Anthony G. Cohn

Qualitative Spatial Representation and Reasoning with the Region Connection Calculus

This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned.

Qualitative spatial representation and reasoning

Publisher Summary Early attempts at qualitative spatial reasoning within the qualitative reasoning (QR) community led to the poverty conjecture. The need for spatial representations and spatial reasoning is ubiquitous in artificial intelligence (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 (GIScience) have also driven the spatial representation and reasoning community to produce efficient, expressive, and useful calculi. There has been considerable research in spatial representations that are based on metric measurements, in particular within the vision and robotics communities, and also on raster and vector representations in GIScience. This chapter focuses on symbolic and, in particular, qualitative representations. The challenge of qualitative spatial reasoning (QSR) is to provide calculi that allow a machine to represent and reason with spatial entities without resort to the traditional quantitative techniques prevalent in, for example, computer graphics or computer vision communities.

Qualitative Spatial Representation and Reasoning Techniques

The field of Qualitative Spatial Reasoning is now an active research area in its own right within AI (and also in Geographical Information Systems) having grown out of earlier work in philosophical logic and more general Qualitative Reasoning in AI. In this paper (which is an updated version of [25]) I will survey the state of the art in Qualitative Spatial Reasoning, covering representation and reasoning issues as well as pointing to some application areas.

Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning

In this paper we advocate the use of multi-dimensional modal logics as a framework for knowledge representation and, in particular, for representing spatio-temporal information. We construct a two-dimensional logic capable of describing topological relationships that change over time. This logic, called PSTL (Propositional Spatio-Temporal Logic) is the Cartesian product of the well-known temporal logic PTL and the modal logic S4u, which is the Lewis system S4 augmented with the universal modality. Although it is an open problem whether the full PSTL is decidable, we show that it contains decidable fragments into which various temporal extensions (both point-based and interval based) of the spatial logic RCC-8 can be embedded. We consider known decidability and complexity results that are relevant to computation with multi-dimensional formalisms and discuss possible directions for further research.

Qualitative and Topological Relationships in Spatial Databases

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed.

Representing and Reasoning with Qualitative Spatial Relations About Regions

Qualitative Reasoning (QR) has now become a mature subfield of AI as its tenth annual international workshop, several books (e.g. (Weld and de Kleer, 1990; Faltings and Struss, 1992)) and a wealth of conference and journal publications testify. QR tries to make explicit our everyday commonsense knowledge about the physical world and also the underlying abstractions used by scientists and engineers when they create models. Given this kind of knowledge and appropriate reasoning methods, a computer could make predictions and diagnoses and explain the behavior of physical systems in a qualitative manner, even when a precise quantitative description is not available or is computationally intractable. Note that a representation is not normally deemed to be qualitative by the QR community simply because it is symbolic and utilizes discrete quantity spaces but because the distinctions made in these discretizations are relevant to high-level descriptions of the system or behavior being modeled.

Computing Transivity Tables: A Challenge For Automated Theorem Provers

Implementations of Allens interval-based temporal logic and a recently developed simulation system for reasoning about space and time, both require the use of transitivity tables. Although strategies exist to construct such tables, the proofs which underly the entries in the table are both tedious to do and in some cases difficult to secure. Often a difficult proof is only obtained via lemmas; moreover, finding models for satisfiable sets of dyadic relations in the theory introduces its own difficulties. This paper presents the problems. Any automated theorem prover which can effectively generate the entries for such transitivity tables would mark significant progress in automated theorem proving.

Calculi for Qualitative Spatial Reasoning

Although Qualitative Reasoning has been a lively subfield of AI for many years now, it is only comparatively recently that substantial work has been done on qualitative spatial reasoning; this paper lays out a guide to the issues involved and surveys what has been achieved. The papers is generally informal and discursive, providing pointers to the literature where full technical details may be found.

Constructing qualitative event models automatically from video input

Abstract We describe an implemented technique for generating event models automatically based on qualitative reasoning and a statistical analysis of video input. Using an existing tracking program which generates labelled contours for objects in every frame, the view from a fixed camera is partitioned into semantically relevant regions based on the paths followed by moving objects. The paths are indexed with temporal information so objects moving along the same path at different speeds can be distinguished. Using a notion of proximity based on the speed of the moving objects and qualitative spatial reasoning techniques, event models describing the behaviour of pairs of objects can be built, again using statistical methods. The system has been tested on a traffic domain and learns various event models expressed in the qualitative calculus which represent human observable events. The system can then be used to recognise subsequent selected event occurrences or unusual behaviours.

The EGG/YOLK reliability hierarchy: semantic data integration using sorts with prototypes

Integration of disparate heterogeneous databases requires translation of types. Because a type in one system often has no exact counterpart in the others, fully reliable integration requires deep understanding of the subject domain, with conceptual analysis of type meanings. So far, reliable translation has had to be done by hand. In practice, few types are so crucial as to require full reliability. The EGG/YOLK hierarchy ranks types by the tolerable rashness in translation, based on prototypes in each type. Each defined class (EGG) has a subclass of typical members (YOLK) defined. We exploit Cui, Cohn and Randells Qualitative Spatial Simulation program to create the hierarchy of all possible relations between source and target EGG/YOLK types, ranked by reliability. Our eventual ranking is based on a poset combining four different preference criteria.