Multi lingual sequent calculus and coherent spaces

• Autorzy: Jung, A. , Kegelmann, M.
• Języki publikacji: EN

Abstrakty

EN

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 be seen as a consequence between different 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 different logical systems because it mixes formulas from antecedent and succedent. We propose a different cut rule which addresses this problem. The new cut rule can be used as a basis for composition in a suitable category of logical sys-tems. As it turns out, this category is equivalent to coherent spaces with certain relations be-tween 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.

Słowa kluczowe

EN

domain theory; coherent space; sequent calculus; observation logic; cut elimination

• Czasopismo: Fundamenta Informaticae
• Rocznik: 1999
• Tom: Vol. 37, Nr 4
• Strony: 369-412
• Opis fizyczny: bibliogr. 16 poz.

Twórcy

autor

Jung, A.

autor

Kegelmann, M.

• School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, England,