# Interpolable Formulas in Equilibrium Logic and Answer Set Programming

arXiv: https://arxiv.org/abs/1401.3897 · HTML: https://mlsanity.com/paper/1401.3897/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 2 of 2)

- [Forgetting in Answer Set Programming -- A Survey](https://mlsanity.com/paper/2107.07016/) (2021)
- [Interpolation in Knowledge Representation](https://mlsanity.com/paper/2512.08833/) (2025)

## Abstract (arXiv)

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting. The first-order version of equilibrium logic has analogous Interpolation properties whenever the collection of equilibrium models is (first-order) definable. Since this is the case for so-called safe programs and theories, it applies to the usual situations that arise in practical answer set programming.