Notre Dame Journal of Formal Logic

A Note on Freedom from Detachment in the Logic of Paradox

Jc Beall, Thomas Forster, and Jeremy Seligman


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

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

First available in Project Euclid: 14 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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