The strong proof from hypotheses and conditionals: Some theorems of deduction for relevant systems (Q1061116)

This paper states three deduction theorems for relevant logics and gives in each case a sketch of their proofs. Apparently the standard notion of validity does not work here so that the author finds it necessary to introduce a concept he calls d-validity based on a modified version of his concept of strong proof from hypotheses. For example, using the standard notion of proof from hypotheses \(\Gamma\) in the system of relevant logic R he proves that the deduction of B from A together with \(\Gamma\) is d-valid if and only if the deduction of the conditional \(A\to B\) from \(\Gamma\) alone is valid.