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A note on freedom from detachment in the logic of paradox. (English) Zbl 1272.03115

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

MSC:

03B53 Paraconsistent logics
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B80 Other applications of logic
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References:

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