PP-2011-07: Dependence and Independence

PP-2011-07: Grädel, Erich and Väänänen, Jouko (2011) Dependence and Independence. [Report]

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Abstract

We introduce an atomic formula \vec{y} ⊥_\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 D based on the atomic formula =(\vec{x}, \vec{y}), actually a special case of \vec{y} ⊥_\vec{x} \vec{z}, saying that the variables y are totally determined by the variables \vec{x}. We show that \vec{y} ⊥_\vec{x} \vec{z} gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that \vec{y} ⊥_\vec{x} \vec{z} can be used to give partially ordered quantifiers and IF-logic a compositional interpretation without some of the shortcomings related to so called signaling that interpretations using =(\vec{x}, \vec{y}) have.

Item Type: Report
Report Nr: PP-2011-07
Series Name: Prepublication (PP) Series
Year: 2011
Uncontrolled Keywords: dependence; independence; IF logic
Subjects: Logic
Depositing User: Jouko
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/411

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