Quantum logic and meaning

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic - compatible with realism about quantum mechanics - can be maintained, albeit at the price of truth-functionality. Finally, the paper improves on Hellman (1980)’s argument that this lack of truth-functionality entails a change of meaning between classical and quantum logical connectives