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DOI: 10.4230/LIPIcs.CSL.2020.25
On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics

Authors: Matthias Hoelzel and Richard Wilke

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella.
Cite as

Matthias Hoelzel and Richard Wilke. On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hoelzel_et_al:LIPIcs.CSL.2020.25,
  author =	{Hoelzel, Matthias and Wilke, Richard},
  title =	{{On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.25},
  URN =		{urn:nbn:de:0030-drops-116681},
  doi =		{10.4230/LIPIcs.CSL.2020.25},
  annote =	{Keywords: Higher order logic, Existential second-order logic, Team semantics, Closure properties, Union closure, Model-checking games, Syntactic charactisations of semantical fragments}
}
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