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Documents authored by Kontinen, Juha


Document
Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity

Authors: Juha Kontinen, Max Sandström, and Jonni Virtema

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We relate the new semantics with the original semantics based on multisets and establish one of the first positive complexity theoretic results in the temporal team semantics setting. In particular we show that both logics enjoy normal forms that can be utilised to obtain results related to expressivity and complexity (decidability) of the new logics.

Cite as

Juha Kontinen, Max Sandström, and Jonni Virtema. Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 60:1-60:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kontinen_et_al:LIPIcs.MFCS.2023.60,
  author =	{Kontinen, Juha and Sandstr\"{o}m, Max and Virtema, Jonni},
  title =	{{Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.60},
  URN =		{urn:nbn:de:0030-drops-185949},
  doi =		{10.4230/LIPIcs.MFCS.2023.60},
  annote =	{Keywords: Hyperproperties, Linear Temporal Logic, Team Semantics}
}
Document
Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity

Authors: Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
We study the expressivity and complexity of model checking of linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL -extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable.

Cite as

Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang. Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 52:1-52:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{virtema_et_al:LIPIcs.FSTTCS.2021.52,
  author =	{Virtema, Jonni and Hofmann, Jana and Finkbeiner, Bernd and Kontinen, Juha and Yang, Fan},
  title =	{{Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{52:1--52:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.52},
  URN =		{urn:nbn:de:0030-drops-155634},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.52},
  annote =	{Keywords: Linear temporal logic, Hyperproperties, Model Checking, Expressivity}
}
Document
On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic

Authors: Miika Hannula, Juha Kontinen, Martin Lück, and Jonni Virtema

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)


Abstract
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to term constructions, 2) restrictions to the form of the Boolean matrix. Of the first sort, we consider two kinds of restrictions: firstly, disallowing nested use of proper function variables, and secondly stipulating that each function variable must appear with a fixed sequence of arguments. Of the second sort, we consider Horn, Krom, and core fragments of the Boolean matrix. We classify the complexity of logics obtained by combining these two types of restrictions. We show that, in most cases, logics with k alternating blocks of function quantifiers are complete for the kth or (k-1)th level of the exponential time hierarchy. Furthermore, we establish NL-completeness for the Krom and core fragments, when k = 1 and both restrictions of the first sort are in effect.

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Miika Hannula, Juha Kontinen, Martin Lück, and Jonni Virtema. On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 27:1-27:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{hannula_et_al:LIPIcs.CSL.2021.27,
  author =	{Hannula, Miika and Kontinen, Juha and L\"{u}ck, Martin and Virtema, Jonni},
  title =	{{On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{27:1--27:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.27},
  URN =		{urn:nbn:de:0030-drops-134610},
  doi =		{10.4230/LIPIcs.CSL.2021.27},
  annote =	{Keywords: quantified Boolean formulae, computational complexity, second-order logic, Horn and Krom fragment}
}
Document
Counting of Teams in First-Order Team Logics

Authors: Anselm Haak, Juha Kontinen, Fabian Müller, Heribert Vollmer, and Fan Yang

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We study descriptive complexity of counting complexity classes in the range from #P to #*NP. A corollary of Fagin’s characterization of NP by existential second-order logic is that #P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae. In this paper we extend this study to classes beyond #P and extensions of first-order logic with team semantics. These team-based logics are closely related to existential second-order logic and its fragments, hence our results also shed light on the complexity of counting for extensions of first-order logic in Tarski’s semantics. Our results show that the class #*NP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of #*NP and #P, respectively. We also study the function class generated by inclusion logic and relate it to the complexity class TotP, which is a subclass of #P. Our main technical result shows that the problem of counting satisfying assignments for monotone Boolean Sigma_1-formulae is #*NP-complete with respect to Turing reductions as well as complete for the function class generated by dependence logic with respect to first-order reductions.

