Computations are often viewed as proofs of specific sentences in some computational logic describing the operational semantics of the programming language or computational system. Since the semantics of programs (i.e., the set of such specific sentences that are provable in the logic) is usually incomputable, and most program properties undecidable, abstraction is essential in program analysis. Abstractions can be formalized as semantic models which should be automatically generated in a push-the-button-and-wait style of program analysis and verification. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis. Our development systematically uses the recently introduced convex domains which are well-suited for representing domains for different sorts; we use them to interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra (e.g., Farkas’ Lemma), real algebraic geometry, and arithmetic constraint solving in the implementation of the analyses.