Relations between ex falso, tertium non datur, and double negation elimination

TL;DR

This paper investigates the logical relationships between ex falso, tertium non datur, and double negation elimination within minimal logic, clarifying how these principles interconnect.

Contribution

It establishes the implicational relations among these three classical principles in the context of minimal logic, providing a clearer understanding of their logical dependencies.

Findings

Identifies which principles imply others within minimal logic.

Clarifies the logical status of each principle relative to the others.

Provides a formal framework for understanding classical principles in minimal logic.

Abstract

We show which implicational relations hold between the three principles ex falso sequitur quodlibet, tertium non datur, and double negation elimination, on the basis of minimal logic.