33 Search Results for "Spreen, Dieter"


Document
Duality in Computer Science (Dagstuhl Seminar 15441)

Authors: Mai Gehrke, Achim Jung, Victor Selivanov, and Dieter Spreen

Published in: Dagstuhl Reports, Volume 5, Issue 10 (2016)


Abstract
This report documents the programme and outcomes of Dagstuhl Seminar 15441 `Duality in Computer Science'. This seminar served as a follow-up seminar to the seminar `Duality in Computer Science' (Dagstuhl Seminar 13311). In this seminar, we focused on applications of duality to semantics for probability in computation, to algebra and coalgebra, and on applications in complexity theory. A key objective of this seminar was to bring together researchers from these communities within computer science as well as from mathematics with the goal of uncovering commonalities, forging new collaborations, and sharing tools and techniques between areas based on their common use of topological methods and duality.

Cite as

Mai Gehrke, Achim Jung, Victor Selivanov, and Dieter Spreen. Duality in Computer Science (Dagstuhl Seminar 15441). In Dagstuhl Reports, Volume 5, Issue 10, pp. 66-88, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@Article{gehrke_et_al:DagRep.5.10.66,
  author =	{Gehrke, Mai and Jung, Achim and Selivanov, Victor and Spreen, Dieter},
  title =	{{Duality in Computer Science (Dagstuhl Seminar 15441)}},
  pages =	{66--88},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{5},
  number =	{10},
  editor =	{Gehrke, Mai and Jung, Achim and Selivanov, Victor and Spreen, Dieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.5.10.66},
  URN =		{urn:nbn:de:0030-drops-56999},
  doi =		{10.4230/DagRep.5.10.66},
  annote =	{Keywords: coalgebra, domain theory, probabilistic systems, recognizability, semantics of non-classical logics, Stone duality}
}
Document
Duality in Computer Science (Dagstuhl Seminar 13311)

Authors: Mai Gehrke, Jean-Eric Pin, Victor Selivanov, and Dieter Spreen

Published in: Dagstuhl Reports, Volume 3, Issue 7 (2013)


Abstract
Duality allows one to move between the two worlds: the world of certain algebras of properties and a spacial world of individuals, thereby leading to a change of perspective that may, and often does, lead to new insights. Dualities have given rise to active research in a number of areas of theoretical computer science. Dagstuhl Seminar 13311 "Duality in Computer Science" was held to stimulate research in this area. This report collects the ideas that were presented and discussed during the course of the seminar.

Cite as

Mai Gehrke, Jean-Eric Pin, Victor Selivanov, and Dieter Spreen. Duality in Computer Science (Dagstuhl Seminar 13311). In Dagstuhl Reports, Volume 3, Issue 7, pp. 54-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@Article{gehrke_et_al:DagRep.3.7.54,
  author =	{Gehrke, Mai and Pin, Jean-Eric and Selivanov, Victor and Spreen, Dieter},
  title =	{{Duality in Computer Science (Dagstuhl Seminar 13311)}},
  pages =	{54--73},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{3},
  number =	{7},
  editor =	{Gehrke, Mai and Pin, Jean-Eric and Selivanov, Victor and Spreen, Dieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.3.7.54},
  URN =		{urn:nbn:de:0030-drops-43068},
  doi =		{10.4230/DagRep.3.7.54},
  annote =	{Keywords: Stone-Priestley duality, Point free topology, Infinite computations Exact real number computation, Computability in analysis, Hierarchies, Reducibilit Topological complexity, Domain theory, Semantics, Recognizability, Profinite topology}
}
Document
Computing with Infinite Data: Topological and Logical Foundations (Dagstuhl Seminar 11411)

Authors: Ulrich Berger, Vasco Brattka, Victor Selivanov, Dieter Spreen, and Hideki Tsuiki

Published in: Dagstuhl Reports, Volume 1, Issue 10 (2012)


Abstract
There is a large gap between mathematical structures and the structures computer implementations are based on. To stimulate research to overcome this---especially for infinitary structures---highly non-trivial problem the Dagstuhl Seminar 11411 ``Computing with Infinite Data: Topological and Logical Foundations'' was held. This report collects the ideas that were presented and discussed during the course of the seminar.

