From fibring to cryptofibring. A solution to the collapsing problem

Logica Universalis 1 (1):71-92 (2007)
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Abstract

.  The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For illustration, we revisit the example of combining intuitionistic and classical propositional logics.

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Jaime Ramos
Universidad Nacional de Colombia

Citations of this work

Juxtaposition: A New Way to Combine Logics.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):560-606.
Modular Many-Valued Semantics for Combined Logics.Carlos Caleiro & Sérgio Marcelino - 2024 - Journal of Symbolic Logic 89 (2):583-636.
Combining logics.Walter Carnielli & Marcelo E. Coniglio - 2008 - Stanford Encyclopedia of Philosophy.
On graph-theoretic fibring of logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.

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References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
Fibring logics.Dov M. Gabbay - 1999 - New York: Clarendon Press.
Fibring Logics.Dov M. Gabbay - 2000 - Studia Logica 66 (3):440-443.

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