In an earlier paper in this journal I provided detailed motivation for the constructive and relevant system of Core Logic; explained its main features; and established that, even though Cut is not a rule of the system, nevertheless Cut is admissible for it, and indeed with potential epistemic gain. If Π is a proof of the sequent Δ : A, and Σ is a proof of the sequent Г, A : θ, then there is a computable reduct [Π, Σ] of some subsequent of the ‘overall target sequent’ Δ, Г : θ. In the constructive case the potential epistemic gain consists in the possibility that the subsequent in question be a proper subsequent of Δ, Г : θ, and indeed even logically stronger than Δ, Г : θ.
In this paper it is established that Cut is likewise admissible for Classical Core Logic, which is obtained from Core Logic by adding a suitably relevantized form of the rule of Classical Dilemma. In the classical case there is an additional feature of potential epistemic gain: the proof [Π, Σ] might have a lower degree of non-constructivity than do Π and Σ.