  Recent developments in termination analysis for declarative programs
emphasize the use of appropriate models for the logical theory representing the
program at stake as a generic approach to prove termination of declarative
programs. In this setting, Order-Sorted First-Order Logic provides a powerful
framework to represent declarative programs. It also provides a target logic to
obtain models for other logics via transformations. We investigate the
automatic generation of numerical models for order-sorted first-order logics
and its use in program analysis, in particular in termination analysis of
declarative programs. We use convex domains to give domains to the different
sorts of an order-sorted signature; we 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 and arithmetic constraint solving to synthesize the models.
