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39
Boolean Connection Algebras: A New Approach to the RegionConnection Calculus
 Artificial Intelligence
, 1999
"... The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and prove ..."
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Cited by 50 (7 self)
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The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: RegionConnection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...
A RelationAlgebraic Approach to the Region Connection Calculus
 Fundamenta Informaticae
, 2001
"... We explore the relationalgebraic aspects of the region connection calculus (RCC) of Randell et al. (1992a). In particular, we present a refinement of the RCC8 table which shows that the axioms provide for more relations than are listed in the present table. We also show that each RCC model leads ..."
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Cited by 26 (0 self)
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We explore the relationalgebraic aspects of the region connection calculus (RCC) of Randell et al. (1992a). In particular, we present a refinement of the RCC8 table which shows that the axioms provide for more relations than are listed in the present table. We also show that each RCC model leads to a Boolean algebra. Finally, we prove that a refined version of the RCC5 table has as models all atomless Boolean algebras B with the natural ordering as the "part  of" relation, and that the table is closed under first order definable relations iff B is homogeneous. 1 Introduction Qualitative reasoning (QR) has its origins in the exploration of properties of physical systems when numerical information is not sufficient  or not present  to explain the situation at hand (Weld and Kleer, 1990). Furthermore, it is a tool to represent the abstractions of researchers who are constructing numerical systems which model the physical world. Thus, it fills a gap in data modeling which often l...
GQR – A Fast Reasoner for Binary Qualitative Constraint Calculi
"... 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 reasone ..."
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Cited by 26 (8 self)
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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 hardcoded 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 objectoriented framework. GQR is free software distributed under the terms of the GNU General Public License.
A Proximity Approach to Some RegionBased Theories of Space
, 2002
"... This paper is a continuation of [41]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to... ..."
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Cited by 23 (13 self)
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This paper is a continuation of [41]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to...
A Proof System for Contact Relation Algebras
"... Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa & Sikorski (1963) for relatio ..."
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Cited by 17 (12 self)
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Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa & Sikorski (1963) for relation algebras generated by a contact relation. 1 Introduction Contact relations arise in the context of qualitative geometry and spatial reasoning, going back to the work of de Laguna (1922), Nicod (1924), Whitehead (1929), and, more recently, of Clarke (1981), Cohn et al. (1997), Pratt & Schoop (1998, 1999) and others. They are a generalisation of the "overlap relation" , obtained from a "part of" relation, which for the first time was formalised by Lesniewski (1916), (see also Lesniewski, 1983). One of Lesniewski's main concerns was to build a paradoxfree foundation of Mathematics, one pillar of which was mereology 1 or, as it was originally called, the general theory of manifolds or colle...
Beyond modalities: Sufficiency and mixed algebras
 In E. Orłowska & A. Szałas (Eds.), Relational Methods in Computer Science Applications, 277– 299
, 2000
"... this paper for a discussion on the merits or otherwise of Kripke semantics and its "sufficiency" extension. Just as Kripke frames are dual to a class of Boolean algebras with modal operators [18, 24], one can build a duality for frames and Boolean algebras with sufficiency operators. Mixed ..."
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Cited by 14 (12 self)
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this paper for a discussion on the merits or otherwise of Kripke semantics and its "sufficiency" extension. Just as Kripke frames are dual to a class of Boolean algebras with modal operators [18, 24], one can build a duality for frames and Boolean algebras with sufficiency operators. Mixed structures occur when modal and sufficiency operators arise from the same accessibility relation. In this paper we introduce the classes of sufficiency algebras and that of mixed algebras which include both a modal and a sufficiency operator, and study representation and duality theory for these classes of algebras. We also give examples for classes of firstorder definable frames, where such operators are required for a "modalstyle" axiomatisation. 2 Why sufficiency and mixed algebras?
A Necessary Relation Algebra for Mereotopology
 Studia Logica
, 2001
"... We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the Region Connection Calculus [33], and we show how to interpret these relations in the collection of regular open sets in the twodimensional Euclidean plan ..."
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Cited by 13 (4 self)
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We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the Region Connection Calculus [33], and we show how to interpret these relations in the collection of regular open sets in the twodimensional Euclidean plane. 1 Introduction Mereotopology is an area of qualitative spatial reasoning (QSR) which aims to develop formalisms for reasoning about spatial entities [1, 12, 30, 31]. The structures used in mereotopology consist of three parts: 1. A relational (or mereological) part, 2. An algebraic part, 3. A topological part. The algebraic part is often an atomless Boolean algebra, or, more generally, an orthocomplemented lattice, both without smallest element. Due to the presence of the binary relations "partof" and "contact" in the relational part of mereotopology, composition based reasoning with binary relations has been of interest to the QSR community, and the expressive power, consistency and complexity o...
KnowledgeBased Spatial Reasoning for Automated Scene Generation from Text Descriptions
, 2004
"... is the culmination of many years of hard work and sacrifice as much by me as by those special people in my life who have accompanied me throughout the process. Without you, this would not be possible. First, of course, I thank my family for their continued support in every way to get me this far. Af ..."
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Cited by 10 (2 self)
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is the culmination of many years of hard work and sacrifice as much by me as by those special people in my life who have accompanied me throughout the process. Without you, this would not be possible. First, of course, I thank my family for their continued support in every way to get me this far. After so many years of watching me overcome one selfimposed challenge after another, you can finally stop asking whether I will ever get out of school. As I now embark on an academic career, the answer is obviously never. But I will finally graduate, and before my brother even. So, Dave, just face it: complete and thorough domination yet again! Credit goes out to all my friends with neat toys, hobbies, plans, and ideas who successfully managed to divert my attention away from work and get me hooked on countless other activities. While you all have unquestionably prolonged my student career, you have also made the journey far more
AXIOMS, ALGEBRAS, AND TOPOLOGY
"... This work explores the interconnections between a number of different perspectives on the formalisation of space. We begin with an informal discussion of the intuitions that motivate these formal representations. ..."
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Cited by 9 (0 self)
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This work explores the interconnections between a number of different perspectives on the formalisation of space. We begin with an informal discussion of the intuitions that motivate these formal representations.
Weak contact structures
 RELATIONAL METHODS IN COMPUTER SCIENCE, LNCS NO
, 2006
"... In this paper we investigate weak contact relations C on a lattice L, in particular, the relation between various axioms for contact, and their connection to the algebraic structure of the lattice. Furthermore, we will study a notion of orthogonality which is motivated by a weak contact relation in ..."
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Cited by 8 (5 self)
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In this paper we investigate weak contact relations C on a lattice L, in particular, the relation between various axioms for contact, and their connection to the algebraic structure of the lattice. Furthermore, we will study a notion of orthogonality which is motivated by a weak contact relation in an inner product space. Although this is clearly a spatial application, we will show that, in case L is distributive and C satisfies the orthogonality condition, the only weak contact relation on L is the overlap relation; in particular no RCC model satisfies this condition.