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We study a Gentzen style sequent calculus where the formulas on the left and right of the turnstile need not necessarily come from the same logical system. Such a sequent can beseenas a consequence between di erent domains of reasoning. We discuss the ingredients needed to set up the logic generalized in this fashion. The usual cut rule does not make sense for sequents which connect di erent logical systems because it mixes formulas from antecedent and succedent. We propose a di erent cut ruledoi:10.1016/s1571-0661(05)80160-4 fatcat:3nv4xskxmzcxhanqwg5tmkezvq