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URN: urn:nbn:de:0030-drops-142487
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A Bicategorical Model for Finite Nondeterminism

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Abstract

Finiteness spaces were introduced by Ehrhard as a refinement of the relational model of linear logic. A finiteness space is a set equipped with a class of finitary subsets which can be thought of being subsets that behave like finite sets. A morphism between finiteness spaces is a relation that preserves the finitary structure. This model provided a semantics for finite non-determism and it gave a semantical motivation for differential linear logic and the syntactic notion of Taylor expansion. In this paper, we present a bicategorical extension of this construction where the relational model is replaced with the model of generalized species of structures introduced by Fiore et al. and the finiteness property now relies on finite presentability.

BibTeX - Entry

@InProceedings{galal:LIPIcs.FSCD.2021.10,
  author =	{Galal, Zeinab},
  title =	{{A Bicategorical Model for Finite Nondeterminism}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14248},
  URN =		{urn:nbn:de:0030-drops-142487},
  doi =		{10.4230/LIPIcs.FSCD.2021.10},
  annote =	{Keywords: Differential linear logic, Species of structures, Finiteness, Bicategorical semantics}
}

Keywords: Differential linear logic, Species of structures, Finiteness, Bicategorical semantics
Seminar: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue date: 2021
Date of publication: 06.07.2021


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