Beyond Uniform: To Boldly Abstract What Has Not Been Abstracted Before

The ability to abstract is important in AI systems and in problem solving, as generalizing over irrelevant details facilitates finding solutions. In the context of Answer Set Programming (ASP), abstraction has been recently investigated with a focus on the omission of unnecessary details, which is related to forgetting, as well as on clustering vocabulary of similar concepts into a common abstract representation. In the latter case, a characterization has been provided that identifies when such abstraction is possible without affecting the answer sets under the addition of any set of facts, in the spirit of uniform equivalence and aligned with the ASP methodology where a general problem encoding is used with varying instances. However, when this characterization fails, no abstraction is possible, and even if it succeeds, computing an abstracted program syntactically is only possible for a limited subclass of programs. In this paper, we consider that not all kinds of facts are required to be added in general, and investigate under which conditions such abstraction is indeed always possible as well as when and how to compute abstracted programs, generalizing at the same time (compared to related work) to a larger class of programs with wider applicability.