📝 SummarXiv

Abstract

Logical reasoning is a fundamental capability of large language models (LLMs). However, existing studies largely overlook the interplay between logical complexity and semantic complexity, resulting in methods that struggle to address challenging scenarios involving abstract propositions, ambiguous contexts, and conflicting stances, which are central to human reasoning. For this gap, we propose LogicAgent, a semiotic-square-guided framework designed to jointly address logical complexity and semantic complexity. LogicAgent explicitly performs multi-perspective deduction in first-order logic (FOL), while mitigating vacuous reasoning through existential import checks that incorporate a three-valued decision scheme (True, False, Uncertain) to handle boundary cases more faithfully. Furthermore, to overcome the semantic simplicity and low logical complexity of existing datasets, we introduce RepublicQA, a benchmark that reaches college-level difficulty (FKGL = 11.94) and exhibits substantially greater lexical and structural diversity than prior benchmarks. RepublicQA is grounded in philosophical concepts, featuring abstract propositions and systematically organized contrary and contradictory relations, making it the most semantically rich resource for evaluating logical reasoning. Experiments demonstrate that LogicAgent achieves state-of-the-art performance on RepublicQA, with a 6.25% average gain over strong baselines, and generalizes effectively to mainstream logical reasoning benchmarks including ProntoQA, ProofWriter, FOLIO, and ProverQA, achieving an additional 7.05% average gain. These results highlight the strong effectiveness of our semiotic-grounded multi-perspective reasoning in boosting LLMs' logical performance.