Dependence of variables construed as an atomic formula

作者：Vaananen Jouko^*; Hodges Wilfrid

来源：Annals of Pure and Applied Logic, 2010, 161(6): 817-828.

DOI：10.1016/j.apal.2009.06.009

• Dependence logic
• Game-theoretic semantics
• Henkin quantifier
• Second order logic

We define a logic D capable of expressing dependence of a variable on designated variables only. Thus D has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic D achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our D avoids some difficulties arising in the original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth of 0 is definable inside D. We give such a definition for D in the spirit of [11,2] and [1].

• 出版日期2010-3