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Relevant Implication and the Weak Deduction Theorem
Studia Logica: An International Journal for Symbolic Logic
Vol. 46, No. 3 (1987), pp. 239-245
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015314
Page Count: 7
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It is shown that the implicational fragment of Anderson and Belnap's R, i.e. Church's weak implicational calculus, is not uniquely characterized by MP (modus ponens), US (uniform substitution), and WDT (Church's weak deduction theorem). It is also shown that no unique logic is characterized by these, but that the addition of further rules results in the implicational fragment of R. A similar result for E is mentioned.
Studia Logica: An International Journal for Symbolic Logic © 1987 Springer