Fibring: Completeness Preservation

Journal of Symbolic Logic 66 (1):414-439 (2001)
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A completeness theorem is established for logics with congruence endowed with general semantics. As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by fibring logics endowed with standard semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings.



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References found in this work

Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
Modal Logic and Classical Logic.R. A. Bull - 1987 - Journal of Symbolic Logic 52 (2):557-558.
Fibring Logics.Dov M. Gabbay - 2000 - Studia Logica 66 (3):440-443.
Why Combine Logics?Patrick Blackburn & Maarten de Rijke - 1997 - Studia Logica 59 (1):5 - 27.

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