New Neuro-Symbolic AI Improves Enthymeme Completion with Logical Selection

Arguments often contain omitted premises or claims, known as enthymemes, which natural language processing (NLP) methods struggle to complete while explicitly showing the inference path. Existing logic-based approaches, conversely, often assume the necessary logical formulae and background knowledge are readily available. This research extends a neuro-symbolic pipeline to address missing-premise and missing-claim selection, replacing binary entailment outcomes with more nuanced "logical-resistance scores." The paper introduces Possible-World Atom-Link Formalization (PWAL), an advancement over the prior Top-Link method. While Top-Link uses weighted Partial MaxSAT under a single, highest-confidence configuration of semantic links, PWAL keeps translated formulae fixed and instead marginalizes logical resistance across various alternative semantic-link configurations between formulae. This approach accounts for uncertainty in how semantic links connect different parts of an argument. PWAL was evaluated across five tasks, including missing-premise and missing-claim selection, and abductive hypothesis selection. The results show that PWAL significantly increased strict accuracy (by 2.95-30.86 percentage points) and substantially reduced tie rates (by 4.57-58.00 percentage points) compared to Top-Link. Furthermore, PWAL provides a transparent trace of each score, detailing translated formulae, sampled link configurations, and resistance components, enhancing the interpretability of its logical selections.