nLab dependence logic

Idea

Dependence logic adds the concept of dependence to first order logic. That is, we may add new atomic formulas of the form

$$= (x_1,x_2,\ldots,x_n,y)$$

meaning that the values of $x_1,\ldots,x_n$ completely determine the value of $y$.

It “aims to establish a basic theory of dependence and independence underlying such seemingly unrelated subjects as causality, random variables, bound variables in logic, database theory, the theory of social choice, and even quantum physics” (from the abstract of Galliani, Väänänen 2014).

Team logic is a further extension of dependence logic by classical negation.

Literature

• Jouko Väänänen, Dependence logic: A new approach to independence friendly logic, London Mathematical Society Student Texts 70, Cambridge University Press 2007
• P. Galliani, J. Väänänen, On dependence logic, In: Baltag A., Smets S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. 2014 doi
• Samson Abramsky, Juha Kontinen, Jouko Väänänen, Heribert Vollmer (eds.), Dependence logic: theory and applications, Birkhäuser, Basel, 2016