Boolean negation and non-conservativity II: The variable-sharing property
Journal article, Peer reviewed
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Original versionLogic Journal of the IGPL. 2020 10.1093/jigpal/jzaa020
Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean extended logic.