English

Craig Interpolation for Decidable First-Order Fragments

Logic in Computer Science 2025-09-03 v6

Abstract

We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable fragment and the forward fragment with Craig interpolation. Similarly, we also show that all extensions of the two-variable fragment and of the fluted fragment with Craig interpolation are undecidable.

Cite

@article{arxiv.2310.08689,
  title  = {Craig Interpolation for Decidable First-Order Fragments},
  author = {Balder ten Cate and Jesse Comer},
  journal= {arXiv preprint arXiv:2310.08689},
  year   = {2025}
}
R2 v1 2026-06-28T12:49:14.967Z