Speaker: Álvaro Diaz Ramos (Carnegie Mellon University)
Date and Time: Thursday, November 19th 2026, 16:30-18:00
Venue: online only.
Title: Pregeometry semantics for LFD
Abstract. In their 2021 paper introducing the logic of functional dependence (LFD), Baltag and van Benthem posed the problem of axiomatizing the logic of vector space dependence in the language of LFD. They proposed that the basic LFD axiomatic system extended with the Steinitz exchange axiom (LFDS) might yield such an axiomatization.
In this talk, I will present my resolution of this problem using the natural semantics for LFD based on pregeometries. I will show that LFDS is complete with respect to pregeometries, but fails to be complete with respect to the restricted class of pregeometries generated by vector spaces.
By adding the new axiom of avoidance, I will explain how LFDS can be extended to yield a complete, recursive axiomatization for the logic of vector space dependence. Finally, I will present the proof of completeness, which uses tools from commutative algebra and ultraproducts.