# Safe Formulas in the General Theory of Stable Models

arXiv: https://arxiv.org/abs/2307.09166 · HTML: https://mlsanity.com/paper/2307.09166/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 18 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Abstract (arXiv)

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding -- to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that the stable models of a safe sentence can be characterized by a formula of a simple syntactic form.