From Non-Convex Aggregates to Monotone Aggregates in ASP / 4100
Mario Alviano, Wolfgang Faber, Martin Gebser
In answer set programming, knowledge involving sets of objects collectively is naturally represented by aggregates, which are rewritten into simpler forms known as monotone aggregates by current implementations. However, there is a complexity gap between general and monotone aggregates. In this paper, this gap is filled by means of a polynomial, faithful, and modular translation function, which can introduce disjunction in rule heads. The translation function is now part of the recent version 4.5 of the grounder Gringo. This paper focuses on the key points of the translation function, and in particular on the mapping from non-convex sums to monotone sums.