Pascal Wullschleger, Christian Kreis, Martin A. Walter +2cs.CL
Biomedical literature is increasingly mined for knowledge beyond the questions it was written to answer. Because the target concepts are not known in advance, annotators prefer open-ended labels, whose agreement is hard to quantify. We study soft inter-rater reliability for annotators providing unstructured texts for biomedical annotation tasks. Synthetic experiments show that soft reliability can be quantified using a variety of semantic equivalence measures, and that the choice of measure affects failure modes of the estimation. Embeddings are scalable, but limited when differentiating similar but distinct concepts. Large language models are promising, but limited by scalability for estimating agreement by chance. Finally, we suggest measures based on natural language inference as a sensible compromise.
SHACL is a core technology for validating the conformance of RDF knowledge graphs (KGs). Yet, authoring SHACL shapes requires technical expertise that most domain experts lack. Translating natural language requirements into SHACL (NL2SHACL) would lower this barrier. However, there is no dedicated benchmark for NL2SHACL, and evaluating generated shapes requires methods beyond string comparison, as semantically equivalent shapes can differ in serialisation and structure. To tackle these challenges, we present NL2SHACL-Bench, a benchmark suite for natural language to SHACL translation. Using NL2SHACL-Bench, we evaluate four state-of-the-art large language models (LLMs) for this task. Our results show that current LLMs are highly capable of generating syntactically valid SHACL, but still struggle to produce semantically equivalent constraints for complex logical and structural patterns. This indicates that NL2SHACL-Bench provides a meaningful basis for measuring advances in the NL2SHACL state of the art.
Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce \emph{Bidirectional Provability Fingerprinting} (\bpf{}), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) \emph{Counterfactual Probe Generation} (\cpg{}), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the \emph{Equivalence Spectrum}, a continuous faithfulness score that replaces brittle binary verdicts; (iii) \emph{Adaptive Probe Budget Allocation} (\apba{}), an information-theoretic budget router; and (iv) \emph{Faithfulness-Guided Decoding} (\fgd{}), which uses \bpf{} signals as a reward during autoformalization. We prove a \emph{drift detection theorem} and a \emph{PAC-faithfulness} result establishing that the equivalence class of a natural language statement is learnable from $\mathcal{O}(\log(1/δ)/\varepsilon)$ probes under mild assumptions. We release \driftbench{}, a benchmark of $2{,}183$ NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \bpf{}\,+\,\cpg{} detects $89.6\%$ of drifted formalizations at a $3.0\%$ false-positive rate-against $41.2\%$ for typecheck and $63.3\%$ for LLM-judge baselines, and \fgd{} reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by $47\%$. https://pmlrbd.github.io/BPF/