자료유형  

 학위논문

Control Number  

0016934300

International Standard Book Number  

9798380313346

Dewey Decimal Classification Number  

004

Main Entry-Personal Name  

Azevedo de Amorim, Pedro Henrique.

Publication, Distribution, etc. (Imprint  

[S.l.] : Cornell University., 2023

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2023

Physical Description  

1 online resource(200 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

General Note  

Advisor: Kozen, Dexter.

Dissertation Note  

Thesis (Ph.D.)--Cornell University, 2023.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약There 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.

Subject Added Entry-Topical Term  

Computer science.

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Applied mathematics.

Index Term-Uncontrolled  

Probabilistic semantics

Index Term-Uncontrolled  

Probabilistic programming

Index Term-Uncontrolled  

Programming languages

Index Term-Uncontrolled  

Probability theory

Index Term-Uncontrolled  

Measure theory

Added Entry-Corporate Name  

Cornell University Computer Science

Host Item Entry  

Dissertations Abstracts International. 85-03B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:641691