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Journal of Logic and Computation
Volume 13, Issue 4, June 2003: pp. 595-624
Fibring Logics with Topos Semantics
Marcelo E. Coniglio1, Amilcar C. Sernadas2 and Cristina S. Sernadas2
1Departamento de Filosofia, Universidade Estadual de Campinas, Brazil. E-mail: firstname.lastname@example.org
2CLC, Departamento de Matemática, IST, Portugal. E-mail: email@example.com, firstname.lastname@example.org
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.
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