Rewriting recursive aggregates in answer set programming: back to monotonicity
This addresses a foundational gap in logic programming for researchers and practitioners by enabling the use of arbitrary recursive aggregates with current solvers, though it is incremental as it builds on existing rewriting approaches.
The paper tackles the problem of rewriting recursive aggregates in answer set programming into monotone forms to enable efficient evaluation, introducing a polynomial, faithful, and modular translation method that is implemented in a prototype system and integrated into the gringo grounder version 4.5.
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the grounder \textsc{gringo}, using the methods presented in this paper. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.