Approximating Extended Answer Sets

We present an approximation theory for the extended answer set semantics, using the concept of an approximation constraint. Intuitively, an approximation constraint, while satisfied by a “perfect” solution, may be left unsatisfied in an approximate extended answer set. Approximations improve as the number of unsatisfied constraints decreases. We show how the framework can also capture the classical answer set semantics, thus providing an approximative version of the latter.