Learning Proposition-Level Links from Sentence-Level Supervision for Neuro-Symbolic NLI

While Large Language Model (LLM)-based Natural Language Inference (NLI) systems achieve high accuracy, their decision-making processes lack auditable structures. This paper explores whether NLI can be performed using only interpretable, graph-based representations of evidence. We introduce a fully graph-based pipeline where the classifier never directly processes the input text. Instead, sentences are decomposed into atomic propositions, converted into ConceptNet triples via constrained decoding, and represented as three graphs per pair: premise, hypothesis, and a retrieved ConceptNet subgraph. These graphs are then fed into a fine-tuned 0.8-billion-parameter language model. On the SNLI dataset, our pipeline achieves 89.7% accuracy, just 1.9 points below an identically trained text-based model. On ANLI, it matches the published performance of RoBERTa-large on rounds R2 and R3 (48.0% vs. 48.9% and 44.9% vs. 44.4%) but trails by 16 points on R1, resulting in an overall gap of 9 to 14 points compared to its text counterpart. We term this gap the price of interpretability and demonstrate that it stems from representational limitations rather than data constraints. Ablation studies further reveal that graphs and text are complementary: combining both modalities achieves 92.1% accuracy on SNLI.

Arguments often omit premises or claims, forming enthymemes. We study pairwise logical selection between two candidates for the omitted component. Existing natural language methods can identify or generate candidates but often do not expose how the selected candidate completes the inference, while logic-based approaches usually assume that the required formulae and background knowledge are available. We extend a prior neuro-symbolic pipeline from missing-premise to missing-claim selection and replace binary entailment outcomes with logical-resistance scores. Top-Link uses weighted Partial MaxSAT under a single configuration of highest-confidence semantic links. We then introduce Possible-World Atom-Link Formalization (PWAL), which keeps translated formulae fixed and marginalizes logical resistance over alternative cross-formula semantic-link configurations. We evaluate PWAL on five tasks: ARCT and a CDED-derived task for missing-premise selection, iDebate- and AAE2-derived tasks for missing-claim selection, and alphaNLI for abductive hypothesis selection. Relative to Top-Link, PWAL raises strict accuracy by 2.95-30.86 percentage points and reduces tie rates by 4.57-58.00 percentage points on all five tasks. When ties receive half credit, accuracy still increases by 0.45-6.04 percentage points. PWAL also records the translated formulae, sampled link configurations, and resistance components for every comparison, providing a transparent trace of each score.

Natural language understanding requires interleaving textual and logical reasoning, yet large language models often fail to perform such reasoning reliably. Existing neurosymbolic systems combine LLMs with solvers but remain limited to fully formalizable tasks such as math or program synthesis, leaving natural documents with only partial logical structure unaddressed. We introduce Logitext, a neurosymbolic language that represents documents as natural language text constraints (NLTCs), making partial logical structure explicit. We develop an algorithm that integrates LLM-based constraint evaluation with satisfiability modulo theory (SMT) solving, enabling joint textual-logical reasoning. Experiments on a new content moderation benchmark, together with LegalBench and Super-Natural Instructions, show that Logitext improves both accuracy and coverage. This work is the first that treats LLM-based reasoning as an SMT theory, extending neurosymbolic methods beyond fully formalizable domains.