The stable model semantics treats a logic program as a mechanism for specifying its intensional predicates. In this paper we discuss a modification of that semantics in which functions, rather than predicates, are intensional. The idea of the new definition comes from nonmonotonic causal logic.

In classical logic, nonBoolean fluents, such as the location of an object and the color of a ball, can be naturally described by functions, but this is not the case with the traditional stable model semantics, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow intensional functions. The new formalism is closely related to multi-valued nonmonotonic causal logic, logic programs with intensional functions, and other extensions of logic programs with functions, while keeping similar properties as those of the first-order stable model semantics. We show how to eliminate intensional functions in favor of intensional predicates and vice versa, and use these results to encode fragments of the language in the input language of ASP solvers and CSP solvers.