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Journal of Logic and Computation 2002 12(3):443-473; doi:10.1093/logcom/12.3.443
© 2002 by Oxford University Press
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Original Article

Fibring Labelled Deduction Systems

João Rasga1, Amílcar Sernadas1, Cristina Sernadas1 and Luca Viganò2

1 CMA, Departamento de Matemática, IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal. E-mail: {jfr,acs,css}@math.ist.utl.pt 2 Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee 52, D-79110 Freiburg, Germany. E-mail: luca@informatik.uni-freiburg.de

We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.

Keywords: Fibring of logics; labelled deduction systems; natural deduction; general semantics; category theory

Received 1 June 2000.


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