Cite as

Ulrich Berger, Vasco Brattka, Victor Selivanov, Dieter Spreen, and Hideki Tsuiki. Computing with Infinite Data: Topological and Logical Foundations (Dagstuhl Seminar 11411). In Dagstuhl Reports, Volume 1, Issue 10, pp. 14-36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@Article{berger_et_al:DagRep.1.10.14,
  author =	{Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki},
  title =	{{Computing with Infinite Data: Topological and Logical Foundations (Dagstuhl Seminar 11411)}},
  pages =	{14--36},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2012},
  volume =	{1},
  number =	{10},
  editor =	{Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.1.10.14},
  URN =		{urn:nbn:de:0030-drops-33721},
  doi =		{10.4230/DagRep.1.10.14},
  annote =	{Keywords: Exact real number computation, Stream computation, Infinite computations, Computability in analysis, Hierarchies, Reducibility, Topological complexity}
}
Document
06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality

Authors: Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, and Dieter Spreen

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, and Dieter Spreen. 06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{kopperman_et_al:DagSemProc.06341.1,
  author =	{Kopperman, Ralph and Panangaden, Prakash and Smyth, Michael B. and Spreen, Dieter},
  title =	{{06341 Abstracts Collection – Computational Structures for Modelling Space, Time and Causality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--23},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.1},
  URN =		{urn:nbn:de:0030-drops-9000},
  doi =		{10.4230/DagSemProc.06341.1},
  annote =	{Keywords: Borel hierarchy, causets, Chu spaces, computations in higher types, computable analysis, constructive topology, differential calculus, digital topology, dihomotopy, domain theory, domain representation, formal topology, higher dimensional automata, mereo\backslash-topology, partial metrics}
}
Document
A convenient category of domains

Authors: Ingo Battenfeld, Matthias Schröder, and Alex Simpson

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
We motivate and define a category of "topological domains", whose objects are certain topological spaces, generalising the usual $omega$-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains combining such properties.

Cite as

Ingo Battenfeld, Matthias Schröder, and Alex Simpson. A convenient category of domains. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{battenfeld_et_al:DagSemProc.06341.2,
  author =	{Battenfeld, Ingo and Schr\"{o}der, Matthias and Simpson, Alex},
  title =	{{A convenient category of domains}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.2},
  URN =		{urn:nbn:de:0030-drops-8945},
  doi =		{10.4230/DagSemProc.06341.2},
  annote =	{Keywords: Domain theory, topology of datatypes}
}
Document
Closure and Causality

Authors: John L. Pfaltz

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
We present a model of causality which is defined by the intersection of two distinct closure systems, ${cal I}$ and ${cal T}$. Next we present empirical evidence to demonstrate that this model has practical validity by examining computer trace data to reveal causal dependencies between individual code modules. From over 498,000 events in the transaction manager of an open source system we tease out 66 apparent causal dependencies. Finally, we explore how to mathematically model the transformation of a causal topology resulting from unforlding events.

Cite as

John L. Pfaltz. Closure and Causality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{pfaltz:DagSemProc.06341.3,
  author =	{Pfaltz, John L.},
  title =	{{Closure and Causality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.3},
  URN =		{urn:nbn:de:0030-drops-8978},
  doi =		{10.4230/DagSemProc.06341.3},
  annote =	{Keywords: Closure, causality, antimatroid, temporal, software engineering}
}
Document
Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces

Authors: Howard Blair

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
We unify a variety of continuous and discrete types of change of state phenomena using a scheme whose instances are differential calculi on structures that embrace both topological spaces and graphs as well as hybrid ramifications of such structures. These calculi include the elementary differential calculus on real and complex vector spaces. One class of spaces that has been increasingly receiving attention in recent years is the class of convergence spaces [cf. Heckmann, R., TCS v.305, (159--186)(2003)]. The class of convergence spaces together with the continuous functions among convergence spaces forms a Cartesian-closed category CONV that contains as full subcategories both the category TOP of topological spaces and an embedding of the category DIGRAPH of reflexive directed graphs. (More can importantly be said about these embeddings.) These properties of CONV serve to assure that we can construct continuous products of continuous functions, and that there is always at least one convergence structure available in function spaces with respect to which the operations of function application and composition are continuous. The containment of TOP and DIGRAPH in CONV allows to combine arbitrary topological spaces with discrete structures (as represented by digraphs) to obtain hybrid structures, which generally are not topological spaces. We give a differential calculus scheme in CONV that addresses three issues in particular. 1. For convergence spaces $X$ and $Y$ and function $f: X longrightarrow Y$, the scheme gives necessary and sufficient conditions for a candidate differential $df: X longrightarrow Y$ to be a (not necessarily "the", depending on the spaces involved) differential of $f$ at $x_0$. 2. The chain rule holds and the differential relation between functions distributes over Cartesian products: e.g. if $Df$, $Dg$ and $Dh$ are, respectively, differentials of $f$ at $(g(x_0),h(x_0))$ and $g$ and $h$ at $x_0$, then $Df circ (Dg times Dh)$ is a differential of $f circ (g times h)$ at $x_0$. 3. When specialized to real and complex vector spaces, the scheme is in agreement with ordinary elementary differential calculus on these spaces. Moreover, with two additional constraints having to do with self-differentiation of differentials and translation invariance (for example, a linear operator on, say, $C^2$, is its own differential everywhere) there is a (unique) maximum differential calculus in CONV.