Cite as

Anselm Haak, Juha Kontinen, Fabian Müller, Heribert Vollmer, and Fan Yang. Counting of Teams in First-Order Team Logics. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 19:1-19:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{haak_et_al:LIPIcs.MFCS.2019.19,
  author =	{Haak, Anselm and Kontinen, Juha and M\"{u}ller, Fabian and Vollmer, Heribert and Yang, Fan},
  title =	{{Counting of Teams in First-Order Team Logics}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.19},
  URN =		{urn:nbn:de:0030-drops-109634},
  doi =		{10.4230/LIPIcs.MFCS.2019.19},
  annote =	{Keywords: team-based logics, counting classes, finite model theory, descriptive complexity}
}
Document
Logics for Dependence and Independence (Dagstuhl Seminar 19031)

Authors: Erich Grädel, Phokion G. Kolaitis, Juha Kontinen, and Heribert Vollmer

Published in: Dagstuhl Reports, Volume 9, Issue 1 (2019)


Abstract
This report documents the programme and outcomes of Dagstuhl Seminar 19031 "Logics for Dependence and Independence". This seminar served as a follow-up seminar to the highly successful seminars "Dependence Logic: Theory and Applications" (13071) and "Logics for Dependence and Independence" (15261). A key objective of the seminar was to bring together researchers working in dependence logic and in the application areas so that they can communicate state-of-the-art advances and embark on a systematic interaction. The goal was especially to reach those researchers who have recently started working in this thriving area as well as researchers working on several aspects of database theory, separation logic, and logics of uncertainy.

Cite as

Erich Grädel, Phokion G. Kolaitis, Juha Kontinen, and Heribert Vollmer. Logics for Dependence and Independence (Dagstuhl Seminar 19031). In Dagstuhl Reports, Volume 9, Issue 1, pp. 28-46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@Article{gradel_et_al:DagRep.9.1.28,
  author =	{Gr\"{a}del, Erich and Kolaitis, Phokion G. and Kontinen, Juha and Vollmer, Heribert},
  title =	{{Logics for Dependence and Independence (Dagstuhl Seminar 19031)}},
  pages =	{28--46},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{9},
  number =	{1},
  editor =	{Gr\"{a}del, Erich and Kolaitis, Phokion G. and Kontinen, Juha and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.1.28},
  URN =		{urn:nbn:de:0030-drops-105682},
  doi =		{10.4230/DagRep.9.1.28},
  annote =	{Keywords: dependence logic, mathematical logic, computational complexity, finite model theory, game theory}
}
Document
Tutorial
Computational Aspects of Logics in Team Semantics (Tutorial)

Authors: Juha Kontinen

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)


Abstract
Team Semantics is a logical framework for the study of various dependency notions that are important in many areas of science. The starting point of this research is marked by the publication of the monograph Dependence Logic (Jouko Väänänen, 2007) in which first-order dependence logic is developed and studied. Since then team semantics has evolved into a flexible framework in which numerous logics have been studied. Much of the work in team semantics has so far focused on results concerning either axiomatic characterizations or the expressive power and computational aspects of various logics. This tutorial provides an introduction to team semantics with a focus on results regarding expressivity and computational aspects of the most prominent logics of the area. In particular, we discuss dependence, independence and inclusion logics in first-order, propositional, and modal team semantics. We show that first-order dependence and independence logic are equivalent with existential second-order logic and inclusion logic with greatest fixed point logic. In the propositional and modal settings we characterize the expressive power of these logics by so-called team bisimulations and determine the complexity of their model checking and satisfiability problems.

