# ABD: Default Exception Abduction in Finite First Order Worlds

arXiv: https://arxiv.org/abs/2602.18843 · HTML: https://mlsanity.com/paper/2602.18843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Abductive Commonsense Reasoning](https://mlsanity.com/paper/1908.05739/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Learning to Prove Theorems via Interacting with Proof Assistants](https://mlsanity.com/paper/1905.09381/) (2019)
- [Learning higher-order logic programs](https://mlsanity.com/paper/1907.10953/) (2019)

## Abstract (arXiv)

We introduce ABD, a benchmark for default-exception abduction over finite first-order worlds. Given a background theory with an abnormality predicate and a set of relational structures, a model must output a first-order formula that defines exceptions, restoring satisfiability while keeping exceptions sparse. We formalize three observation regimes (closed-world, existential completion, universal completion) with exact SMT verification. Evaluating ten frontier LLMs on 600 instances, the best models achieve high validity but parsimony gaps remain, and holdout evaluation reveals distinct generalization failure modes across regimes.