# The Stable Model Semantics for Higher-Order Logic Programming

arXiv: https://arxiv.org/abs/2408.10563 · HTML: https://mlsanity.com/paper/2408.10563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [Planning with Incomplete Information in Quantified Answer Set Programming](https://mlsanity.com/paper/2108.06405/) (2021)
- [Beyond NP: Quantifying over Answer Sets](https://mlsanity.com/paper/1907.09559/) (2019)
- [Fixpoint Semantics for Recursive SHACL](https://mlsanity.com/paper/2109.08285/) (2021)
- [Stable-Unstable Semantics: Beyond NP with Normal Logic Programs](https://mlsanity.com/paper/1608.01835/) (2016)
- [Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs](https://mlsanity.com/paper/1804.08335/) (2018)
- [Semantics of templates in a compositional framework for building logics](https://mlsanity.com/paper/1507.06778/) (2015)
- [Fixed Point Semantics for Stream Reasoning](https://mlsanity.com/paper/2005.08384/) (2020)
- [The Intricacies of 3-Valued Extensional Semantics for Higher-Order Logic Programs](https://mlsanity.com/paper/1707.04704/) (2017)
- [The Expressive Power of Higher-Order Datalog](https://mlsanity.com/paper/1907.09820/) (2019)

## Abstract (arXiv)

We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems.