Where Gamma Fails

A major question for the relevant logics has been, "Under what conditions is Ackermann's rule γ, from$-A\vee B$and A to infer B, admissible for one of these logics?" For a large number of logics and theories, the question has led to an affirmative answer to the γ problem itself, so th...

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Bibliographic Details
Published inStudia logica Vol. 43; no. 3; pp. 247 - 256
Main Authors Meyer, Robert K., Giambrone, Steve, Brady, Ross T.
Format Journal Article
LanguageEnglish
Published Wroclaw, Poland Ossolineum and D. Reidel 1984
Ossolineum
Subjects
Algebra
Axioms
Boolean data
Entailment
Excluded middle
Logic
Logical theorems
Mathematical logic
Mathematical set theory
Relevance logic
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Summary:A major question for the relevant logics has been, "Under what conditions is Ackermann's rule γ, from$-A\vee B$and A to infer B, admissible for one of these logics?" For a large number of logics and theories, the question has led to an affirmative answer to the γ problem itself, so that such an answer has almost come to be expected for relevant logics worth taking seriously. We exhibit here, however, another large and interesting class of logics--roughly, the Boolean extensions of the W -- free relevant logics (and, precisely, the well-behaved subsystems of the 4-valued logic BN4) -- for which γ fails.
ISSN:0039-3215
1572-8730
DOI:10.1007/BF02429841