A propositional calculus: Based on the Łukasiewicz's system

Date

2006-12

Authors

Ford, Dayna Lee

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

In Symbolic Logic, 5th Ed., by Irving M. Copi (Copi, 1979), there is a problem asking for the proof of the independence of each axiom from a set of axioms for a propositional calculus. This problem reads: 4. The Łukasiewicz's system (L.S.) has as primitive operators ∼ and →, with P v Q defined as ∼P→Q. Its Rule is: from P and P□Q to infer Q. Its three axioms are: Axiom 1. P→(Q→P); Axiom 2. [P→(Q→R)]→[(P→Q)→(P→R)]; Axiom 3. (∼P→∼Q)→(Q→P).

This thesis extends this problem into the complete development of the Łukasiewicz's system. The study follows Copi's outline in developing the L. S. and involves discussing Object Language and Metalanguage, primitive symbols and well-formed-formulas, axioms and demonstrations, independence of the axioms, and the development of the calculus.

Description

Keywords

Pure sciences, Mathematics, Object language and metalanguage, Copi's outline, Symbolic logic, Jan Lukasiewicz, Lukasiewicz logic

Citation

Collections