Consequence and Prediction

Given a quantum constructive logic, , that contains a certain fragment, , there is a transformation from either into a classical constructive logic, .

The transformation in

is a prediction. A prediction provides a posterior distribution, , given the observation, , and the transformation (prior), .  Simplistic transformations often produce a scalar posterior .

The transformation in

is a proposition. A consequent

is a strict logical operation.

Bayes, T. (1958), Studies in the History of Probability and Statistics: IX. Thomas Bayes’ Essay Towards Solving a Problem in the Doctrine of Chances, Biometrika, 45, 296-315.

Gentzen, G. (1969), The Collected Papers of Gerhard Gentzen (Ed. M. E. Szabo). Amsterdam, Netherlands: North-Holland.

Jean-Yves Girard. (1993), Linear logic: Its syntax and semantics. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, 1–42. Cambridge University Press.

Flickering and Meditation

A brief record of a working hypothesis.