Abstraction for non-ground answer set programs

Abstract

Abstraction is an important technique utilized by humans in model building and problem solving, in order to figure out key elements and relevant details of a world of interest. This naturally has led to investigations of using abstraction in AI and Computer Science to simplify problems, especially in the design of intelligent agents and automated problem solving. By omitting details, scenarios are reduced to ones that are easier to deal with and to understand, where further details are added back only when they matter. Despite the fact that abstraction is a powerful technique, it has not been considered much in the context of nonmonotonic knowledge representation and reasoning, and specifically not in Answer Set Programming (ASP), apart from some related simplification methods. In this work, we introduce a notion for abstracting from the domain of an ASP program such that the domain size shrinks while the set of answer sets (i.e., models) of the program is over-approximated. To achieve the latter, the program is transformed into an abstract program over the abstract domain while preserving the structure of the rules. We show in elaboration how this can be also achieved for single or multiple sub-domains (sorts) of a domain, and in case of structured domains like grid environments in which structure should be preserved. Furthermore, we introduce an abstraction-&-refinement methodology that makes it possible to start with an initial abstraction and to achieve automatically an abstraction with an associated abstract answer set that matches an answer set of the original program, provided that the program is satisfiable. Experiments based on prototypical implementations reveal the potential of the approach for problem analysis, by its ability to focus on the parts of the program that cause unsatisfiability and by achieving concrete abstract answer sets that merely reflect relevant details. This makes domain abstraction an interesting topic of research whose further use in important areas like Explainable AI remains to be explored.