Dependence Logic

A New Approach to Independence Friendly Logic

By: Jouko Vaananen

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Paperback | 10 May 2007

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236 Pages

Dimensions(cm)
22.86 x 15.24 x 1.27

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Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic.

Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book.

It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.

Industry Reviews

"The material is written in a very friendly way. Definitions of the majority of the important notions are preceded by explanations of the ideas. Moreover, the book contains more than 200 exercises, many of which have a solution at the end of the book. This makes it easier to read the book and understand its material. The book could definitely be interesting to a wide spectrum of mathematicians, philosophers and computer scientists." - Michael Krynicki, Mathematical Reviews

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Preface	p. ix
Introduction	p. 1
Preliminaries	p. 5
Relations	p. 5
Vocabularies and structures	p. 5
Terms and formulas	p. 6
Truth and satisfaction	p. 7
Dependence logic	p. 10
Examples and a mathematical model for teams	p. 11
Formulas as types of teams	p. 16
Logical equivalence and duality	p. 29
First order formulas	p. 37
The flattening technique	p. 42
Dependence/independence friendly logic	p. 44
Examples	p. 48
Even cardinality	p. 48
Cardinality	p. 51
Completeness	p. 53
Well-foundedness	p. 55
Connectedness	p. 56
Natural numbers	p. 57
Real numbers	p. 59
Set theory	p. 60
Game theoretic semantics	p. 63
Semantic game of first order logic	p. 63
Perfect information game for dependence logic	p. 69
Imperfect information game for dependence logic	p. 80
Model theory	p. 86
From D to [sum]1/1	p. 86
Applications of [sum]1/1	p. 90
From [sum]1/1 to D	p. 94
Truth definitions	p. 100
Model existence game	p. 110
Ehrenfeucht-Fraisse game for dependence logic	p. 121
Complexity	p. 134
Decision and other problems	p. 134
Some set theory	p. 135
[sum subscript 2]-completeness in set theory	p. 140
Team logic	p. 144
Preorder of determination	p. 144
Dependence and independence	p. 148
Formulas of team logic	p. 150
From team logic to L[superscript 2]	p. 158
From L[superscript 2] to team logic	p. 161
Ehrenfeucht-Fraisse game for team logic	p. 163
Solutions to selected exercises	p. 169
References	p. 220
Index	p. 223
Table of Contents provided by Ingram. All Rights Reserved.

Dependence Logic

A New Approach to Independence Friendly Logic

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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More in Combinatorics & Graph Theory

Foundations of Graph Theory