ASP has both classical negation and negation-as-failure, but that is not quite why I'd say it is "more declarative". Prolog is capable of performing "imperative" tasks (by this I really mean side effects), while ASP solvers exclusively find stable models (answer sets) that may (or may not) exist for a given logic program. In ASP you can only declare a model with your input, and the output is either one or more stable model(s), or the knowledge that the model was unsatisfiable.
You are right about it being more than just a "modeling language to solve combinatorial problems", I agree that description sells it a bit short. As you pointed out, it is well suited for problems involving non-monotonic reasoning and uncertainty. You can encode reasoning that is more reality-hardened, with logical rules to deal with imperfect information.
You are right about it being more than just a "modeling language to solve combinatorial problems", I agree that description sells it a bit short. As you pointed out, it is well suited for problems involving non-monotonic reasoning and uncertainty. You can encode reasoning that is more reality-hardened, with logical rules to deal with imperfect information.