License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2017.17
URN: urn:nbn:de:0030-drops-80494
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8049/
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Marsden, Dan ; Genovese, Fabrizio

Custom Hypergraph Categories via Generalized Relations

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LIPIcs-CALCO-2017-17.pdf (0.4 MB)

Abstract

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical systems and network theory. When investigating a new application, the question arises of how to identify a suitable process theoretic model.

We present a conceptually motivated parameterized framework for the construction of models for process theories. Our framework generalizes the notion of binary relation along four axes of variation, the truth values, a choice of algebraic structure, the ambient mathematical universe and the choice of proof relevance or provability. The resulting categories are preorder-enriched and provide analogues of relational converse and taking graphs of maps. Our constructions are functorial in the parameter choices, establishing mathematical connections between different application domains. We illustrate our techniques by constructing many existing models from the literature, and new models that open up ground for further development.

BibTeX - Entry

@InProceedings{marsden_et_al:LIPIcs:2017:8049,
  author =	{Dan Marsden and Fabrizio Genovese},
  title =	{{Custom Hypergraph Categories via Generalized Relations}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Filippo Bonchi and Barbara K{\"o}nig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8049},
  URN =		{urn:nbn:de:0030-drops-80494},
  doi =		{10.4230/LIPIcs.CALCO.2017.17},
  annote =	{Keywords: Process Theory, Categorical Compositional Semantics, Generalized Relations, Hypergraph Category, Compact Closed Category}
}

Keywords: Process Theory, Categorical Compositional Semantics, Generalized Relations, Hypergraph Category, Compact Closed Category
Collection: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Issue Date: 2017
Date of publication: 17.11.2017

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