# SoK: Formal Methods for Fact-Checking and Information Integrity

arXiv: https://arxiv.org/abs/2609.23239 · HTML: https://mlsanity.com/paper/2609.23239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 88 of its 152 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 30 of 88)

- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [TabFact: A Large-scale Dataset for Table-based Fact Verification](https://mlsanity.com/paper/1909.02164/) (2019)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [A Survey on Automated Fact-Checking](https://mlsanity.com/paper/2108.11896/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Explainable Automated Fact-Checking for Public Health Claims](https://mlsanity.com/paper/2010.09926/) (2020)
- [HoVer: A Dataset for Many-Hop Fact Extraction And Claim Verification](https://mlsanity.com/paper/2011.03088/) (2020)
- [Certified Robustness to Adversarial Word Substitutions](https://mlsanity.com/paper/1909.00986/) (2019)
- [FEVEROUS: Fact Extraction and VERification Over Unstructured and Structured information](https://mlsanity.com/paper/2106.05707/) (2021)
- [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023)
- [Automated Fact-Checking for Assisting Human Fact-Checkers](https://mlsanity.com/paper/2103.07769/) (2021)
- [AVeriTeC: A Dataset for Real-world Claim Verification with Evidence from the Web](https://mlsanity.com/paper/2305.13117/) (2023)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Achieving Verified Robustness to Symbol Substitutions via Interval Bound Propagation](https://mlsanity.com/paper/1909.01492/) (2019)
- [Explainable Automated Fact-Checking: A Survey](https://mlsanity.com/paper/2011.03870/) (2020)
- [That is a Known Lie: Detecting Previously Fact-Checked Claims](https://mlsanity.com/paper/2005.06058/) (2020)
- [SAFER: A Structure-free Approach for Certified Robustness to Adversarial Word Substitutions](https://mlsanity.com/paper/2005.14424/) (2020)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text](https://mlsanity.com/paper/2307.07696/) (2023)
- [Automated Fact-Checking: A Survey](https://mlsanity.com/paper/2109.11427/) (2021)
- [ProoFVer: Natural Logic Theorem Proving for Fact Verification](https://mlsanity.com/paper/2108.11357/) (2021)
- [Missing Counter-Evidence Renders NLP Fact-Checking Unrealistic for Misinformation](https://mlsanity.com/paper/2210.13865/) (2022)
- [Synthetic Disinformation Attacks on Automated Fact Verification Systems](https://mlsanity.com/paper/2202.09381/) (2022)
- [A Survey on Truth Discovery](https://mlsanity.com/paper/1505.02463/) (2015)
- [Decomposition Dilemmas: Does Claim Decomposition Boost or Burden Fact-Checking Performance?](https://mlsanity.com/paper/2411.02400/) (2024)
- [Claim Detection for Automated Fact-checking: A Survey on Monolingual, Multilingual and Cross-Lingual Research](https://mlsanity.com/paper/2401.11969/) (2024)

## Abstract (arXiv)

An automated fact-checking system returns a label: the claim is true, or it is false. In many such systems the verdict remains the primary output. What is generally missing is a record of which document settled the question, of what would have had to be different for the verdict to change, or of whether the same claim, reworded, would have been judged the same way. We call the missing piece a warrant: a separate statement of what was guaranteed and on what grounds. Formal methods produce evidence of this kind, and regulation is beginning to ask for it, since the Digital Services Act and the AI Act both call for auditable evidence about how systems behave. Surveys of automated fact-checking are usually organised by pipeline stage, and treat logic as one technique among many. We organise the field by what is being formalised instead, which gives five levels: the claim, the reasoning, the system doing the checking, the ecosystem the claim spreads through, and the regulatory obligation. Sorting 121 works into those levels, two patterns stand out. Most of the relevant formal machinery already exists, but it was built for other domains and has rarely been applied here, and the gap is widest for verifying the checking system itself. Several stages of the routine professional fact-checkers follow also have no stated correctness criterion, and two of them, writing a claim in checkable form and correcting a verdict already published, are not formally specified in any work we coded. We close with open problems, each with a suggested first step.