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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2013.116
URN: urn:nbn:de:0030-drops-41935
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4193/
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Bradfield, Julian

Team building in dependence

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Abstract

Hintikka and Sandu's Independence-Friendly Logic was introduced as a logic for partially ordered quantification, in which the independence of (existential) quantifiers from previous (universal) quantifiers is written by explicit syntax. It was originally given a semantics by games of imperfect information; Hodges then gave a (necessarily) second-order Tarskian semantics. More recently, Väänänen (2007) has proposed that the many curious features of IF logic can be better understood in his Dependence Logic, in which the (in)dependence of variables is stated in atomic formula, rather than by changing the definition of quantifier; he gives semantics in Tarskian form, via imperfect information games, and via a routine second-order perfect information game. He then defines Team Logic, where classical negation is added to the mix, resulting in a full second-order expressive logic. He remarks that no game semantics appears possible (other than by playing at second order). In this article, we explore an alternative approach to game semantics for DL, where we avoid imperfect information, yet stay locally apparently first-order, by sweeping the second-order information into longer games (infinite games in the case of countable models). Extending the game to Team Logic is not possible in standard games, but we conjecture a move to transfinite games may achieve a 'natural' game for Team Logic.

BibTeX - Entry

@InProceedings{bradfield:LIPIcs:2013:4193,
  author =	{Julian Bradfield},
  title =	{{Team building in dependence}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{116--128},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Simona Ronchi Della Rocca},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4193},
  URN =		{urn:nbn:de:0030-drops-41935},
  doi =		{10.4230/LIPIcs.CSL.2013.116},
  annote =	{Keywords: partially ordered quantification, independence-friendly logic, game semantics}
}

Keywords: partially ordered quantification, independence-friendly logic, game semantics
Seminar: Computer Science Logic 2013 (CSL 2013)
Issue Date: 2013
Date of publication: 27.08.2013


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