Notre Dame Journal of Formal Logic

A Sound and Complete Proof Theory for Propositional Logical Contingencies

Alexander Hertel, Philipp Hertel, and Charles Morgan

Abstract

There are simple, purely syntactic axiomatic proof systems for both the logical truths and the logical falsehoods of propositional logic. However, to date no such system has been developed for the logical contingencies, that is, formulas that are both satisfiable and falsifiable. This paper formalizes the purely syntactic axiomatic proof systems for the logical contingencies and proves its soundness as well as completeness.

Article information

Source
Notre Dame J. Formal Logic Volume 48, Number 4 (2007), 521-530.

Dates
First available in Project Euclid: 29 October 2007

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1193667709

Digital Object Identifier
doi:10.1305/ndjfl/1193667709

Mathematical Reviews number (MathSciNet)
MR2357526

Zentralblatt MATH identifier
1142.03007

Subjects
Primary: 03B05: Classical propositional logic

Keywords
logical contingencies logically contingent formulas classical propositional logic purely syntactic proof systems

Citation

Morgan, Charles; Hertel, Alexander; Hertel, Philipp. A Sound and Complete Proof Theory for Propositional Logical Contingencies. Notre Dame Journal of Formal Logic 48 (2007), no. 4, 521--530. doi:10.1305/ndjfl/1193667709. http://projecteuclid.org/euclid.ndjfl/1193667709.


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References

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