Open-world logical entailment requires deciding whether a set of premises entails a conclusion, entails its negation, or leaves it undecided. Many existing methods are deductive in spirit, searching for a proof and reading the label from whether that proof succeeds. When implemented through LLM-based proof search, this makes the prediction depend on a single unstable trajectory, and a failed or partial search is easily mismapped to the wrong label. We propose ABED (Assumption-Based Bidirectional Entailment Diagnosis), a training-free inference-time framework that reframes entailment classification as missing assumption diagnosis. Instead of asking only whether a conclusion can be proved, ABED asks what assumption is missing for it to hold, and classifies that gap as already closed by the premises (Null), contradicted by them (Contra), or left open (Admissible). It applies this diagnosis to both a conclusion and its negation, and determines the label from the resulting dual gap pair. Across FOLIO, ProofWriter, ProntoQA, and LogicNLI, ABED consistently outperforms prompting-based, symbolic, solver-based, and deductive baselines, improving over the strongest baseline on each dataset by 3.4, 5.3, 0.8, and 4.4 points with GPT-4.1.

Large language models with retrieval-augmented generation systematically underutilize evidence in the middle of multi-document contexts, a phenomenon known as Lost in the Middle. Existing mitigation strategies, such as document reordering and attention steering, can reduce boundary bias but remain brittle in noisy settings, where inaccurate relevance estimation and spurious documents still obscure useful evidence in central positions. We propose DuQUAD, a multi-document QA framework that mitigates positional bias through dual-view reasoning and quality-aware evidence pruning. DuQUAD combines a Local Agent guided by a Structural Fusion Score with a Global Agent that reasons over the full document set, providing both targeted evidence recovery and broad contextual understanding. The framework further filters candidate evidence using explicit quality scoring and refines it at the sentence level to reduce noise. DuQUAD consistently outperforms strong Lost-in-the-Middle mitigation baselines, including recent multi-agent and context optimization methods, improving accuracy by 3.9% on average over the strongest competing baseline and gold evidence recall by 9.4%, while substantially reducing computational cost compared to existing multi-agent frameworks.