Whither relevance logic? (Q1198408)

The paper falls into two parts. The first claims to be a critique of standard approaches to relevant logic, though in fact it criticises only the systems \(E\) and \(R\) of Anderson and Belnap. Applied to these and the considerations that are supposed to motivate them --- e.g., the use condition --- the criticisms have much force. There are, however, numerous weaker systems, which have, typically, been motivated by other considerations --- e.g., the desire to avoid suppression. [See \textit{R. Routley} et al., Relevant logics and their rivals. I (1982; Zbl 0579.03011).] By and large, the criticisms get no grip on such systems: they have a simple semantics and proof theory (see, respectively, \textit{G. Priest} and \textit{R. Sylvan} [``Simplified semantics for basic relevant logics'', J. Philos. Logic 21, 217-232 (1992)] and \textit{J. Slaney} [``A general logic'', Austral. J. Philos. 68, 74-88 (1990)] and accommodate extensional connectives without disturbing the intensional machinery (the author's major objection). The second part of the paper provides a useful exposition of the relevant logics \(RMI\) and \(RMI_{\widetilde{\rightarrow}}\) [see the author, J. Symb. Logic 55, 707-732 (1990; Zbl 0705.03007); Notre Dame J. Formal Logic 31, 169-202 (1990; Zbl 0714.03020)]. The only new result here is that the theorems of positive classical logic are embeddable in \(RMI_{\widetilde{\rightarrow}}\). The author claims that his systems are theoretically smoother than standard systems, and are also adequate for all practical purposes. The semantics are, however, more complex than those of the standard weaker relevant systems, and the absence of extensional connectives makes the claim about practice problematic. E.g., suppose that you are entitled to a pension iff you have lost a limb and have no taxable income, \(P\leftrightarrow L\circ T\). Suppose that \(L\) and \(T\) are true. \(P\) cannot be inferred since there is no relevant connection between \(T\) and \(L\).