Johan van Benthem (ILLC/UvA, Stanford University and Tsinghua University)

A Modal Logic of Functional Dependence

Abstract: Dependence is a notion pervading many areas, from probability to reasoning with quantifiers, and from informational correlation in data bases to causal connections, or interactive behavior in games. Not surprisingly, dependence has caught the attention of logicians, and various systems have been proposed for capturing basic notions of dependence and their fundamental logical laws. In this talk, I will present a new decidable modal logic of functional dependence that models both ontic and epistemic dependence, and explore its expressive strength and complete proof calculus. I also discuss dynamic extensions when new information comes in, and boundaries with more complex logical systems, e.g., for reasoning about independence. Finally, I will discuss connections with some richer notions of dependence coming from linear algebra, causal networks, game theory, and topology. The approach presented here emanates most straightforwardly from the 'generalized assignment models' from the 1990s, but in the full paper, we include comparisons with other systems of dependence logic. This is joint work with Alexandru Baltag.