A Detailed Examination of Methods for Unifying, Simplifying and Extending Several Results About Self-Justifying Logics

TL;DR

This paper develops a unified framework for self-justifying logics, simplifying previous results and exploring new approaches to reflection principles and self-awareness in formal systems.

Contribution

It introduces a comprehensive framework that unifies and extends prior work on self-justifying axiom systems and proposes an alternative to traditional reflection principles.

Findings

A new unified framework for self-justifying logics

Extension of prior results on partial self-knowledge

An alternative approach to reflection principles

Abstract

This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps single most surprising new result will be its exploration of a viable alternative to conventional reflection principles.