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DOI: 10.4230/LIPIcs.STACS.2011.344
URN: urn:nbn:de:0030-drops-30256
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3025/

ten Cate, Balder ; Segoufin, Luc

Unary negation

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Abstract

We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the mu-calculus, as well as conjunctive queries and monadic Datalog. We show that satisfiability and finite satisfiability are decidable for both fragments, and we pinpoint the complexity of satisfiability, finite satisfiability, and model checking. We also show that the unary negation fragment of first-order logic is model-theoretically very well behaved. In particular, it enjoys Craig interpolation and the Beth property.

BibTeX - Entry

@InProceedings{tencate_et_al:LIPIcs:2011:3025,
  author =	{Balder ten Cate and Luc Segoufin},
  title =	{{Unary negation}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{344--355},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3025},
  URN =		{urn:nbn:de:0030-drops-30256},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2011.344},
  annote =	{Keywords: Decidability, Logic, Unary negation}
}

Keywords: Decidability, Logic, Unary negation
Seminar: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue date: 2011
Date of publication: 11.03.2011


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