L-Fuzzy Relations in Coq
type: CreativeWork
description: Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.
abstract: Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.
author: Jackson, Ethan
language: eng
keywords: L-Fuzzy Relations, Allegories, Arrow Categories, Coq
date published: 2014-09-05
date modified: 2026-07-24T01:22:54Z
provider: Brock University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Brock University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/10464/5673