Formalizing Probability Concepts in a Type Theory

Date
2018-11-12
Authors
Kachapova, F
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
Science Publications
Abstract

In this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our formalizations we assign an appropriate type to each object in order to create a framework where further development of formalized probability theory will be possible. Our formalizations are based on mathematical results developed in the COQ standard library; we use mainly the parts with logic and formalized real analysis. In the future we aim to create COQ coding for our formalizations of probability concepts and theorems. In this paper the definitions and some proofs are presented as flag-style derivations while other proofs are more informal.

Description
Keywords
Type Theory; Kolmogorov's Axiomatics; Probability Theory; Calculus of Inductive Constructions; Flag-Style Derivation
Source
Journal of Mathematics and Statistics 2018, Retrieved from: https://thescipub.com/abstract/10.3844/ofsp.12176
Rights statement
© 2018 Farida Kachapova. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.