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Characterizing quantifier extensions of dependence logic

Published online by Cambridge University Press:  12 March 2014

Fredrik Engström  and
Juha Kontinen
Fredrik Engström
Affiliation:
Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Box 200, 405 30 Gothenburg, Sweden, E-mail: fredrik.engstrom@gu.se
Juha Kontinen
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Finland, E-mail: juha.kontinen@helsinki.fi
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Abstract

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 307 - 316
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Abramsky, Samson and Väänänen, Jouko, From IF to BI: a tale of dependence and separation, Synthese, vol. 167 (2009), no. 2, pp. 207–230.CrossRefGoogle Scholar
[2]Durand, Arnaud, Ebbing, Johannes, Kontinen, Juha, and Vollmer, Heribert, Dependence logic with a majority quantifier, Foundations of software technology and theoretical computer science (Chakraborty, Supratik and Kumar, Amit, editors), Leibniz International Proceedings in Informatics, vol. 13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2011, pp. 252–263.Google Scholar
[3]Durand, Arnaud and Kontinen, Juha, Hierarchies in dependence logic, ACM Transactions on Computational Logic, vol. 13 (2012), no. 4, pp. 31:1–31:21.CrossRefGoogle Scholar
[4]Engström, Fredrik, Generalized quantifiers in dependence logic, Journal of Logic, Language and Information, vol. 21 (2012), no. 3, pp. 299–324.CrossRefGoogle Scholar
[5]Galliani, Pietro, Inclusion and exclusion dependencies in team semantics—on some logics of imperfect information, Annals of Pure and Applied Logic, vol. 163 (2012), no. 1, pp. 68–84.CrossRefGoogle Scholar
[6]Grädel, Erich and Väänänen, Jouko, Dependence and independence, Studia Logica, to appear.Google Scholar
[7]Henkin, L., Some remarks on infinitely long formulas, Infinitistic Methods (Proceeding of the Symposium on Foundations of Mathematics, Warsaw, 1959), Pergamon, Oxford, 1961, pp. 167–183.Google Scholar
[8]Hintikka, Jaakko and Sandu, Gabriel, Informational independence as a semantical phenomenon, Logic, methodology and philosophy of science, VIII (Moscow, 1987) (Fenstad, Jens Erik, Frolov, Ivan T., and Hilpinen, Risto, editors), Studies in Logic and the Foundations of Mathematics, vol. 126, North-Holland, Amsterdam, 1989, pp. 571–589.Google Scholar
[9]Kontinen, Juha and Väänänen, Jouko A., On definability in dependence logic, Journal of Logic, Language and Information, vol. 18 (2009), no. 3, pp. 317–332.CrossRefGoogle Scholar
[10]Lindström, Per, First order predicate logic with generalized quantifiers, Theoria, vol. 32 (1966), pp. 186–195.CrossRefGoogle Scholar
[11]Mostowski, Andrzej, On a generalization of quantifiers, Fundamenta Mathematical vol. 44 (1957), pp. 12–36.CrossRefGoogle Scholar
[12]Väänänen, Jouko, Dependence logic: A new approach to independence friendly logic, London Mathematical Society Student Texts, vol. 70, Cambridge University Press, Cambridge, 2007.CrossRefGoogle Scholar