Submitted:
03 December 2021
Posted:
06 December 2021
You are already at the latest version
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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.