Year: 2020
Type: conference-paper
Abstract: In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of an algebra of probabilities is the real unit interval. In this paper we try to explain this phenomenon. We will show that the structure of the real unit interval naturally arises from a few reasonable assumptions. We do this by studying effect monoids, an abstraction of the algebraic structure of the real unit interval: it has an addition x + y which is only defined when x + y ≤ 1 and an involution x~1 -- x which make it an effect algebra, in combination with an associative (possibly non-commutative) multiplication. Examples include the unit intervals of ordered rings and Boolean algebras.
Authors: Abraham Westerbaan, Bas Westerbaan, John van de Wetering
Institutions: Radboud University Nijmegen, University College London
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Awards: G1764870811, G3591598716
OpenAlex ID: W3030890936