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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.

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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.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}
}

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DOI: 10.4230/DagSemProc.04351.4

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.

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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.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}
}

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Documents authored by Pfaltz, John L.

Closure and Causality

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A Category of Discrete Closure Spaces

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