Abstract
The development of “operational quantum logic” points out that classical Boolean structures are too rigid to describe the actual and potential properties of quantum systems. Operational quantum logic bears upon basic axioms which are motivated by empirical facts and as such supports the dynamic shift from classical to non-classical logic resulting into a dynamics of logic.
On the other hand, an intuitionistic perspective on operational quantum logic, guides us in the direction of incorporating dynamics logically by reconsidering the primitive propositions required to describe the behavior of a quantum system, in particular in view of the emergent disjunctivity due to the non-determinism of quantum measurements.
A further elaboration on “intuitionistic quantum logic” emerges into a “dynamic operational quantum logic”, which allows us to express dynamic reasoning in the sense that we can capture how actual properties propagate, including their temporal causal structure. It is in this sense that passing from static operational quantum logic to dynamic operational quantum logic results in a true logic of dynamics that provides a unified logical description of systems which evolve or which are submitted to measurements. This setting reveals that even static operational quantum logic bears a hidden dynamic ingredient in terms of what is called “the orthomodularity” of the lattice-structure.
Focusing on the quantale semantics for dynamic operational quantum logic, we delineate some points of difference with the existing quantale semantics for (non)-commutative linear logic. Linear logic is here to be conceived of as a resource-sensitive logic capable of dealing with actions or in other words, it is a logic of dynamics.
We take this opportunity to dedicate this paper to Constantin Piron at the occasion of his retirement.
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Coecke, B., Moore, D.J., Smets, S. (2009). Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples. In: Rahman, S., Symons, J., Gabbay, D.M., Bendegem, J.P.v. (eds) Logic, Epistemology, and the Unity of Science. Logic, Epistemology, And The Unity Of Science, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2808-3_24
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