Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems

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...

Full description

Saved in:
Bibliographic Details
Published in:Logic journal of the IGPL 2008-04, Vol.16 (2), p.121-153
Main Authors: Cruz-Filipe, Luíis, Sernadas, Amíicar, Sernadas, Cristina
Format: Article
Language:English
Subjects:
abstract proof system
heterogeneous fibring
preservation
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/jzm057