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Journal of Logic and Computation 2003 13(4):595-624; doi:10.1093/logcom/13.4.595
© 2003 by Oxford University Press
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Original Article

Fibring Logics with Topos Semantics

Marcelo E. Coniglio1, Amilcar C. Sernadas2 and Cristina S. Sernadas2

1 Departamento de Filosofia, Universidade Estadual de Campinas, Brazil. E-mail: coniglio{at}cle.unicamp.br 2 CLC, Departamento de Matemática, IST, Portugal. E-mail: acs{at}math.ist.utl.pt, css{at}math.ist.utl.pt

The concept of fibring is extended to higher-order logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the meta-theorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich logics. This result is extended to weaker logics in the cases where fibring preserves conservativeness of HOL-enrichments. Soundness is shown to be preserved by fibring without any further assumptions.

Keywords: Modal higher-order logic, categorical logic, completeness, conservative extensions.

Received 19 March 2002.


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