Institut für Informatik und Computational Science
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Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration 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.
Answer Set Programming (ASP) is a successful rule-based formalism for modeling and solving knowledge-intense combinatorial (optimization) problems. Despite its success in both academic and industry, open challenges like automatic source code optimization, and software engineering remains. This is because a problem encoded into an ASP might not have the desired solving performance compared to an equivalent representation. Motivated by these two challenges, this paper has three main contributions. First, we propose a developing process towards a methodology to implement ASP programs, being faithful to existing methods. Second, we present ASP encodings that serve as the basis from the developing process. Third, we demonstrate the use of ASP to reverse the standard solving process. That is, knowing answer sets in advance, and desired strong equivalent properties, “we” exhaustively reconstruct ASP programs if they exist. This paper was originally motivated by the search of propositional formulas (if they exist) that represent the semantics of a new aggregate operator. Particularly, a parity aggregate. This aggregate comes as an improvement from the already existing parity (xor) constraints from xorro, where lacks expressiveness, even though these constraints fit perfectly for reasoning modes like sampling or model counting. To this end, this extended version covers the fundaments from parity constraints as well as the xorro system. Hence, we delve a little more in the examples and the proposed methodology over parity constraints. Finally, we discuss our results by showing the only representation available, that satisfies different properties from the classical logic xor operator, which is also consistent with the semantics of parity constraints from xorro.