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We present a semantics for architectural specifications in CASL, including an extended static analysis compatible with model-theoretic requirements. The main obstacle here is the lack of amalgamation for CASL models. To circumvent this problem, we extend the CASL logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor has amalgamation, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion. Concretizing to the CASL institution, we discuss a calculus for discharging the static amalgamation conditions. These are in general undecidable, but can be dealt with by approximative algorithms in all practically relevant cases.
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