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Modulated fibring and the collapsing problem

Published online by Cambridge University Press:  12 March 2014

Cristina Sernadas ,
João Rasga  and
Walter A. Carnielli
Cristina Sernadas
Affiliation:
Center For Logic and Computation - CLC, Department of Mathematics IST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: [email protected] URL: http://www.cs.math.ist.utl.pt/s84.www/cs/css.html
João Rasga
Affiliation:
Center for Logic and Computation - CLC, Department of Mathematics 1ST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: [email protected] URL: http://www.cs.math.ist.utl.pt/s84.www/cs/jfr.html
Walter A. Carnielli
Affiliation:
Center For Logic, Epistemology and the History of Science - CLE, Department of Philosophy IFCH Unicamp, P.O. Box 6133, 13083-970 Campinas - SP -, Brazil, E-mail: [email protected] URL: http://www.cle.unicamp.br/prof/carnielli/
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Abstract

Fibring is recognized as one of the main mechanisms in combining logics, with great significance in the theory and applications of mathematical logic. However, an open challenge to fibring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that fibring imposes unwanted interconnections between the given logics. Modulated fibring allows a finer control of the combination, solving the collapsing problem both at the semantic and deductive levels. Main properties like soundness and completeness are shown to be preserved, comparison with fibring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1541 - 1569
Copyright
Copyright © Association for Symbolic Logic 2002

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