Classical and Quantum Probabilities as Truth Values
  We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension of our existing work on a topos approach to quantum theory. Earlier results on the representation of arbitrary quantum states are complemented with a purely logical perspective. 
Andreas Doering, Chris J. Isham
quant-ph math-ph math.MP math.PR