On Pushout Consistency, Modularity and Interpolation for Logical Specifications

Abstract We generalize three known results concerning (conservative) extensions to (faithful) interpretations. These results are Extension Modularity (a special case of the Modularization Theorem for logical specifications) and two familiar logical theorems, namely Robinson's Joint Consistency and Craig-Robinson Interpolation. Their generalizations involve a pushout construction, in lieu of union, and their proofs rely on internalization techniques, including a novel one, which reduce — to a large extent — interpretations to extensions.

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