Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems

Fibring is a meta-logical constructor that applied to two logicsproduces a new logic whose formulas allow the mixing of symbols.Homogeneous fibring assumes that the original logics are presentedin 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 asequent calculus), has been an open problem. Herein, consequencesystems are shown to be a good solution for heterogeneous fibringwhen one of the logics is presented in a semantic way and theother by a calculus and also a solution for the heterogeneousfibring of calculi. The new notion of abstract proof systemis shown to provide a better solution to heterogeneous fibringof calculi namely because derivations in the fibring keep theconstructive nature of derivations in the original logics. Preservationof compactness and semi-decidability is investigated.