Quantum probabilities and the Born rule in the intuitionistic   interpretation of quantum mechanics
  This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of constructive logic makes it possible (through a replacement of the concept of truth with the concept of constructive probability) to abandon the law of excluded middle in the intuitionistic interpretation. 
Arkady Bolotin
quant-ph