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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