 Another logic which lacks bivalence is quantum logic, which also typically rejects the distributive laws of classical logic (Birkhoff and von Neumann 1936; Putnam 1968). Quantum logic was started by Birkoff and von Neumann for studying the relation among physical observables in quantum physics. Quantum logic rejects bivalence because a state in a quantum system typically assigns probability values to experimental propositions rather than plain true or false. To see why quantum physics can be taken to provide evidence against the distributive laws of classical logic consider a particle moving on a line. Suppose \(p\) asserts that the particle’s momentum is within a certain interval, while \(q\) and \(r\) assert that the particle’s position is in the intervals \(\alpha\) and \(\beta\) respectively. Suppose the statement \(p \wedge (q \vee r)\) is confirmed by our observation, so is true (or has value 1). By the distributive laws we can classically conclude \((p \wedge q) \vee (p \wedge r)\). But in quantum theory the latter might still be false (have value 0), since both conjunctions \((p \wedge q)\) and \((p \wedge r)\) might assert tighter restrictions on simultaneous values of position and momentum than is allowed by Heisenberg’s uncertainty principle (see the entry on  the uncertainty principle).  So in the “logic of quantum physics” a disjunction \((q \vee r)\) can have value 1 in a state without any of the disjuncts having value 1: if \(q\) has value 1 or \(r\) has value 1, then \((q \vee r)\) has value 1, but the other direction fails.