Where gamma fails

Studia Logica 43 (3):247 - 256 (1984)
A major question for the relevant logics has been, “Under what conditions is Ackermann's ruleγ from -A ∨B andA to inferB, admissible for one of these logics?” For a large number of logics and theories, the question has led to an affirmative answer to theγ 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 theW — free relevant logics (and, precisely, the well-behaved subsystems of the 4-valued logicBN4) — for which γ fails.
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References found in this work BETA
Clarence Irving Lewis (1959). Symbolic Logic. [New York]Dover Publications.

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Eunsuk Yang (2013). R and Relevance Principle Revisited. Journal of Philosophical Logic 42 (5):767-782.

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