From Ambiguity to Verdict: A Semiotic-Grounded Multi-Perspective Agent for LLM Logical Reasoning

TL;DR

This paper tackles the challenge of reasoning under simultaneous semantic and logical complexity by introducing LogicAgent, a semiotic-square-guided framework with three stages: semantic structuring, logical reasoning, and reflective verification. It grounds semantic oppositions in Greimas’ semiotic square, translates NL premises to FOL, and verifies conclusions through a three-tier reflection mechanism, addressing ambiguity and abstract concepts. To evaluate joint semantic and logical depth, the authors construct RepublicQA, a philosophically rich benchmark with high FKGL and systematic contrary-constructs, and demonstrate state-of-the-art performance on RepublicQA and strong generalization to ProntoQA, ProofWriter, FOLIO, and ProverQA. The work highlights the importance of multi-perspective, symbolically grounded reasoning for robust logical performance in semantically dense, abstract contexts.

Abstract

Logical reasoning is a fundamental capability of large language models. However, existing studies often overlook the interaction between logical complexity and semantic complexity, leading to systems that struggle with abstract propositions, ambiguous contexts, and conflicting stances that 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 support evaluation under these conditions, we introduce RepublicQA, a benchmark that couples semantic complexity with logical depth. RepublicQA reaches college-level semantic difficulty (FKGL 11.94), contains philosophically grounded abstract propositions with systematically constructed contrary and contradictory forms, and offers a semantically rich setting for assessing logical reasoning in large language models. Experiments show that LogicAgent achieves state-of-the-art performance on RepublicQA with a 6.25 percent average improvement over strong baselines, and generalizes effectively to mainstream logical reasoning benchmarks including ProntoQA, ProofWriter, FOLIO, and ProverQA, achieving an additional 7.05 percent average gain. These results demonstrate the effectiveness of semiotic-grounded multi-perspective reasoning in enhancing logical performance.

Figures (10)

• Figure 1: Overview of LogicAgent and the proposed RepublicQA benchmark. (Top-left) RepublicQA features abstract, philosophical propositions from Plato's Republic with diverse contextual premises, enabling multiple semantic interpretations. (Bottom-left) LogicAgent consists of three stages. (Top-right) A multi-step reasoning process explores contraries and contradictions when S1 is indeterminate. (Bottom-right) LogicAgent outperforms strong baselines across four benchmarks, demonstrating robust generalization in symbolic, multi-perspective reasoning.
• Figure 2: Greimas’ Semiotic Square: illustrating contraries ($S_1$ vs. $S_2$), contradictions ($S_1$ vs. $\lnot S_1$, $S_2$ vs. $\lnot S_2$), and implications ($S_1$$\Rightarrow$$\lnot S_2$, $S_2$$\Rightarrow$$\lnot S_1$).
• Figure 3: Overview of the LogicAgent framework. The agent processes a natural language proposition through three stages. (1) Semantic Structuring Stage constructs a Greimas’ Semiotic Square, generating four interrelated propositions: the primary proposition $\textcolor{blue}{S_1}$, its contradiction $\textcolor{red}{\lnot S_1}$, the contrary $\textcolor{teal}{S_2}$, and the contradiction of the contrary $\textcolor{orange}{\lnot S_2}$. These are verified for FOL-consistency using a CFG-based parser. (2) Logical Reasoning Stage transforms the premises into FOL, plans deductive steps for each proposition, and performs symbolic reasoning to evaluate their answers. (3) Reflective Verification Stage adjudicates the final judgment via three procedures: Direct Resolution, applied when $\textcolor{blue!80!black}{S_1}$ and $\textcolor{red!70!black}{\lnot S_1}$ offer a contradictory answer; Quick Reflection, used when either $\textcolor{blue!80!black}{S_1}$ or $\textcolor{red!70!black}{\lnot S_1}$ is uncertain; and Deep Reflection, used when both $\textcolor{blue!80!black}{S_1}$ and $\textcolor{red!70!black}{\lnot S_1}$ yield the same value, requiring further validation through the semiotic implication relations involving $\textcolor{teal!80!black}{S_2}$ and $\textcolor{orange!80!black}{\lnot S_2}$.
• Figure 4: Complexity metrics comparison. Red is our benchmark.
• Figure 5: Ablation studies: (a) input modalities and (b) reasoning efficiency.

Theorems & Definitions (3)

• Theorem 1: Semantic Implication Theorem
• Definition 1: Existential Import Check
• Lemma 1: Soundness of Conditional Contrariety