# Conservative Extensions in Guarded and Two-Variable Fragments

arXiv: https://arxiv.org/abs/1705.10115 · HTML: https://mlsanity.com/paper/1705.10115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 1 of 1)

- [Conservative Extensions for Existential Rules](https://mlsanity.com/paper/2202.05689/) (2022)

## Abstract (arXiv)

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO2 and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO2 or GF (even the three-variable fragment thereof), and that they are decidable and 2ExpTime-complete in the intersection GF2 of FO2 and GF.