#### Graduation Year

2019

#### Document Type

Thesis

#### Degree

M.A.

#### Degree Name

Master of Arts (M.A.)

#### Degree Granting Department

Mathematics and Statistics

#### Major Professor

Gregory L. McColm, Ph.D.

#### Committee Member

Dmytro Savchuk, Ph.D.

#### Committee Member

Alex Levine, Ph.D.

#### Keywords

cyclic negation, Epstein lattice, Hasse diagram, logically equivalent formulas, many-valued logic

#### Abstract

In 1942, Paul C. Rosenbloom put out a definition of a Post algebra after Emil L. Post published a collection of systems of many–valued logic. Post algebras became easier to handle following George Epstein’s alternative definition. As conceived by Rosenbloom, Post algebras were meant to capture the algebraic properties of Post’s systems; this fact was not verified by Rosenbloom nor Epstein and has been assumed by others in the field. In this thesis, the long–awaited demonstration of this oft–asserted assertion is given.

After an elemental history of many–valued logic and a review of basic Classical Propositional Logic, the systems given by Post are introduced. The definition of a Post algebra according to Rosenbloom together with an examination of the meaning of its notation in the context of Post’s systems are given. Epstein’s definition of a Post algebra follows the necessary concepts from lattice theory, making it possible to prove that Post’s systems of many–valued logic do in fact form a Post algebra.

#### Scholar Commons Citation

Leyva, Daviel, "The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact" (2019). *Graduate Theses and Dissertations.*

https://scholarcommons.usf.edu/etd/7844