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Juha Kontinen. Computational Aspects of Logics in Team Semantics (Tutorial). In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, p. 1:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{kontinen:LIPIcs.STACS.2017.1,
  author =	{Kontinen, Juha},
  title =	{{Computational Aspects of Logics in Team Semantics}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.1},
  URN =		{urn:nbn:de:0030-drops-70333},
  doi =		{10.4230/LIPIcs.STACS.2017.1},
  annote =	{Keywords: team semantics, dependence logic, model checking, satisfiability problem, team bisimulation}
}
Document
Descriptive Complexity of #AC^0 Functions

Authors: Arnaud Durand, Anselm Haak, Juha Kontinen, and Heribert Vollmer

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)


Abstract
We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely determine the inclusion structure and show that #P and #AC^0 appear as classes of this hierarchy. In this way, we unconditionally place #AC^0 properly in a strict hierarchy of arithmetic classes within #P. We compare our classes with a hierarchy within #P defined in a model-theoretic way by Saluja et al. We argue that our approach is better suited to study arithmetic circuit classes such as #AC^0 which can be descriptively characterized as a class in our framework.

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Arnaud Durand, Anselm Haak, Juha Kontinen, and Heribert Vollmer. Descriptive Complexity of #AC^0 Functions. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 20:1-20:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{durand_et_al:LIPIcs.CSL.2016.20,
  author =	{Durand, Arnaud and Haak, Anselm and Kontinen, Juha and Vollmer, Heribert},
  title =	{{Descriptive Complexity of #AC^0 Functions}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.20},
  URN =		{urn:nbn:de:0030-drops-65601},
  doi =		{10.4230/LIPIcs.CSL.2016.20},
  annote =	{Keywords: finite model theory, Fagin's theorem, arithmetic circuits, counting classes, Skolem function}
}
Document
Decidability of Predicate Logics with Team Semantics

Authors: Juha Kontinen, Antti Kuusisto, and Jonni Virtema

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)


Abstract
We study the complexity of predicate logics based on team semantics. We show that the satisfiability problems of two-variable independence logic and inclusion logic are both NEXPTIME-complete. Furthermore, we show that the validity problem of two-variable dependence logic is undecidable, thereby solving an open problem from the team semantics literature. We also briefly analyse the complexity of the Bernays-Schoenfinkel-Ramsey prefix classes of dependence logic.

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Juha Kontinen, Antti Kuusisto, and Jonni Virtema. Decidability of Predicate Logics with Team Semantics. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 60:1-60:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{kontinen_et_al:LIPIcs.MFCS.2016.60,
  author =	{Kontinen, Juha and Kuusisto, Antti and Virtema, Jonni},
  title =	{{Decidability of Predicate Logics with Team Semantics}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.60},
  URN =		{urn:nbn:de:0030-drops-64726},
  doi =		{10.4230/LIPIcs.MFCS.2016.60},
  annote =	{Keywords: team semantics, dependence logic, complexity, two-variable logic}
}
Document
Logics for Dependence and Independence (Dagstuhl Seminar 15261)

Authors: Erich Grädel, Juha Kontinen, Jouka Väänänen, and Heribert Vollmer

Published in: Dagstuhl Reports, Volume 5, Issue 6 (2016)


Abstract
This report documents the programme and outcomes of Dagstuhl Seminar 15261 "Logics for Dependence and Independence". This seminar served as a follow-up seminar to the highly successful seminar "Dependence Logic: Theory and Applications" (Dagstuhl Seminar 13071). A key objective of the seminar was to bring together researchers working in dependence logic and in the application areas so that they can communicate state-of-the-art advances and embark on a systematic interaction. The goal was especially to reach those researchers who have recently started working in this thriving area.

