Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Presheaf of Conditional Expectations, a Bridge Between Probability and Intuitionistic Truth Value

Version 1 : Received: 3 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (12:13:38 CET)

How to cite: Laedermann, J. The Presheaf of Conditional Expectations, a Bridge Between Probability and Intuitionistic Truth Value. Preprints 2021, 2021120067. https://doi.org/10.20944/preprints202112.0067.v1 Laedermann, J. The Presheaf of Conditional Expectations, a Bridge Between Probability and Intuitionistic Truth Value. Preprints 2021, 2021120067. https://doi.org/10.20944/preprints202112.0067.v1

Abstract

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

Keywords

category; topos; presheaf; probability; validity; truth; conditional expectation; measurement; quantum mechanics; information; entropy; reduction; collapse; projection; logic; algebra; Wiener; Bayes; Boole; Heyting; Brownian motion; filter; crible; capacity; reservation; context

Subject

Physical Sciences, Mathematical Physics

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