Multi Lingual Sequent Calculus and Coherent Spaces

Achim Jung, Mathias Kegelmann, M. Andrew Moshier
1997 Electronical Notes in Theoretical Computer Science  
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 rule
more » ... hich addresses this problem. The new cut rule can be used as a basis for composition in a suitable category of logical systems. As it turns out, this category is equivalent to coherent spaces with certain relations between them. Finally, cut elimination in this set-up can be employed to provide a new explanation of the domain constructions in Samson Abramsky's Domain Theory in Logical Form.
doi:10.1016/s1571-0661(05)80160-4 fatcat:3nv4xskxmzcxhanqwg5tmkezvq