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Ontology Mapping: The State of the Art
, 2003
"... Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support t ..."
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Cited by 432 (9 self)
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Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the tasks envisaged by a distributed environment like the Semantic Web. Multiple ontologies need to be accessed from several applications. Mapping could provide a common layer from which several ontologies could be accessed and hence could exchange information in semantically sound manners. Developing such mappings has been the focus of a variety of works originating from diverse communities over a number of years. In this article we comprehensively review and present these works. We also provide insights on the pragmatics of ontology mapping and elaborate on a theoretical approach for defining ontology mapping.
MODULAR CONSTRUCTIONS FOR COMBINATORIAL GEOMETRIES
, 1975
"... R. Stanley, in an investigation of modular flats in geometries (Algebra Universalis 12 (1971), 214—217), proved that the characteristic polynomial xW of a modular flat x divides the characteristic polynomial x(G) of a geometry G. In this paper we identify the quotient: THEOREM. / / x is a modular ..."
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Cited by 40 (2 self)
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of two graphs and the polynomial of their vertex join across a common clique generalizes to geometries: THEOREM. Given geometries G and H, if x is a modular flat of G as well as a subgeometry of H, then there exists a geometry P = PX(G, H) which is a pushout in the category of injective strong maps
Combinatorial Group Theory
, 2004
"... An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian ..."
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An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian
Homotopy colimits  comparison lemmas for combinatorial applications
, 1997
"... We provide a "toolkit " of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite different fields of applications. We demonstrate this with respect to 1. Bjorner's " ..."
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Cited by 24 (2 self)
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We provide a "toolkit " of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite different fields of applications. We demonstrate this with respect to 1. Bjorner's "Generalized Homotopy Complementation Formula" [4], 2. the topology of toric varieties, 3. the study of homotopy types of arrangements of subspaces, 4. the analysis of homotopy types of subgroup complexes.
INVERSE SEMIGROUPS AND COMBINATORIAL C*ALGEBRAS
, 2008
"... We describe a special class of representations of an inverse semigroup S on Hilbert’s space which we term tight. These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the tight spectrum, which is in turn shown to be precisely the closure of the sp ..."
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Cited by 29 (6 self)
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We describe a special class of representations of an inverse semigroup S on Hilbert’s space which we term tight. These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the tight spectrum, which is in turn shown to be precisely the closure of the space of ultrafilters, once filters are identified with semicharacters in a natural way. These representations are moreover shown to correspond to representations of the C*algebra of the groupoid of germs for the action of S on its tight spectrum. We then treat the case of certain inverse semigroups constructed from semigroupoids, generalizing and inspired by inverse semigroups constructed from ordinary and higher rank graphs. The tight representations of this inverse semigroup are in onetoone correspondence with representations of the semigroupoid, and consequently the semigroupoid algebra is given a groupoid model. The groupoid which arises from this construction is shown to be the same as the boundary path groupoid of Farthing, Muhly and Yeend, at least in the singly aligned, sourceless case. 1. Introduction.
Products, Joins, Meets, and Ranges in . . .
, 2012
"... Restriction categories provide a convenient abstract formulation of partial functions. However, restriction categories can have a variety of structures such as finite partial products (cartesianess), joins, meets, and ranges which are of interest in computability theory, semigroup theory, topology, ..."
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, and algebraic geometry. This thesis studies these structures. For finite partial products (cartesianess), a construction to add finite partial products to an arbitrary restriction category freely is provided. For joins, we introduce the notion of join restriction categories, describe a construction for the join
Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology)
"... This is a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing directed spaces, breaking the intrinsic symmetries of topological spaces. Cubical sets have a directed homology, consisting of preordered abelian groups where ..."
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Cited by 20 (8 self)
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This is a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing directed spaces, breaking the intrinsic symmetries of topological spaces. Cubical sets have a directed homology, consisting of preordered abelian groups
The geometry of abstract groups and their splittings
 Rev. Mat. Complut
"... I will survey an area of research in group theory which is guided by geometric intuition: indeed, even the groups themselves are to be thought of as having geometric structure in some sense. After a preliminary chapter to give some background and fix notations, I follow a roughly historical approach ..."
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Cited by 9 (1 self)
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, this monograph gives an austerely algebraic account of the theory, and appeared at about the same time as three significant developments, all inspired by geometry: the work of Gromov, and in particular the notion of (word) hyperbolic
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