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, after pointing out the seemingly forgotten fact that bivalence in quantum logic can be maintained, albeit at the price of truth-functionality, it argues that Hellman (1980) fails to show that this lack of truth-functionality entails a change of meaning between classical and quantum logical connectives. Finally, the paper proposes a meaning-variance argument that fares better on our analysis.