\textsc{LogicScore}: Fine-grained Logic Evaluation of Conciseness, Completeness, and Determinateness in Attributed Question Answering

Current evaluation methods for Attributed Question Answering (AQA) suffer from \textit{attribution myopia}: they emphasize verification of isolated statements and their attributions but overlook the global logical integrity of long-form answers. Consequently, Large Language Models (LLMs) often produce factually grounded yet logically incoherent responses with elusive deductive gaps. To mitigate this limitation, we present \textsc{LogicScore}, a unified evaluation framework that shifts the paradigm from local assessment to global reasoning scrutiny. Grounded in Horn Rules, our approach integrates a backward verification mechanism to systematically evaluate three key reasoning dimensions: \textit{Completeness} (logically sound deduction), \textit{Conciseness} (non-redundancy), and \textit{Determinateness} (consistent answer entailment). Extensive experiments across three multi-hop QA datasets (HotpotQA, MusiQue, and 2WikiMultiHopQA) and over 20 LLMs (including GPT-5, Gemini-3-Pro, LLaMA3, and task-specific tuned models) reveal a critical capability gap: leading models often achieve high attribution scores (e.g., 92.85\% precision for Gemini-3 Pro) but struggle with global reasoning quality (e.g., 35.11\% Conciseness for Gemini-3 Pro). Our work establishes a robust standard for logical evaluation, highlighting the need to prioritize reasoning coherence alongside factual grounding in LLM development. Codes are available at: https://github.com/zhichaoyan11/LogicScore.