@inproceedings{karaosmanoglu-2026-proof,
title = "Proof Identity and Divisible Correspondence in Multi-Derivation Reasoning Evaluation",
author = "Karaosmano{\u{g}}lu, Toprak Seda",
editor = "Valentino, Marco and
Ferreira, Deborah and
Thayaparan, Mokanarangan and
Ranaldi, Leonardo and
Cheng, Jo-Ku and
Freitas, Andre",
booktitle = "The Proceedings of the 4th Workshop on Mathematical Natural Language Processing ({M}ath{NLP} 2026)",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.mathnlp-main.24/",
pages = "312--321",
ISBN = "979-8-89176-468-2",
abstract = "Systems that return several valid derivations require explicit choices about proof identity and proof-set correspondence. This study examines both choices on ProofWriter. An application-aware representation distinguishes grounded uses of the same source rule through canonical premise derivations. Source-ID projection collapses distinct reference proofs in 28 of 400 stratified derivable questions (7.0{\%}). The comparison includes exact proof-set F{\ensuremath{_1}}, flattened-atom F{\ensuremath{_1}}, Optimal Subpattern Assignment with Jaccard distance (Jaccard-OSPA), and MCT-J. The label MCT-J denotes a balanced optimal-transport distance with Jaccard distance as the ground metric. On 160 fixed outputs from 32 derivable questions, source-ID projection lowers MCT-J distance by 0.0606 on average. A cluster bootstrap over the underlying ProofWriter worlds gives a 95{\%} interval of 0.0316{--}0.0955. MCT-J equals Jaccard-OSPA on all 117 equal-cardinality outputs, while Jaccard-OSPA has the larger distance on 38 of 43 unequal-cardinality outputs. Of 433 generated proof members, 430 pass independent rule-level replay. Excluding the three replay failures changes the mean representation effect from 0.0606 to 0.0589. Proof identity and proof-set correspondence therefore change structural evaluation on fixed outputs."
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<abstract>Systems that return several valid derivations require explicit choices about proof identity and proof-set correspondence. This study examines both choices on ProofWriter. An application-aware representation distinguishes grounded uses of the same source rule through canonical premise derivations. Source-ID projection collapses distinct reference proofs in 28 of 400 stratified derivable questions (7.0%). The comparison includes exact proof-set F\ensuremath₁, flattened-atom F\ensuremath₁, Optimal Subpattern Assignment with Jaccard distance (Jaccard-OSPA), and MCT-J. The label MCT-J denotes a balanced optimal-transport distance with Jaccard distance as the ground metric. On 160 fixed outputs from 32 derivable questions, source-ID projection lowers MCT-J distance by 0.0606 on average. A cluster bootstrap over the underlying ProofWriter worlds gives a 95% interval of 0.0316–0.0955. MCT-J equals Jaccard-OSPA on all 117 equal-cardinality outputs, while Jaccard-OSPA has the larger distance on 38 of 43 unequal-cardinality outputs. Of 433 generated proof members, 430 pass independent rule-level replay. Excluding the three replay failures changes the mean representation effect from 0.0606 to 0.0589. Proof identity and proof-set correspondence therefore change structural evaluation on fixed outputs.</abstract>
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%0 Conference Proceedings
%T Proof Identity and Divisible Correspondence in Multi-Derivation Reasoning Evaluation
%A Karaosmanoğlu, Toprak Seda
%Y Valentino, Marco
%Y Ferreira, Deborah
%Y Thayaparan, Mokanarangan
%Y Ranaldi, Leonardo
%Y Cheng, Jo-Ku
%Y Freitas, Andre
%S The Proceedings of the 4th Workshop on Mathematical Natural Language Processing (MathNLP 2026)
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-468-2
%F karaosmanoglu-2026-proof
%X Systems that return several valid derivations require explicit choices about proof identity and proof-set correspondence. This study examines both choices on ProofWriter. An application-aware representation distinguishes grounded uses of the same source rule through canonical premise derivations. Source-ID projection collapses distinct reference proofs in 28 of 400 stratified derivable questions (7.0%). The comparison includes exact proof-set F\ensuremath₁, flattened-atom F\ensuremath₁, Optimal Subpattern Assignment with Jaccard distance (Jaccard-OSPA), and MCT-J. The label MCT-J denotes a balanced optimal-transport distance with Jaccard distance as the ground metric. On 160 fixed outputs from 32 derivable questions, source-ID projection lowers MCT-J distance by 0.0606 on average. A cluster bootstrap over the underlying ProofWriter worlds gives a 95% interval of 0.0316–0.0955. MCT-J equals Jaccard-OSPA on all 117 equal-cardinality outputs, while Jaccard-OSPA has the larger distance on 38 of 43 unequal-cardinality outputs. Of 433 generated proof members, 430 pass independent rule-level replay. Excluding the three replay failures changes the mean representation effect from 0.0606 to 0.0589. Proof identity and proof-set correspondence therefore change structural evaluation on fixed outputs.
%U https://aclanthology.org/2026.mathnlp-main.24/
%P 312-321
Markdown (Informal)
[Proof Identity and Divisible Correspondence in Multi-Derivation Reasoning Evaluation](https://aclanthology.org/2026.mathnlp-main.24/) (Karaosmanoğlu, MathNLP 2026)
ACL