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Logic Journal of IGPL Advance Access originally published online on October 16, 2007
Logic Journal of IGPL 2008 16(2):121-153; doi:10.1093/jigpal/jzm057
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems

Luíis Cruz-Filipe

SQIG-IT and Dep. Informatics, FC, U Lisbon

Amíicar Sernadas

SQIG-IT and Dep. Mathematics, IST, TU Lisbon

Cristina Sernadas

SQIG-IT and Dep. Mathematics, IST, TU Lisbon


  Abstract

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have different presentations (e.g. one presented by a Hilbert calculus and the other by a sequent calculus), has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated.

Key Words: heterogeneous fibring • abstract proof system • preservation


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