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