Cite as

Erich Grädel, Juha Kontinen, Jouka Väänänen, and Heribert Vollmer. Logics for Dependence and Independence (Dagstuhl Seminar 15261). In Dagstuhl Reports, Volume 5, Issue 6, pp. 70-85, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@Article{gradel_et_al:DagRep.5.6.70,
  author =	{Gr\"{a}del, Erich and Kontinen, Juha and V\"{a}\"{a}n\"{a}nen, Jouka and Vollmer, Heribert},
  title =	{{Logics for Dependence and Independence (Dagstuhl Seminar 15261)}},
  pages =	{70--85},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{5},
  number =	{6},
  editor =	{Gr\"{a}del, Erich and Kontinen, Juha and V\"{a}\"{a}n\"{a}nen, Jouka and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.5.6.70},
  URN =		{urn:nbn:de:0030-drops-55084},
  doi =		{10.4230/DagRep.5.6.70},
  annote =	{Keywords: team semantics, dependence logic, mathematical logic, computational complexity, finite model theory, game theory}
}
Document
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
Hierarchies in independence logic

Authors: Pietro Galliani, Miika Hannula, and Juha Kontinen

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)


Abstract
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential second-order logic.

Cite as

Pietro Galliani, Miika Hannula, and Juha Kontinen. Hierarchies in independence logic. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 263-280, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{galliani_et_al:LIPIcs.CSL.2013.263,
  author =	{Galliani, Pietro and Hannula, Miika and Kontinen, Juha},
  title =	{{Hierarchies in independence logic}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{263--280},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.263},
  URN =		{urn:nbn:de:0030-drops-42021},
  doi =		{10.4230/LIPIcs.CSL.2013.263},
  annote =	{Keywords: Existential second-order logic, Independence logic, Inclusion logic, Expressiveness hierarchies}
}
Document
Dependence Logic: Theory and Applications (Dagstuhl Seminar 13071)

Authors: Samson Abramsky, Juha Kontinen, Jouko Väänanen, and Heribert Vollmer

Published in: Dagstuhl Reports, Volume 3, Issue 2 (2013)


Abstract
This report documents the programme and outcomes of Dagstuhl Seminar 13071 "Dependence Logic: Theory and Applications". The seminar brought together researchers from different areas such as mathematical logic, quantum mechanics, statistics, social choice theory, and theoretical computer science. A key objective of the seminar was to bring together, for the first time, researchers working in dependence logic and in the application areas so that they can communicate state-of-the-art advances and embark on a systematic interaction.

Cite as

Samson Abramsky, Juha Kontinen, Jouko Väänanen, and Heribert Vollmer. Dependence Logic: Theory and Applications (Dagstuhl Seminar 13071). In Dagstuhl Reports, Volume 3, Issue 2, pp. 45-54, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@Article{abramsky_et_al:DagRep.3.2.45,
  author =	{Abramsky, Samson and Kontinen, Juha and V\"{a}\"{a}nanen, Jouko and Vollmer, Heribert},
  title =	{{Dependence Logic: Theory and Applications (Dagstuhl Seminar 13071)}},
  pages =	{45--54},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{3},
  number =	{2},
  editor =	{Abramsky, Samson and Kontinen, Juha and V\"{a}\"{a}nanen, Jouko and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.3.2.45},
  URN =		{urn:nbn:de:0030-drops-40127},
  doi =		{10.4230/DagRep.3.2.45},
  annote =	{Keywords: Data structures, Algorithms, Complexity, Verification, Logic}
}
Document
Dependence logic with a majority quantifier

Authors: Arnaud Durand, Johannes Ebbing, Juha Kontinen, and Heribert Vollmer

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)


Abstract
We study the extension of dependence logic D by a majority quantifier M over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, D(M) captures the complexity class counting hierarchy.

Cite as

Arnaud Durand, Johannes Ebbing, Juha Kontinen, and Heribert Vollmer. Dependence logic with a majority quantifier. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 252-263, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)


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@InProceedings{durand_et_al:LIPIcs.FSTTCS.2011.252,
  author =	{Durand, Arnaud and Ebbing, Johannes and Kontinen, Juha and Vollmer, Heribert},
  title =	{{Dependence logic with a majority quantifier}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{252--263},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.252},
  URN =		{urn:nbn:de:0030-drops-33467},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.252},
  annote =	{Keywords: dependence logic, counting hierarchy, majority quantifier, second order logic, descriptive complexity, finite model theory}
}
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