Title: The Modal Logic of Functional Dependency (or how to use questions to answer other questions)
Abstract: If /to be is to be the value of a variable, /then to know is /to know/
a /functional dependence between variables/. (Moreover, the conclusion
may still be arguably be true even if Quine's premise is wrong...) .
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, simple, decidable modal logic of functional dependence
that models both ontic and epistemic dependence, and explore its
expressive strength and complete proof calculus. The approach
presented here connects back to the 'generalized assignment models'
from the 1990s, aimed at `modalizing' First-Order Logic..
Time-permitting, I will discuss richer notions of dependence, coming
from linear algebra, causal networks, game theory, and topology. In
particular, in natural sciences the exact value of an empirical
variables might not be knowable, and instead only inexact
approximations can be known.This leads to a topological conception of
such variables, /as maps from the state space into a topological
space/. I argue that knowability of a dependency amounts in such an
empirical context to the /continuity/ of the given functional
correlation. To know (in natural science) is/to know a continuous
dependence./ This is joint work with Johan van Benthem.