Declarative Encodings of Acyclicity Properties?

Abstract. Many knowledge representation tasks involve trees or similar struc-tures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challeng-ing indeed. In this paper, we take a number of acyclicity properties into consid-eration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.