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.CSL.2018.25
URN: urn:nbn:de:0030-drops-96921
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9692/
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Grädel, Erich ; Hoelzel, Matthias

Dependency Concepts up to Equivalence

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LIPIcs-CSL-2018-25.pdf (0.6 MB)

Abstract

Modern logics of dependence and independence are based on different variants of atomic dependency statements (such as dependence, exclusion, inclusion, or independence) and on team semantics: A formula is evaluated not with a single assignment of values to the free variables, but with a set of such assignments, called a team.
In this paper we explore logics of dependence and independence where the atomic dependency statements cannot distinguish elements up to equality, but only up to a given equivalence relation (which may model observational indistinguishabilities, for instance between states of a computational process or between values obtained in an experiment).
Our main goal is to analyse the power of such logics, by identifying equally expressive fragments of existential second-order logic or greatest fixed-point logic, with relations that are closed under the given equivalence. Using an adaptation of the Ehrenfeucht-Fraïssé method we further study conditions on the given equivalences under which these logics collapse to first-order logic, are equivalent to full existential second-order logic, or are strictly between first-order and existential second-order logic.

BibTeX - Entry

@InProceedings{grdel_et_al:LIPIcs:2018:9692,
  author =	{Erich Gr{\"a}del and Matthias Hoelzel},
  title =	{{Dependency Concepts up to Equivalence}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic  (CSL 2018)},
  pages =	{25:1--25:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Dan Ghica and Achim Jung},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9692},
  URN =		{urn:nbn:de:0030-drops-96921},
  doi =		{10.4230/LIPIcs.CSL.2018.25},
  annote =	{Keywords: Logics of dependence and independence, Team semantics, Existential second-order logic, Observational equivalence, Expressive power}
}

Keywords: Logics of dependence and independence, Team semantics, Existential second-order logic, Observational equivalence, Expressive power
Collection: 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)
Issue Date: 2018
Date of publication: 29.08.2018

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