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16
A representation Theorem for Boolean Contact Algebras
, 2003
"... We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T 1 spaces. ..."
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Cited by 36 (13 self)
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We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T 1 spaces.
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 21 (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...
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.
Regionbased theory of discrete spaces: A proximity approach
 Proceedings of the Fourth International Conference Journées de l’informatique Messine
, 2004
"... We introduce Boolean proximity algebras as a generalization of Efremovi c proximities which are suitable in reasoning about discrete regions. Following Stone's representation theorem for Boolean algebras, it is shown that each such algebra is isomorphic to a substructure of a complete and atomi ..."
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Cited by 9 (5 self)
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We introduce Boolean proximity algebras as a generalization of Efremovi c proximities which are suitable in reasoning about discrete regions. Following Stone's representation theorem for Boolean algebras, it is shown that each such algebra is isomorphic to a substructure of a complete and atomic Boolean proximity algebra. Key words: Proximity algebras, discrete spaces, qualitative spatial reasoning 1
Construction of Boolean Contact Algebras
 AI Communications
, 2004
"... We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two nonempty regular closed sets are connected if they have a nonempty intersection. These are standard e ..."
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Cited by 7 (6 self)
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We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two nonempty regular closed sets are connected if they have a nonempty intersection. These are standard examples for structures used in qualitative reasoning, mereotopology, and proximity theory. We exhibit various methods how such algebras can be constructed and give several nonstandard examples, the most striking one being a countable model of the Region Connection Calculus in which every proper region has infinitely many holes. 1
Approximation Operators in Qualitative Data Analysis
 PROCEEDINGS OF THE 2002 IEEE INTERNATIONAL CONFERENCE ON DATA MINING
, 2002
"... ... In his paper, we present various forms of set approximations via the unifying concept of modalstyle operators. Two examples indicate the usefulness of the approach. ..."
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Cited by 7 (0 self)
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... In his paper, we present various forms of set approximations via the unifying concept of modalstyle operators. Two examples indicate the usefulness of the approach.
Effective presentability of Boolean algebras of CantorBendixson rank 1
 Journal of Symbolic Logic
, 1999
"... We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B/I is of CantorBendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even tho ..."
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Cited by 6 (6 self)
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We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B/I is of CantorBendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite CantorBendixson rank.
Algebraization and representation of mereotopological structures
 JoRMiCS
, 2004
"... Abstract. Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems. 1 ..."
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Cited by 4 (1 self)
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Abstract. Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems. 1
The lattice of contact relations on a Boolean algebra
 in ‘Conf. on Relational Methods in Computer Science (RelMiCS10)’, LNCS 4988
, 2008
"... Abstract. Contact relations on an algebra have been studied since the early part of the previous century, and have recently become a powerful tool in several areas of artificial intelligence, in particular, qualitative spatial reasoning and ontology building. In this paper we investigate the structu ..."
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Abstract. Contact relations on an algebra have been studied since the early part of the previous century, and have recently become a powerful tool in several areas of artificial intelligence, in particular, qualitative spatial reasoning and ontology building. In this paper we investigate the structure of the set of all contact relations on a Boolean algebra. 1