The Journal of Symbolic Logic

Research Article

Modulated fibring and the collapsing problem

Cristina Sernadasa1, João Rasgaa2 and Walter A. Carniellia3

a1 Center For Logic and Computation - CLC, Department of Mathematics IST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: css@math.ist.utl.pt URL: http://www.cs.math.ist.utl.pt/s84.www/cs/css.html

a2 Center for Logic and Computation - CLC, Department of Mathematics 1ST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: jfr@math.ist.utl.pt URL: http://www.cs.math.ist.utl.pt/s84.www/cs/jfr.html

a3 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: carniell@cle.unicamp.br URL: http://www.cle.unicamp.br/prof/carnielli/

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.

(Received June 21 2001)

(Revised May 14 2002)