Results 11  20
of
39
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 ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
(Show Context)
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.
CASL specifications of qualitative calculi
 Spatial Information Theory: Cognitive and Computational Foundations, Proceedings of COSIT’05, LNCS 3693
, 2005
"... Abstract. In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s car ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s cardinal direction calculus, Freksa’s double cross calculus, Egenhofer and Franzosa’s intersection calculi, and Randell, Cui, and Cohn’s region connection calculi. These calculi are designed for modeling specific aspects of space or time, respectively, to the effect that the class of intended models may vary widely with the calculus at hand. But from a formal point of view these calculi are often closely related to each other. For example, the spatial region connection calculus RCC5 may be considered a coarsening of Allen’s (temporal) interval calculus. And vice versa, intervals can be used to represent spatial objects that feature an internal direction. The central question of this paper is how these calculi as well as their mutual dependencies can be axiomatized by algebraic specifications. This question will be investigated within the framework of the Common Algebraic Specification Language (CASL), a specification language developed by the Common Framework Initiative for algebraic specification and development (COFI). We explain scope and expressiveness of CASL by discussing the specifications of some of the calculi mentioned before. 1
An algebraic and logical approach to the approximation of regions, in
 Proc. 5th Seminar on Relational Methods in Computer Science
, 2000
"... ..."
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 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
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
Regionbased Theories of Space: Mereotopology and Beyond (PhD Qualifying Exam Report, 2009)
"... The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of pheno ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of phenomenological processes in nature (Husserl, 1913; Whitehead, 1920, 1929) – what we call today ‘commonsensical ’ in Artificial Intelligence. There have been plenty of other motivations to
A 4dimensionalist mereotopology
 Formal Ontology in Information Systems
, 2004
"... ..."
(Show Context)
A categorical perspective on qualitative constraint calculi
 QUALITATIVE CONSTRAINT CALCULI: APPLICATION AND INTEGRATION, WORKSHOP PROCEEDINGS
, 2006
"... In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the last 25 years, a large number of calculi for efficient reasoning about space and time has been developed. Reasoning problems in such calculi are usually formulated as constraint satisfaction problems. For t ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the last 25 years, a large number of calculi for efficient reasoning about space and time has been developed. Reasoning problems in such calculi are usually formulated as constraint satisfaction problems. For temporal and spatial reasoning, these problems often have infinite domains, which need to be abstracted to (finite) algebras in order to become computationally feasible. Ligozat [13] has argued that the notion of weak representation plays a crucial rôle: it not only captures the correspondence between abstract relations (in a relation algebra or nonassociative algebra) and relations in a concrete domain, but also corresponds to algebraically closed constraint networks. In this work, we examine properties of the category of weak representations and treat the relations between partition schemes, nonassociative algebras and concrete domains in a systematic way. This leads to the notion of semistrong representation, which captures the correspondence between abstract and concrete relations better than the notion of weak representation does. The slogan is that semistrong representations avoid unnecessary loss of information. Furthermore, we hope that the categorical perspective will help in the future to provide new insights on the important problem of determining whether algebraic closedness decides consistency of constraint networks. In this
Tangent Circle Algebras
, 2002
"... In relational reasoning, one is concerned with the algebras generated by a given set of relations, when one allows only basic relational operations such as the Boolean operations, relational composition, and converse. According to a result by A. Tarski, the relations obtained in this way are exactly ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
In relational reasoning, one is concerned with the algebras generated by a given set of relations, when one allows only basic relational operations such as the Boolean operations, relational composition, and converse. According to a result by A. Tarski, the relations obtained in this way are exactly the relations which are definable in the threevariable fragment of first order logic. Thus, a relation algebra is a first indicator of the expressive power of a given set of relations. In this paper, we investigate relation algebras which arise in the context of preference relations. In particular, we study the tangent circle orders introduced by Abbas & Vincke [2]. 1
A modeltheoretic characterization of Asher and Vieu’s ontology of mereotopology
 In Proc. of KR’08
, 2008
"... Abstract We characterize the models of Asher and Vieu's firstorder mereotopology RT 0 in terms of mathematical structures with welldefined properties: topological spaces, lattices, and graphs. We give a full representation theorem for the models of the subtheory RT − (RT 0 without existentia ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract We characterize the models of Asher and Vieu's firstorder mereotopology RT 0 in terms of mathematical structures with welldefined properties: topological spaces, lattices, and graphs. We give a full representation theorem for the models of the subtheory RT − (RT 0 without existential axioms) as portholattices (pseudocomplemented, orthocomplemented). We further prove that the finite models of RT − EC , an extension of RT − , are isomorphic to a graph representation of portholattices extended by additional edges and we show how to construct finite models of the full mereotopology. The results are compared to representations of Clarke's mereotopology and known models of the Region Connection Calculus (RCC). Although soundness and completeness of the theory RT 0 has been proved with respect to a topological translation of the axioms, our characterization provides more insight into the structural properties of the mereotopological models.
A Reconciliation of Logical Representations of Space: from Multidimensional Mereotopology to Geometry
, 2013
"... Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between highlevel and lowlevel spatial knowledge, while computers have traditionally relied only on lowlevel spatial information. Qualitative spatial representation and reasoning is concer ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between highlevel and lowlevel spatial knowledge, while computers have traditionally relied only on lowlevel spatial information. Qualitative spatial representation and reasoning is concerned with devising highlevel, qualitative, representations of certain aspects of space using small sets of intuitive spatial relations that lend themselves to efficient reasoning. Many such representations have been developed over the years, but their use in practical applications seems to be inhibited. One reason preventing more widespread adoption of qualitative spatial representations may be the gap between simple but inexpressive qualitative representations at one end and geometric or quantitative representations with the expressivity of Euclidean geometry at the other end. Another factor may be the lack of semantic integration between the various spatial representations ranging from qualitative to geometric ontologies. We will address both issues in this thesis with a focus on spatial ontologies that involve some kind of mereotopological relations such as contact and parthood. We design a family of spatial ontologies with varying restrictiveness and increasingly more expressive nonlogical languages, organized into hierarchies of ontologies of equal expressivity. As the most foundational spatial ontology we propose a multidimensional mereotopology based only on ‘containment’ and