Team Logic and Second-Order Logic

• Autorzy: Kontinen J. , Nurmi V.
• Języki publikacji: EN

Abstrakty

EN

Team logic is a new logic, introduced by V¨a¨an¨anen [12], extending dependence logic by classical negation. Dependence logic adds to first-order logic atomic formulas expressing functional dependence of variables on each other. It is known that on the level of sentences dependence logic and team logic are equivalent with existential second-order logic and full second-order logic, respectively. In this article we show that, in a sense that we make explicit, team logic and secondorder logic are also equivalent with respect to open formulas. A similar earlier result relating open formulas of dependence logic to the negative fragment of existential second-order logic was proved in [8].

Słowa kluczowe

EN

dependence logic; team logic; team

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2011
• Tom: Vol. 106, nr 2-4
• Strony: 259--272
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Kontinen J.

autor

Nurmi V.

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, Finland,

Bibliografia

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• [7] Kontinen, J., Väänänen, J.: Erratum: On definability in dependence logic, To appear in Journal of Logic, Language and Information, DOI: 10.1007/s10849-010-9125-6.
• [8] Kontinen, J., Väänänen, J.: On definability in dependence logic, Journal of Logic, Language and Information, 18(3), 2009, 317-332.
• [9] Nurmi, V.: Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams, Ph.D. Thesis, University of Helsinki, 2009.
• [10] Skolem, T.: Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichteMengen, Skrifter utgit av Videnskappsselskapet i Kristiania, 1920.
• [11] Skolem, T.: Selected works in logic, Edited by Jens Erik Fenstad, Universitetsforlaget, Oslo, 1970.
• [12] Väänänen, J.: Dependence logic: A New Approach to Independence Friendly Logic, vol. 70 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 2007, ISBN 9780521876599.
• [13] Väänänen, J.: personal communication, 2009.
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