LogiPlan Benchmark for LLM Relational Reasoning

• LogiPlan Benchmark is a structured evaluation framework designed to test LLM capabilities in logical planning and relational reasoning over complex directed graphs.
• It employs three tasks – plan generation, consistency detection, and comparison questions – with dynamic difficulty adjustments to assess multi-step inference and cycle detection accuracy.
• The benchmark measures self-correction and performance under increased graph complexity, providing insights into model confidence calibration and reasoning limitations.

LogiPlan Benchmark is a structured evaluation framework developed to test the logical planning and relational reasoning capabilities of LLMs, particularly in contexts involving complex directed relational graphs. Its design emphasizes the capacity for models to handle intricate, multi-step reasoning required in practical domains such as business process planning, network infrastructure design, and knowledge base management. The benchmark systematically varies core parameters governing complexity, incorporates dynamic assessment across three core tasks, benchmarks state-of-the-art models, and introduces mechanisms for gauging self-reflection and correction in LLM outputs (Cai et al., 12 Jun 2025).

1. Definition and Benchmark Structure

The LogiPlan benchmark provides a rigorous methodology for evaluating an LLM’s performance in logical planning and reasoning over relational structures. Tasks within the benchmark are devised to test not only direct acyclic graph generation but also more subtle verification skills such as cycle detection or relationship inference.

The structure of LogiPlan is defined by controlling:

• The number of objects: This parameter typically ranges from small sets (e.g., 3 objects) up to larger graphs (e.g., 50 objects).
• The number of relations: Varies from minimally sufficient (equal to the object count) to near the maximal $n(n-1)/2$ for densely connected graphs.
• The minimum depth of relational chains: Specifies the minimum length/steps in relational inferences or cycles.

Task input/output is standardized, with models required to produce specified JSON formats and enumerate identified cycles in numbered lists, ensuring consistency in evaluation (Cai et al., 12 Jun 2025).

2. Core Task Archetypes

LogiPlan encompasses three complementary tasks, each specifically targeting distinct aspects of logical relational skills:

a. Plan Generation:

Models receive a prompt specifying the desired number of objects and relationships and must construct a valid directed, acyclic relational graph conforming to those requirements. Model outputs are evaluated for overall accuracy, structural consistency (including acyclicity), proper cardinality, and uniqueness of relationships. Explicit output formatting (using, e.g., $A > B > C > \dots > Z$ and JSON notation) allows for automated consistency checks.

b. Consistency Detection:

Presented with lists of relational statements, often containing implicit cycles or contradictions, models must decide whether the statements admit any logical inconsistency. For affirmative cases, the cycle (e.g., $A > B > C > A$) must be enumerated. Precision, recall, and F1 metrics are used for quantitative assessment. The computational complexity for this task, per Johnson’s algorithm, is $O((V+E)\times(C+1))$, highlighting the algorithmic depth required for robust cycle detection (Cai et al., 12 Jun 2025).

c. Comparison Question:

Given a relational graph and a provided query (e.g., "Is X greater than Y?"), the LLM determines “True”, “False”, or “Unknown”. This tests inference chains over varying depths, where “Unknown” is assigned if relationship cannot be established even indirectly. Overall accuracy is the primary evaluation metric.

3. Dynamic Difficulty Scaling

LogiPlan's framework enables systematic variation of difficulty via its parametrization. By adjusting the number of objects, relationship density, and chain/cycle depth, the benchmark can target:

• Simple reasoning: e.g., chain-like structures readily admitting topological ordering ($A > B > C > D$).
• Complex reasoning: e.g., large, densely connected graphs requiring multi-hop inference and sophisticated cycle detection.

Controlled scaling ensures fine-grained assessment of a model’s capabilities from pattern-recognition at low difficulty to genuine logical planning and relational reasoning in more demanding regimes.

4. Model Evaluation and Comparative Findings

State-of-the-art models—including DeepSeek R1, Gemini 2.0 Pro, Gemini 2 Flash Thinking, GPT-4.5, GPT-4o, Llama 3.1 405B, O3-mini, O1, and Claude 3.7 Sonnet—were evaluated across all LogiPlan tasks.

Performance Insights:

• In Plan Generation, reasoning-specialized models (O3-mini, O1) achieve accuracies up to 97% on moderate complexity instances, while Gemini 2 Flash Thinking and instruction-tuned models (GPT-4.5, GPT-4o) often introduce duplicate relationships or suffer performance drops as scale increases.
• Consistency Detection and Comparison Question highlight further gaps: best models (O1, O3-mini) outperform instruction-based ones by factors close to 2× as problem size and relational chain depth increase. For comparison tasks, overall accuracy drops close to random baseline for certain instances as inference chain depth grows.
• Notable is the tendency for models to adopt simplistic algorithms (editor’s term: “naive ordering strategies,” e.g., always generating chains $A > B > C$), which fail to generalize in denser or complex instances.

5. Evaluation of Self-Correction in LLMs

LogiPlan uniquely assesses self-correction by prompting models with queries such as “Are you sure?” to elicit potential updates or revisions of initial outputs, specifically in the Consistency Detection and Comparison Question tasks.

• Certain models (Gemini 2 Flash Thinking) demonstrated substantial improvements (>10% F1) on follow-up, suggesting a degree of internal uncertainty calibration.
• Other models (e.g., Llama 3.1 405B) exhibited minimal or even negative change upon self-reflection.

This explicit measurement reveals heterogeneity in confidence calibration and the effect of prompt-based self-assessment across model architectures (Cai et al., 12 Jun 2025).

6. Challenges, Limitations, and Research Directions

• Complexity Scaling: As the relational graph size and depth of inference increase, all tested LLMs exhibit substantial degradation in performance, especially in cycle detection and long-chain comparison.
• Algorithmic Robustness: Reasoning models may employ strategies that do not generalize to complex graphs or introduce errors (e.g., duplicate relations).
• Instruction-based Models: These are particularly sensitive to increased relationship density and require architectural improvements for robust generalization.

The findings indicate avenues for future research:

• Development of advanced architectures or reinforcement learning techniques to address multi-step planning, efficient cycle detection (potentially NP-hard contexts), and global graph inference.
• Expansion of self-correction and confidence calibration approaches for iterative output refinement.
• Extension of LogiPlan to encompass wider real-world scenarios and additional variations, facilitating robust benchmarking of reasoning in LLMs (Cai et al., 12 Jun 2025).

7. Contextual Significance in LLM Reasoning Research

LogiPlan sets a methodological precedent for structured, dynamically scalable benchmarks in the evaluation of logical planning and relational reasoning for LLMs. It exposes significant gaps in current model architecture, especially under increased complexity, and provides both a practical test bed and diagnostic tool for ongoing LLM development. Its emphasis on self-correction and detailed performance stratification distinguishes it from prior benchmarks focused on surface-level reasoning or smaller-scale tasks.

The benchmark furthers the field by identifying which architectural traits and training regimes are correlated with reasoning robustness, suggesting that truly systematic improvements in LLM reasoning will require explicit optimization for graph-theoretic and multi-step relational inference domains.