Natural deduction systems for E

Anderson and Belnap [1975] presented a Fitch natural deduction system, FE, for their logic E of entailment as well as Fitch systems for the relevant logics T and R. The system FE is obtained from the system for R through a restriction on the rule of reiteration. Brady [1984] presents Fitch systems for a range of relevant logics, none of which uses a restriction on the rule of reiteration. However, no Fitch system for E was presented. We fill this lacuna by providing two Fitch systems for E, neither of which uses a restriction on the rule of reiteration. We close by discussing their differences and possible connections to other extant systems for E