericity and extensibility in mind, while preserving efficiency and scalability. The user can choose between different data structures and heuristics, and new ones can be easily added to the object-oriented framework. GQR is free software distributed under the terms of the GNU General Public License.

Jae Hee Lee and Diedrich Wolter: A new perspective on reasoning with qualitative spatial knowledge 3

In the past years a lot of research effort has been put into finding tractable subsets of spatial and temporal calculi. It has been shown empirically that large tractable subsets of these calculi not only provide efficient algorithms for reasoning problems that can be expressed with relations contained in the tractable subsets, but also surprisingly efficient solutions to the general, NP-hard reasoning problems of the full calculi. An important step in this direction was the refinement algorithm which provides a heuristic for proving tractability of given subsets of relations. In this paper we extend the refinement algorithm and present a procedure which identifies large tractable subsets of spatial and temporal calculi automatically without any manual intervention and without the need for additional NP-hardness proofs. While we can only guarantee tractability of the resulting sets, our experiments show that for RCC8 and the Interval Algebra, our procedure automatically identifies all maximal tractable subsets. Using our procedure, other researchers and practitioners can automatically develop efficient reasoning algorithms for their spatial or temporal calculi without any theoretical knowledge about how to formally analyse these calculi. 1

Qualitative Spatial and Temporal Reasoning (QSR) is concerned with constraint-based formalisms for representing, and reasoning with, spatial and temporal information over infinite domains. Within the QSR community it has been a widely accepted assumption that genuine qualitative reasoning methods outperform other reasoning methods that are applicable to encodings of qualitative CSP instances. Recently this assumption has been tackled by several authors, who proposed to encode qualitative CSP instances as finite CSP or SAT instances. In this paper we report on the results of a broad empirical study in which we compared the performance of several reasoners on instances from different qualitative formalisms. Our results show that for small-sized qualitative calculi (e.g., Allen’s interval algebra and RCC-8) a state-of-theart implementation of QSR methods currently gives the most efficient performance. However, on recently suggested large-size calculi, e.g., OPRA4, finite CSP encodings provide a considerable performance gain. These results confirm a conjecture by Bessière stating that support-based constraint propagation algorithms provide better performance for large-sized qualitative calculi. 1

Abstract. In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s cardinal direction calculus, Freksa’s double cross calculus, Egenhofer and Franzosa’s intersection calculi, and Randell, Cui, and Cohn’s region connection calculi. These calculi are designed for modeling specific aspects of space or time, respectively, to the effect that the class of intended models may vary widely with the calculus at hand. But from a formal point of view these calculi are often closely related to each other. For example, the spatial region connection calculus RCC5 may be considered a coarsening of Allen’s (temporal) interval calculus. And vice versa, intervals can be used to represent spatial objects that feature an internal direction. The central question of this paper is how these calculi as well as their mutual dependencies can be axiomatized by algebraic specifications. This question will be investigated within the framework of the Common Algebraic Specification Language (CASL), a specification language developed by the Common Framework Initiative for algebraic specification and development (COFI). We explain scope and expressiveness of CASL by discussing the specifications of some of the calculi mentioned before. 1

In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the past 25 years, a large number of calculi for efficient reasoning about spatial and temporal entities has been developed. Reasoning techniques developed for these constraint calculi typically rely on so-called composition tables of the calculus at hand, which allow for replacing semantic reasoning by symbolic operations. Often these composition tables are developed in a quite informal, pictorial manner and hence composition tables are prone to errors. In view of possible safety critical applications of qualitative calculi, however, it is desirable to formally verify these composition tables. In general, the verification of composition tables is a tedious task, in particular in cases where the semantics of the calculus depends on higher-order constructs such as sets. In this paper we address this problem by presenting a heterogeneous proof method that allows for combining a higherorder proof assistance system (such as Isabelle) with an automatic (first order) reasoner (such as SPASS or VAMPIRE). The benefit of this method is that the number of proof obligations that is to be proven interactively with a semi-automatic reasoner can be minimized to an acceptable level.

Abstract. A multitude of calculi for qualitative spatial reasoning (QSR) have been proposed during the last two decades. The number of practical applications that make use of QSR techniques is, however, comparatively small. One reason for this may be seen in the difficulty for people from outside the field to incorporate the required reasoning techniques into their software. Sometimes, proposed calculi are only partially specified and implementations are rarely available. With the SparQ toolbox presented in this text, we seek to improve this situation by making common calculi and standard reasoning techniques accessible in a way that allows for easy integration into applications. We hope to turn this into a community effort and encourage researchers to incorporate their calculi into SparQ. This text is intended to present SparQ to potential users and contributors and to provide an overview on its features and utilization. 1

Current research on qualitative spatial representation and reasoning usually focuses on one single aspect of space. However, in real world applications, several aspects are often involved together. This paper extends the well-known RCC8 constraint language to deal with both topological and directional information, and then investigates the interaction between the two kinds of information. Given a topological (RCC8) constraint network and a directional constraint network, we ask when the joint network is satisfiable. We show that when the topological network is over one of the three maximal tractable subclasses of RCC8, the problem can be reduced into satisfiability problems in the RCC8 algebra and the rectangle algebra (RA). Therefore, reasoning techniques developed for RCC8 and RA can be used to solve the satisfiability problem of a joint network. 1

Abstract. Qualitative spatial and temporal calculi are usually formulated on a particular level of granularity and with a particular domain of spatial or temporal entities. If the granularity or the domain of an existing calculus doesn’t match the requirements of an application, it is either possible to express all information using the given calculus or to customize the calculus. In this paper we distinguish the possible ways of customizing a spatial and temporal calculus and analyze when and how computational properties can be inherited from the original calculus. We present different algorithms for customizing calculi and proof techniques for analyzing their computational properties. We demonstrate our algorithms and techniques on the Interval Algebra for which we obtain some interesting results and observations. We close our paper with results from an empirical analysis which shows that customizing a calculus can lead to a considerably better reasoning performance than using the non-customized calculus. 1