Fundamenta Informaticae - Volume 46, issue 1-2

Authors: Düntsch, Ivo

Article Type: Other

Keywords:

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. v-vi, 2001

Authors: Cohn, A.G. | Hazarika, S.M.

Article Type: Research Article

Abstract: The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33,34].

Keywords: Qualitative Spatial Reasoning, Ontology

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 1-29, 2001

Authors: Davis, Ernest

Article Type: Research Article

Abstract: A natural approach to defining continuous change of shape is in terms of a metric that measures the difference between two regions. We consider four such metrics over regions: the Hausdorff distance, the dual-Hausdorff distance, the area of the symmetric difference, and the optimal-homeomorphism metric (a generalization of the Fréchet distance). Each of these gives a different criterion for continuous change. We establish qualitative properties of all of these; in particular, the continuity of basic functions …such as union, intersection, set difference, area, distance, and smoothed circumference and the transition graph between RCC-8 relations. We also show that the history-based definition of continuity proposed by Muller is equivalent to continuity with respect to the Hausdorff distance. Show more

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Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 31-54, 2001

Authors: Galton, Antony

Article Type: Research Article

Abstract: Dominance diagrams are an extension of the conceptual neighbourhood diagrams (CNDs) that have become familiar in the areas of qualitative spatial and temporal knowledge representation. They are also related to the envisionment diagrams of qualitative physics. This paper explains the concept of dominance between qualitative states and shows how, by adding a representation of this relation to CNDs, it is possible to reason more effectively about the temporal incidence of the qualitative states represented …in the diagrams; in addition, dominance turns out to be of importance in determining the structure of composite diagrams formed as the product of existing diagrams. It is further shown that the appropriate theoretical underpinning for dominance diagrams is the mathematical theory of T0 topological spaces. Show more

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 55-70, 2001

Authors: Düntsch, Ivo | Orłowska, Ewa | Wang, Hui

Article Type: Research Article

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 71-82, 2001

Authors: Polkowski, Lech

Article Type: Research Article

Abstract: Rough mereology is a paradigm for reasoning under uncertainty whose primitive notion is that of being a part to a degree; hence, rough mereology falls in the province of mereology-based theories for reasoning about complex objects. Among mereological theories of objects, theories based on the primitive notion of a connection distinguish themselves by a variety of applications of which we would like to mention the area of Qualitative Spatial Reasoning. In this paper, we define rough …mereologies within the realm of mereologies based on the primitive notion of a part and we show that in this framework one may induce notions of connection closely related to initial rough mereologies in the sense that they induce the same notion of a part. We also address the distributed environment proving some results about connection preservation throughout the reasoning system. Show more

Keywords: ontology, mereology, rough mereology, connection, Čech topology

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 83-96, 2001

Authors: Bittner, Thomas

Article Type: Research Article

Abstract: This paper provides an ontological analysis of built environments. It shows that boundaries are ontologically salient features of built environments and that there are different kinds of boundaries that that need to be considered. It discusses in particular the important role of fiat boundaries. At the level of objects built environments are formed by partition forming objects and populated by non-partition forming objects. The underlying partition structure is the main organizational structure of a …built environment. Non-partition forming objects are potentially movable and their movement is constrained by the barrier properties of the boundaries of other objects forming or populating the environment. This paper argues that the qualitative formalization of built environments needs to take into account: (1) the fundamental role of boundaries, (2) the distinction between bona-fide and fiat boundaries and objects, (3) the different character of constraints on relations between these different kinds of boundaries and objects, (4) the distinction between partition forming and non-partition forming objects, and (5) the fundamental organizational structure of regional partitions. It discusses the notion of object-boundary sensitive rough location and shows that a formalization based on this notion takes these points into account. Show more

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 97-128, 2001

Authors: Schoop, Dominik J.

Article Type: Research Article

Abstract: It is considered the virtue of mereotopology that it takes regions instead of points to be the primitive entities of space. As mereotopology is assumed to avoid the difficulties incurred by considering points as primitive entities, mereotopology is thought to provide the means for common-sense spatial representation and reasoning. However, we show that considering regions as primitive entities in mereotopology does not prevent us referring to points in a commonly used mereotopological first-order language. Therefore, the …difficulties attributed to taking points as primitive entities must be considered even for point-free mereotopologies. Consequently, the virtue of mereotopology cannot lie in taking regions instead of points as primitive entities. On the contrary, we argue that the virtue of mereotopology is its capability to treat regions and points as primitive entities. Show more

Keywords: mereotopology, ontology, spatial representation and reasoning

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 129-143, 2001

Authors: Bennett, Brandon

Article Type: Research Article

Abstract: Region Based Geometry (RBG) is an axiomatic theory of qualitative configurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1st-order axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting …inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over R. Show more

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Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 145-158, 2001

Authors: Pratt-Hartmann, Ian

Article Type: Research Article

Abstract: Suppose we want to develop a theory of space in which the primary entities are not points, but regions. How do we proceed? Historically, the most popular approach is to select a group of spatial relations corresponding to familiar spatial concepts, and then to construct an axiomatic system …governing these relations. The appropriateness of this axiomatic system is to be judged on the basis of its ability to chime with pre-theoretic intuition and of its success in a larger theory of scientific or commonsense spatial reasoning. In this paper, we argue that this approach is flawed, and leads only to labyrinthine systems of doubtful theoretical or practical value. We present an alternative approach which substitutes mathematical rigour for pre-theoretic intuition, and which at the same time provides a real guarantee of practical applicability. Show more

Keywords: Spatial reasoning, mereology, topology, ontology

Citation: Fundamenta Informaticae, vol. 46, no. 1-2, pp. 159-186, 2001