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Rewriting recursive aggregates in answer set programming: back to monotonicity

Published online by Cambridge University Press:  03 September 2015

MARIO ALVIANO ,
WOLFGANG FABER  and
MARTIN GEBSER
MARIO ALVIANO
Affiliation:
University of Calabria, Italy
WOLFGANG FABER
Affiliation:
University of Huddersfield, UK
MARTIN GEBSER
Affiliation:
Aalto University, HIIT, Finland
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Abstract

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 gringo, using the methods presented in this paper.

Keywords

answer set programmingpolynomialfaithfuland modular translationaggregation functions
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Special Issue 4-5: 31st International Conference on Logic Programming , July 2015 , pp. 559 - 573
Copyright
Copyright © Cambridge University Press 2015 

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