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Documents authored by Schnoor, Henning

Document
DOI: 10.4230/LIPIcs.CSL.2015.277
A Van Benthem Theorem for Modal Team Semantics

Authors: Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal dependence logic (MDL) and team semantics. We show that Modal Team Logic (MTL) extending MDL by classical negation captures exactly the FO-definable bisimulation invariant properties of Kripke structures and teams. We also compare the expressive power of MTL to most of the variants and extensions of MDL recently studied in the area.
Cite as

Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer. A Van Benthem Theorem for Modal Team Semantics. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 277-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kontinen_et_al:LIPIcs.CSL.2015.277,
  author =	{Kontinen, Juha and M\"{u}ller, Julian-Steffen and Schnoor, Henning and Vollmer, Heribert},
  title =	{{A Van Benthem Theorem for Modal Team Semantics}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{277--291},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.277},
  URN =		{urn:nbn:de:0030-drops-54206},
  doi =		{10.4230/LIPIcs.CSL.2015.277},
  annote =	{Keywords: modal logic, dependence logic, team semantics, expressivity, bisimulation, independence, inclusion, generalized dependence atom}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1356
On the Complexity of Elementary Modal Logics

Authors: Edith Hemaspaandra and Henning Schnoor

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide class of relevant logics: Many important subclasses of modal logics can be obtained by restricting the allowed models with first-order Horn formulas. We show that the satisfiability problem for each of these logics is either NP-complete or PSPACE-hard, and exhibit a simple classification criterion. Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard logics.
Cite as

Edith Hemaspaandra and Henning Schnoor. On the Complexity of Elementary Modal Logics. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 349-360, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{hemaspaandra_et_al:LIPIcs.STACS.2008.1356,
  author =	{Hemaspaandra, Edith and Schnoor, Henning},
  title =	{{On the Complexity of Elementary Modal Logics}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{349--360},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1356},
  URN =		{urn:nbn:de:0030-drops-13561},
  doi =		{10.4230/LIPIcs.STACS.2008.1356},
  annote =	{Keywords: }
}
Document
DOI: 10.4230/DagSemProc.06401.6
Enumerating all Solutions for Constraint Satisfaction Problems

Authors: Henning Schnoor and Ilka Schnoor

Published in: Dagstuhl Seminar Proceedings, Volume 6401, Complexity of Constraints (2006)

Abstract
We contribute to the study of efficient enumeration algorithms for all solutions of constraint satisfaction problems. The only algorithm known so far, presented by Creignou and Hébrard and generalized by Cohen, reduces the enumeration problem for a constraint language $Gamma$ to the decision problem for a slightly enlarged constraint language $Gamma^+,$ i.e., it yields an efficient enumeration algorithm for the case where $mathrm{CSP}(Gamma^+)$ is tractable. We develop a new class of algorithms, yielding efficient enumeration algorithms for a broad class of constraint languages. For the three-element domain, we achieve a first step towards a dichotomy theorem for the enumeration problem.
Cite as

Henning Schnoor and Ilka Schnoor. Enumerating all Solutions for Constraint Satisfaction Problems. In Complexity of Constraints. Dagstuhl Seminar Proceedings, Volume 6401, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{schnoor_et_al:DagSemProc.06401.6,
  author =	{Schnoor, Henning and Schnoor, Ilka},
  title =	{{Enumerating all Solutions for Constraint Satisfaction Problems}},
  booktitle =	{Complexity of Constraints},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6401},
  editor =	{Nadia Creignou and Phokion Kolaitis and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06401.6},
  URN =		{urn:nbn:de:0030-drops-8040},
  doi =		{10.4230/DagSemProc.06401.6},
  annote =	{Keywords: Complexity, constraint satisfaction, enumeration}
}
Document
DOI: 10.4230/DagSemProc.06401.7
New Algebraic Tools for Constraint Satisfaction

Authors: Henning Schnoor and Ilka Schnoor

Published in: Dagstuhl Seminar Proceedings, Volume 6401, Complexity of Constraints (2006)

Abstract
The Galois correspondence involving polymorphisms and co-clones has received a lot of attention in regard to constraint satisfaction problems. However, it fails if we are interested in a reduction giving equivalence instead of only satisfiability-equivalence. We show how a similar Galois connection involving weaker closure operators can be applied for these problems. As an example of the usefulness of our construction, we show how to obtain very short proofs of complexity classifications in this context.
Cite as

Henning Schnoor and Ilka Schnoor. New Algebraic Tools for Constraint Satisfaction. In Complexity of Constraints. Dagstuhl Seminar Proceedings, Volume 6401, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{schnoor_et_al:DagSemProc.06401.7,
  author =	{Schnoor, Henning and Schnoor, Ilka},
  title =	{{New Algebraic Tools for Constraint Satisfaction}},
  booktitle =	{Complexity of Constraints},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6401},
  editor =	{Nadia Creignou and Phokion Kolaitis and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06401.7},
  URN =		{urn:nbn:de:0030-drops-8057},
  doi =		{10.4230/DagSemProc.06401.7},
  annote =	{Keywords: Constraints, Partial Clones, Galois Correspondence}
}
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