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An Isaac Newton Institute Programme

Logic and Algorithms

Team Logic

21st April 2006

Author: Jouko Vaananen (Helsinki)

Abstract

I discuss logic based on dependence as a basic concept. What is the logic of dependence? What is the mathematics of dependence? Typical examples of dependence in the sense that I am interested in are the dependence of a field on other fields in a database, the dependence of a move in a strategy on other moves, and the dependence of a quantifier on other quantifiers in formulas of formal or natural languages. I describe a new logic, called team logic, for the study of types of dependence and give it semantics in terms of team structures. I discuss connections to other logics such as linear logic, modal logic, first order logic, independence friendly logic, Henkin quantifier logic, and second order logic.