# Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory

arXiv: https://arxiv.org/abs/2104.14789 · HTML: https://mlsanity.com/paper/2104.14789/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 50 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 1 of 1)

- [Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs](https://mlsanity.com/paper/1804.08335/) (2018)

## Built on by (most cited first, 6 of 6)

- [On the Foundations of Grounding in Answer Set Programming](https://mlsanity.com/paper/2108.04769/) (2021)
- [Aggregate Semantics for Propositional Answer Set Programs](https://mlsanity.com/paper/2109.08662/) (2021)
- [Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)](https://mlsanity.com/paper/2305.10846/) (2023)
- [On Nested Justification Systems (full version)](https://mlsanity.com/paper/2205.04541/) (2022)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [Operator-based semantics for choice programs: is choosing losing? (full version)](https://mlsanity.com/paper/2407.21556/) (2024)

## Abstract (arXiv)

Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of Approximation Fixpoint Theory (AFT). We introduce an AFT formalisation equivalent with the Gelfond-Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyse how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalisation of aggregates. This paper is under consideration for acceptance in TPLP.