 Going further afield, very pretty natural deduction systems can be given for at least fragments of systems of relevant logics. Early in the literature on these logics the naturalness of these systems was presented as evidence for the naturalness of the logics (see Anderson 1960; Anderson &amp; Belnap 1962b; with some rearrangement, Anderson &amp; Belnap 1962b, is reprinted in chapter 1 of Anderson &amp; Belnap 1975). The key connectives of relevant logics are implicational: entailment or relevant implication. The natural deduction rules for these connectives are modifications of the standard rules for conditionals: the usual modus ponens for the \(\rightarrow\)-E rule; and for the \(\rightarrow\)-I, a variant of the standard rule with a restriction (formulated in Anderson &amp; Belnap 1962b, with the aid of a simple and elegant bit of notation) ensuring that the hypothesis of the \(\rightarrow\)-I subproof is actually used in deriving the consequent. The pure implicational systems defined in Anderson and Belnap (1962b) are very elegant, and the conceptual arguments based on them impressive! Another fragment of the standard relevant logics, having quantifiers and the “Boolean” operators \(\neg,\ \land\) and \(\lor\), but lacking the characteristic \(\rightarrow\) operator, also has a nice natural deduction formulation: the positive and negative rules for the quantifiers and Booleans mentioned above in  §5.3,  but omitting the ex falso quodlibet version of its \(\neg\)-E rule. (The propositional part of this fragment of relevant logic is discussed in Anderson &amp; Belnap 1962a, which is reproduced in chapter 3 of Anderson &amp; Belnap 1975.) Unfortunately natural deduction systems for full relevant logics, incorporating all the connectives, require rules and restrictions that may strike many as ad hoc.