# From Non-Convex Aggregates to Monotone Aggregates in ASP

@inproceedings{Alviano2016FromNA, title={From Non-Convex Aggregates to Monotone Aggregates in ASP}, author={Mario Alviano and Wolfgang Faber and M. Gebser}, booktitle={IJCAI}, year={2016} }

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…

## Topics from this paper

## 4 Citations

Aggregates in Answer Set Programming

- Computer ScienceKI - Künstliche Intelligenz
- 2018

Common use cases of aggregates in ASP are reported in this paper, which mainly focus on the semantics implemented by mainstream solvers, namely the F-stable model semantics.

Shared aggregate sets in answer set programming

- Computer Science, MathematicsTheory and Practice of Logic Programming
- 2018

New data structures and techniques to handle aggregations on the same aggregate set identified in the ground program in input are introduced and the proposed solution reduces the memory footprint of the solver without sacrificing efficiency.

Recursive Rules with Aggregation: A Simple Unified Semantics

- Computer ScienceLFCS
- 2022

The key idea is to support simple expression of the different assumptions underlying different semantics, and orthogonally interpret aggregation operations straightforwardly using their simple usual meaning.

Enhancing Magic Sets with an Application to Ontological Reasoning

- Computer ScienceTheory and Practice of Logic Programming
- 2019

It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program.

## References

SHOWING 1-10 OF 27 REFERENCES

Evaluating Answer Set Programming with Non-Convex Recursive Aggregates

- Computer ScienceRCRA@AI*IA
- 2015

A preliminary evaluation of ASP programs with non-convex recursive aggregates is reported in this paper, and it is reported that the user can finally use non- Convex recursion over aggregates in ASP programs, either on purpose or accidentally.

Rewriting recursive aggregates in answer set programming: back to monotonicity

- Computer ScienceTheory and Practice of Logic Programming
- 2015

A polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers is introduced.

Semantics and complexity of recursive aggregates in answer set programming

- Computer ScienceArtif. Intell.
- 2011

This paper defines a semantics for programs with arbitrary aggregates in the full ASP language allowing also for disjunction in the head (disjunctive logic programming - DLP), and proves that this semantics guarantees the minimality (and therefore the incomparability) of answer sets, and demonstrates that it coincides with the standard answer set semantics on aggregate-free programs.

On Solution Correspondences in Answer-Set Programming

- Mathematics, Computer ScienceIJCAI
- 2005

A general framework for specifying program correspondence under the answer-set semantics is introduced, including previously defined notions like strong and uniform equivalence, in which programs are extended with rules from a given context, and correspondence is determined by means of a binary relation.

Properties and Applications of Programs with Monotone and Convex Constraints

- Computer Science, MathematicsJ. Artif. Intell. Res.
- 2006

The results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs, which imply a method to compute stable models of l parse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

Logic programs with propositional connectives and aggregates

- Computer Science, MathematicsTOCL
- 2011

First the definition of an answer set/stable model is extended to cover arbitrary propositional theories; then aggregates are defined on top of them both as primitive constructs and as abbreviations for formulas.

The Complexity Boundary of Answer Set Programming with Generalized Atoms under the FLP Semantics

- Computer ScienceLPNMR
- 2013

This paper provides the precise boundary of this complexity gap: programs with convex generalized atom never increase complexity, while allowing a single non-convex generalized atoms under reasonable conditions always does.

Weight constraints as nested expressions

- Computer ScienceTheory and Practice of Logic Programming
- 2005

It is shown that there is a simple, modular translation from the language of weight constraints into thelanguage of nested expressions that preserves the program's answer sets and makes it possible to compute answer sets for some programs with weight constraints using satisfiability solvers and to prove the strong equivalence of programs withWeight constraints using the logic of here-and-there.

On the computational cost of disjunctive logic programming: Propositional case

- Computer Science, MathematicsAnnals of Mathematics and Artificial Intelligence
- 2005

This paper shows that the consistency check is Σ2p-complete for the disjunctive stable model semantics, the iterated closed world assumption, and the perfect model semantics; analogous results are derived for the answer sets semantics of extendeddisjunctive logic programs.

Applying Visible Strong Equivalence in Answer-Set Program Transformations

- Mathematics, Computer ScienceCorrect Reasoning
- 2012

This paper proposes a new generalization of strong equivalence which takes the visibility of atoms into account and is characterized in terms of revised SE-models and presents a translation which enables the task of verifying the visibleStrong equivalence of smodels programs having enough visible atoms.