# Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)

arXiv: https://arxiv.org/abs/2305.10846 · HTML: https://mlsanity.com/paper/2305.10846/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 30 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 3 of 3)

- [Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory](https://mlsanity.com/paper/2104.14789/) (2021)
- [Aggregate Semantics for Propositional Answer Set Programs](https://mlsanity.com/paper/2109.08662/) (2021)
- [Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming](https://mlsanity.com/paper/2211.17262/) (2022)

## Built on by (most cited first, 3 of 3)

- [An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation (full version)](https://mlsanity.com/paper/2412.13712/) (2024)
- [Argumentative Characterizations of (Extended) Disjunctive Logic Programs](https://mlsanity.com/paper/2306.07126/) (2023)
- [Operator-based semantics for choice programs: is choosing losing? (full version)](https://mlsanity.com/paper/2407.21556/) (2024)

## Abstract (arXiv)

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e. operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola, et al., and (3) we generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.