The geometric semantics of algebraic quantum mechanics
  In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. 
John Alex Cruz Morales and Boris Zilber
math-ph math.MP math.QA