Fibring Modal First-Order Logics: Completeness Preservation

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula nor its converse hold.