Cite as

Howard Blair. Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{blair:DagSemProc.06341.4,
  author =	{Blair, Howard},
  title =	{{Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.4},
  URN =		{urn:nbn:de:0030-drops-8956},
  doi =		{10.4230/DagSemProc.06341.4},
  annote =	{Keywords: Hybrid space, convergence space, differential, calculus, chain rule, hybrid dynamical system, discrete structure, topological space}
}
Document
Enriched categories and models for spaces of dipaths

Authors: Timothy Porter

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
Partially ordered sets, causets, partially ordered spaces and their local counterparts are now often used to model systems in computer science and theoretical physics. The order models `time' which is often not globally given. In this setting directed paths are important objects of study as they correspond to an evolving state or particle traversing the system. Many physical problems rely on the analysis of models of the path space of space-time manifold. Many problems in concurrent systems use `spaces' of paths in a system. Here we review some ideas from algebraic topology that suggest how to model the dipath space of a pospace by a simplicially enriched category.

Cite as

Timothy Porter. Enriched categories and models for spaces of dipaths. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{porter:DagSemProc.06341.5,
  author =	{Porter, Timothy},
  title =	{{Enriched categories and models for spaces of dipaths}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.5},
  URN =		{urn:nbn:de:0030-drops-8989},
  doi =		{10.4230/DagSemProc.06341.5},
  annote =	{Keywords: Enriched category}
}
Document
Instant topological relationships hidden in the reality

Authors: Martin Maria Kovár

Published in: Dagstuhl Seminar Proceedings, Volume 6341, Computational Structures for Modelling Space, Time and Causality (2007)


Abstract
In most applications of general topology, topology usually is not the first, primary structure, but the information which finally leads to the construction of the certain, for some purpose required topology, is filtered by more or less thick filter of the other mathematical structures. This fact has two main consequences: (1) Most important applied constructions may be done in the primary structure, bypassing the topology. (2) Some topologically important information from the reality may be lost (filtered out by the other, front-end mathematical structures). Thus some natural and direct connection between topology and the reality could be useful. In this contribution we will discuss a pointless topological structure which directly reflects relationship between various locations which are glued together by possible presence of a physical object or a virtual ``observer".

Cite as

Martin Maria Kovár. Instant topological relationships hidden in the reality. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{kovar:DagSemProc.06341.6,
  author =	{Kov\'{a}r, Martin Maria},
  title =	{{Instant topological relationships hidden in the reality}},
  booktitle =	{Computational Structures for Modelling Space, Time and Causality},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6341},
  editor =	{Ralph Kopperman and Prakash Panangaden and Michael B. Smyth and Dieter Spreen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06341.6},
  URN =		{urn:nbn:de:0030-drops-8962},
  doi =		{10.4230/DagSemProc.06341.6},
  annote =	{Keywords: Pointless topology, reality}
}
Document
What do partial metrics represent?

Authors: Ralph Kopperman, Steve Matthews, and Homeira Pajoohesh

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
Partial metrics were introduced in 1992 as a metric to allow the distance of a point from itself to be non zero. This notion of self distance, designed to extend metrical concepts to Scott topologies as used in computing, has little intuition for the mainstream Hausdorff topologist. The talk will show that a partial metric over a set can be represented by a metric over that set with a so-called 'base point'. Thus we establish that a partial metric is essentially a structure combining both a metric space and a skewed view of that space from the base point. From this we can deduce what it is that partial metrics are really all about.

