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An Introduction to Logic Algebras

by Kramer, Nick

Abstract

We utilize the setting of Universal Algebra to introduce a new class of objects called logics, with the aim of generalizing the structure of familiar binary logic to a family of finite and countably infinite multi-valued logics. In Section 2, we explore several concepts and results parallel to those of more familiar algebraic structures and provide as an example an independent proof of the first isomorphism theorem for logics. In Section 3, we review some basic notions from Category Theory, which give us another lens through which to view logics, then prove several categorical results about them. In Section 4 we discuss implications of the idea of logics for various areas of mathematics, for the sake of brevity providing only a skeletal outline of what these might be, and in the last section we discuss the implications of logics on formal languages and natural deduction, providing a framework through which one might create generalized propositional logic.

Note

The author has given permission for this work to be deposited in the Digital Archive of Colorado College.

Colorado College Honor Code upheld.

Includes bibliographical references.

Administrative Notes

The author has given permission for this work to be deposited in the Digital Archive of Colorado College.

Colorado College Honor Code upheld.

Copyright
Copyright restrictions apply.
Publisher
Colorado College
PID
coccc:25858
Digital Origin
born digital
Extent
17 pages
Thesis
Senior Thesis -- Colorado College
Thesis Advisor
Penn, Michael
Department/Program
Math and Computer Science
Degree Name
Bachelor of Arts
Degree Type
bachelor
Degree Grantor
Colorado College
Date Issued
2016-05