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). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/7844
