# Dependence and Independence

Studia Logica 101 (2):399-410 (2013)

# 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

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2013-03-17

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# Author's Profile

Jouko A Vaananen
University of Helsinki

# Citations of this work

Explicating Logical Independence.Lloyd Humberstone - 2020 - Journal of Philosophical Logic 49 (1):135-218.
Propositional logics of dependence.Fan Yang & Jouko Väänänen - 2016 - Annals of Pure and Applied Logic 167 (7):557-589.
Questions and Dependency in Intuitionistic Logic.Ivano Ciardelli, Rosalie Iemhoff & Fan Yang - 2020 - Notre Dame Journal of Formal Logic 61 (1):75-115.

# References found in this work

Compositional semantics for a language of imperfect information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
On definability in dependence logic.Juha Kontinen & Jouko Väänänen - 2009 - Journal of Logic, Language and Information 18 (3):317-332.