The principles of mathematics revisited
The principles of mathematics revisited
Dependence Logic: A New Approach to Independence Friendly Logic (London Mathematical Society Student Texts)
On Definability in Dependence Logic
Journal of Logic, Language and Information
Generalized Quantifiers in Dependence Logic
Journal of Logic, Language and Information
The Dynamification of Modal Dependence Logic
Journal of Logic, Language and Information
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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.