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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