Pairwise Logical Selection of Enthymeme Completions under Semantic-Link Uncertainty

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.