Date of Submission

Spring 2016

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Robert McGrail

Abstract/Artist's Statement

The topic of this paper in a broad phrase is “proof theory". It tries to theorize the general

notion of “proving" something using rigorous definitions, inspired by previous less general

theories. The purpose for being this general is to eventually establish a rigorous framework

that can bridge the gap when interrelating different logical systems, particularly ones

that have not been as well defined rigorously, such as sequent calculus. Even as far as

semantics go on more formally defined logic such as classic propositional logic, concepts

like “completeness" and “soundness" between the “semantic" and the “deductive system"

is too arbitrarily defined on the specific system that is applied to for it to carry as an

adequate definition. What we shall do then is come up with an adequate definition for

a characterization of every logic that one has worked with, and show what can be done

with it for a few basic logical systems that include classic propositional logic, intuitionistic

propositional logic and intuitionistic sequent calculus. To make this definition work with

eloquence, we go the category theory route of constructing a category with objects that

correspond to collections of logical formulae and arrows that correspond to deductions

from one such collection to another.

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Open Access

Creative Commons License

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