Logical reasoning is a fundamental capability of large language models (LLMs). However, existing studies largely overlook the interplay between logical complexity and semantic complexity, limiting their robustness under abstract propositions, ambiguous contexts, and conflicting stances, which are central to human reasoning. We propose **LogicAgent**, a semiotic-square–guided framework that jointly addresses these two axes of difficulty. The semiotic square provides a principled structure for multi-perspective semantic analysis, and LogicAgent integrates automated deduction with reflective verification to manage logical complexity across deeper reasoning chains. To evaluate reasoning under coupled semantic and logical complexity, we introduce **RepublicQA**, a benchmark that contains abstract propositions with systematically constructed contrary and contradictory forms, providing a semantically rich setting for assessing logical reasoning in LLMs. Experiments show that LogicAgent achieves state-of-the-art performance on RepublicQA with a 6.25% average gain, and generalizes well to four mainstream logical reasoning benchmarks with an additional 7.05% improvement, highlighting the effectiveness of our semiotic-grounded multi-perspective reasoning in boosting LLMs’ logical performance.