Studia Logica

, Volume 101, Issue 2, pp 399–410 | Cite as

Dependence and Independence

Article

Abstract

We introduce an atomic formula \({\vec{y} \bot_{\vec{x}}\vec{z}}\) intuitively saying that the variables \({\vec{y}}\) are independent from the variables\({\vec{z}}\) if the variables \({\vec{x}}\) are kept constant. We contrast this with dependence logic \({\mathcal{D}}\) based on the atomic formula =\({(\vec{x}, \vec{y})}\) , actually equivalent to \({\vec{y} \bot_{\vec{x}}\vec{y}}\) , saying that the variables \({\vec{y}}\) are totally determined by the variables \({\vec{x}}\) . We show that \({\vec{y} \bot_{\vec{x}}\vec{z}}\) gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that \({\vec{y} \bot_{\vec{x}}\vec{z}}\) can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using =\({(\vec{x}, \vec{y})}\) have.

Keywords

Logics of dependence and independence Team semantics Logics with imperfectinformation Axiomatization of independence 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Mathematische Grundlagen der InformatikRWTH Aachen UniversityAachenGermany
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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