# Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming

arXiv: https://arxiv.org/abs/2211.17262 · HTML: https://mlsanity.com/paper/2211.17262/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 62 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [Fixpoint Semantics for Recursive SHACL](https://mlsanity.com/paper/2109.08285/) (2021)
- [Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs](https://mlsanity.com/paper/1804.08335/) (2018)
- [Vicious Circle Principle and Logic Programs with Aggregates](https://mlsanity.com/paper/1808.07050/) (2018)
- [Reasoning by Cases in Structured Argumentation](https://mlsanity.com/paper/1703.08397/) (2017)
- [Alternating Fixpoint Operator for Hybrid MKNF Knowledge Bases as an Approximator of AFT](https://mlsanity.com/paper/2105.11071/) (2021)

## Built on by (most cited first, 5 of 5)

- [Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)](https://mlsanity.com/paper/2305.10846/) (2023)
- [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)
- [A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)](https://mlsanity.com/paper/2507.16067/) (2025)

## Abstract (arXiv)

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.