On the independence of Robinson's set of axioms for propositional calculus

TL;DR

This paper establishes the independence of two axioms in Robinson's propositional calculus set by providing normal truth-table proofs, addressing previous questions about their independence.

Contribution

It introduces normal truth-table proofs for the independence of axioms in Robinson's propositional calculus, improving upon earlier non-normal truth-table methods.

Findings

Proved independence of one axiom using a five-valued truth-table.

Established independence of another axiom with a four-valued truth-table.

Answered previously open questions about axiom independence.

Abstract

We give a normal five-valued truth-table proving independence of one of the axioms in Robinson's set of axioms for propositional calculus from 1968, answering a question raised in his article, where he uses a non-normal truth-table. We also give a normal four-valued truth-table proving independence of one of the other axioms, where he uses a normal five-valued truth-table.