Notre Dame Journal of Formal Logic

A Note on Freedom from Detachment in the Logic of Paradox

Jc Beall, Thomas Forster, and Jeremy Seligman

Abstract

We shed light on an old problem by showing that the logic LP cannot define a binary connective obeying detachment in the sense that every valuation satisfying φ and ( φ ψ ) also satisfies ψ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

Article information

Source
Notre Dame J. Formal Logic, Volume 54, Number 1 (2013), 15-20.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1355494519

Digital Object Identifier
doi:10.1215/00294527-1731353

Mathematical Reviews number (MathSciNet)
MR3007958

Zentralblatt MATH identifier
1272.03115

Subjects
Primary: 03B53: Paraconsistent logics
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52} 03B80: Other applications of logic

Keywords
LP detachment-free logics detachable connective paradox relevance logics variable-sharing paraconsistent logic

Citation

Beall, Jc; Forster, Thomas; Seligman, Jeremy. A Note on Freedom from Detachment in the Logic of Paradox. Notre Dame J. Formal Logic 54 (2013), no. 1, 15--20. doi:10.1215/00294527-1731353. https://projecteuclid.org/euclid.ndjfl/1355494519


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References

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