Journal of Symbolic Logic

Modulated fibring and the collapsing problem

Walter A. Carnielli, João Rasga, and Cristina Sernadas

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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.

Article information

J. Symbolic Logic, Volume 67, Issue 4 (2002), 1541-1569.

First available in Project Euclid: 18 September 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B22: Abstract deductive systems


Sernadas, Cristina; Rasga, João; Carnielli, Walter A. Modulated fibring and the collapsing problem. J. Symbolic Logic 67 (2002), no. 4, 1541--1569. doi:10.2178/jsl/1190150298.

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