eCommons

 

A UNIFYING SEMANTICS FOR MARKOV KERNELS AND LINEAR OPERATORS

Other Titles

Abstract

There has been much work done in developing semantic structures for interpreting probabilistic programs. In particular, there have been many models based either on Markov kernels or linear operators, each with their own set of strengths and weaknesses. Concurrently, mathematicians have been working on categorical semantics for probability theory with the goal of obtaining a more abstract understanding of the field. This has led to the definition of Markov categories, an abstraction of Markov kernels. However, a similar treatment to the linear operator approach to probability is currently eluded by existing methods. This thesis sits at the intersection of probabilistic semantics and categorical probability theory. We propose a new categorical semantics and core calculus that extends Markov categories with linear operators, we justify its viability by showing how many useful categories used in probabilistic semantics are instances of our framework and, furthermore, we define a new model inspired by a functional-analytic treatment of measure theory. We conclude by showing how this formalism can be used to reason about a generalized notion of probabilistic independence via a substructural type system.

Journal / Series

Volume & Issue

Description

199 pages

Sponsorship

Date Issued

2023-08

Publisher

Keywords

Categorical Semantics; Probabilistic Programming; Programming Languages; Type Theory

Location

Effective Date

Expiration Date

Sector

Employer

Union

Union Local

NAICS

Number of Workers

Committee Chair

Kozen, Dexter

Committee Co-Chair

Committee Member

Damle, Anil
Foster, John
Hsu, Justin

Degree Discipline

Computer Science

Degree Name

Ph. D., Computer Science

Degree Level

Doctor of Philosophy

Related Version

Related DOI

Related To

Related Part

Based on Related Item

Has Other Format(s)

Part of Related Item

Related To

Related Publication(s)

Link(s) to Related Publication(s)

References

Link(s) to Reference(s)

Previously Published As

Government Document

ISBN

ISMN

ISSN

Other Identifiers

Rights

Attribution 4.0 International

Types

dissertation or thesis

Accessibility Feature

Accessibility Hazard

Accessibility Summary

Link(s) to Catalog Record