Cite as

Ralph Kopperman, Steve Matthews, and Homeira Pajoohesh. What do partial metrics represent?. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{kopperman_et_al:DagSemProc.04351.22,
  author =	{Kopperman, Ralph and Matthews, Steve and Pajoohesh, Homeira},
  title =	{{What do partial metrics represent?}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.22},
  URN =		{urn:nbn:de:0030-drops-1239},
  doi =		{10.4230/DagSemProc.04351.22},
  annote =	{Keywords: Metric , partial metric , base point}
}
Document
04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models

Authors: Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, Dieter Spreen, and Julian Webster

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 ``Spatial Representation: Discrete vs. Continuous Computational Models'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, Dieter Spreen, and Julian Webster. 04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{kopperman_et_al:DagSemProc.04351.1,
  author =	{Kopperman, Ralph and Panangaden, Prakash and Smyth, Michael B. and Spreen, Dieter and Webster, Julian},
  title =	{{04351 Abstracts Collection – Spatial Representation: Discrete vs. Continuous Computational Models}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.1},
  URN =		{urn:nbn:de:0030-drops-1742},
  doi =		{10.4230/DagSemProc.04351.1},
  annote =	{Keywords: Domain theory , formal topology , constructive topology , domain representation, space-time , quantum gravity , inverse limit construction, matroid geometry , descriptive set theory , Borel hierarchy , Hausdorff difference hierarchy , Wadge degree partial metric , fractafold , region geometry , oriented projective geometry}
}
Document
A Cartesian Closed Extension of the Category of Locales

Authors: Reinhold Heckmann

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
We present a Cartesian closed category ELOC of equilocales, which contains the category LOC of locales as a reflective full subcategory. The embedding of LOC into ELOC preserves products and all exponentials of exponentiable locales.

Cite as

Reinhold Heckmann. A Cartesian Closed Extension of the Category of Locales. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{heckmann:DagSemProc.04351.3,
  author =	{Heckmann, Reinhold},
  title =	{{A Cartesian Closed Extension of the Category of Locales}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.3},
  URN =		{urn:nbn:de:0030-drops-1339},
  doi =		{10.4230/DagSemProc.04351.3},
  annote =	{Keywords: Locale , Cartesian closed category}
}
Document
A Category of Discrete Closure Spaces

Authors: John L. Pfaltz

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
Discrete systems such as sets, monoids, groups are familiar categories. The internal strucutre of the latter two is defined by an algebraic operator. In this paper we describe the internal structure of the base set by a closure operator. We illustrate the role of such closure in convex geometries and partially ordered sets and thus suggestthe wide applicability of closure systems. Next we develop the ideas of closed and complete functions over closure spaces. These can be used to establish criteria for asserting that "the closure of a functional image under $f$ is equal to the functional image of the closure". Functions with these properties can be treated as categorical morphisms. Finally, the category "CSystem" of closure systems is shown to be cartesian closed.

Cite as

John L. Pfaltz. A Category of Discrete Closure Spaces. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{pfaltz:DagSemProc.04351.4,
  author =	{Pfaltz, John L.},
  title =	{{A Category of Discrete Closure Spaces}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.4},
  URN =		{urn:nbn:de:0030-drops-1253},
  doi =		{10.4230/DagSemProc.04351.4},
  annote =	{Keywords: Category , closure , antimatroid , function}
}
Document
A domain of spacetime intervals in general relativity

Authors: Keye Martin and Prakash Panangaden

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This implies that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emanates from something discrete.

Cite as

Keye Martin and Prakash Panangaden. A domain of spacetime intervals in general relativity. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{martin_et_al:DagSemProc.04351.5,
  author =	{Martin, Keye and Panangaden, Prakash},
  title =	{{A domain of spacetime intervals in general relativity}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.5},
  URN =		{urn:nbn:de:0030-drops-1350},
  doi =		{10.4230/DagSemProc.04351.5},
  annote =	{Keywords: Causality , spacetime , global hyperbolicity , interval domains , bicontinuous posets , spacetime topology}
}
Document
A geometry of information, I: Nerves, posets and differential forms

Authors: Jonathan Gratus and Timothy Porter

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)


Abstract
The main theme of this workshop is 'Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation \emph{of} spaces' and (ii) representation \emph{by} spaces. In this paper we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a 'differential geometry' of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.

Cite as

Jonathan Gratus and Timothy Porter. A geometry of information, I: Nerves, posets and differential forms. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{gratus_et_al:DagSemProc.04351.6,
  author =	{Gratus, Jonathan and Porter, Timothy},
  title =	{{A geometry of information, I: Nerves, posets and differential forms}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.6},
  URN =		{urn:nbn:de:0030-drops-1268},
  doi =		{10.4230/DagSemProc.04351.6},
  annote =	{Keywords: Chu spaces , nerves , differential forms}
}
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