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1

On minimal models of the Region Connection Calculus

Xia L., Li S.

Fundamenta Informaticae

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2006

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Vol. 69, nr 4

427-446

EN

Region Connection Calculus (RCC) is one primary formalism of qualitative spatial reasoning. Standard RCC models are continuous ones where each region is infinitely divisible. This contrasts sharply with the predominant use of finite, discrete models in applications. In a recent paper, Li et al. (2004) initiate a study of countable models that can be constructed step by step from finite models. Of course, some basic problems are left unsolved, for example, how many non-isomorphic countable RCC models are there? This paper investigates these problems and obtains the following results: (i) the exotic RCC model described by Gotts (1996) is isomorphic to the minimal model given by Li and Ying (2004); (ii) there are continuum many non-isomorphic minimal RCC models, where a model is minimal if it can be isomorphically embedded in each RCC model.

2

Contact Algebras and Region-based Theory of Space: Proximity Approach - II

Dimov G., Vakarelov D.

Fundamenta Informaticae

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2006

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Vol. 74, nr 2,3

251-282

EN

This paper is the second part of the paper [2]. Both of them are in the field of region-based (or Whitehedian) theory of space, which is an important subfield of Qualitative Spatial Reasoning (QSR). The paper can be considered also as an application of abstract algebra and topology to some problems arising and motivated in Theoretical Computer Science and QSR. In [2], different axiomatizations for region-based theory of space were given. The most general one was introduced under the name ``Contact Algebra". In this paper some categories defined in the language of contact algebras are introduced. It is shown that they are equivalent to the category of all semiregular T0-spaces and their continuous maps and to its full subcategories having as objects all regular (respectively, completely regular; compact; locally compact) Hausdorff spaces. An algorithm for a direct construction of all, up to homeomorphism, finite semiregular T0-spaces of rank n is found. An example of an RCC model which has no regular Hausdorff representation space is presented. The main method of investigation in both parts is a lattice-theoretic generalization of methods and constructions from the theory of proximity spaces. Proximity models for various kinds of contact algebras are given here. In this way, the paper can be regarded as a full realization of the proximity approach to the region-based theory of space.

3

Contact Algebras and Region-based Theory of Space: A Proximity Approach - I

Dimov G., Vakarelov D.

Fundamenta Informaticae

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2006

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Vol. 74, nr 2,3

209-249

EN

This work is in the field of region-based (or Whitehedian) theory of space, which is an important subfield of Qualitative Spatial Reasoning (QSR). The paper can be considered also as an application of abstract algebra and topology to some problems arising and motivated in Theoretical Computer Science and QSR Different axiomatizations for region-based (or Whiteheadian) theory of space are given. The most general one is introduced under the name ``Contact Algebra". Adding some extra first- or second-order axioms to those of contact algebras, some new or already known algebraic notions are obtained. Representation theorems and completion theorems for all such algebras are proved. Extension theories of the classes of all semiregular T0-spaces and all N-regular (a notion introduced here) T1-spaces are developed.

4

On countable RCC models

Li S., Ying M., Li Y.

Fundamenta Informaticae

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2005

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Vol. 65, nr 4

329--351

EN

Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These `standard' models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers' attention to RCC models that can be constructed from finite models hierarchically. Compared with those `standard' models, these countable models have the nice property that regions where can be constructed in finite steps from basic ones. We first investigate properties of three countable models introduced by Düntsch, Stell, Li and Ying, resp. In particular, we show that (i) the contact relation algebra of our minimal model is not atomic complete; and (ii) these three models are non-isomorphic. Second, for each n > 0, we construct a countable RCC model that is a sub-model of the standard model over the Euclidean unit n-cube; and show that all these countable models are non-isomorphic. Third, we show that every finite model can be isomorphically embedded in any RCC model. This leads to a simple proof for the result that each consistent spatial network has a realization in any RCC model.

5

Extensionality of the RCC8 Composition Table

Li S., Ying M.

Fundamenta Informaticae

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2003

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Vol. 55, nr 3,4

363-385

EN

This paper is mainly concerned with the RCC8 composition table entailed by the Region Connection Calculus (RCC), a well-known formalism for Qualitative Spatial Reasoning. This table has been independently generated by Egenhofer in the context of Geographic Information Systems. It has been known for some time that the table is not extensional for each RCC model. This paper however shows that the Egenhofer model is indeed an extensional one for the RCC8 composition table. Moreover this model is the maximal extensional one for the RCC8 composition table in a sense.

6

Qualitative spatial representation and reasoning: an overview

Cohn A.G., Hazarika S.M.

Fundamenta Informaticae

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2001

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Vol. 46, nr 1,2

1-29

EN

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.

7

Relations algebras in qualitative spatial reasoning

Düntsch I., Wang H., McCloskey S.

Fundamenta Informaticae

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1999

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Vol. 39, Nr 3

229-248

EN

The formalization of the ``part - of'' relationship goes back to the mereology of S. Leśniewski, subsequently taken up by [34], and [11]. In this paper we investigate relation algebras obtained from dixfferent notions of ``part-of'', respectively, ``connectedness'' in various domains. We obtain minimal models for the relational part of mereology in a general setting, and when the underlying set is an atomless Boolean algebra.