LTLBench: Towards Benchmarks for Evaluating Temporal Reasoning in Large Language Models
Using LTL to generate 2000 challenges, evaluating 12 LLMs, revealing three main issues in complex temporal reasoning tasks.
Key Findings
Methodology
This work introduces an automated challenge generation pipeline based on Linear Temporal Logic (LTL), comprising random directed graph creation, LTL formula synthesis, NuSMV model verification, and natural language conversion. The dataset LTLBench contains 2000 tasks, evaluated across 12 models with five reasoning strategies (direct prompting, zero-shot chain-of-thought, few-shot CoT, self-consistency, least-to-most). By manipulating the number of formula operators and events, the study systematically analyzes model performance and failure modes, emphasizing formal logical reasoning in temporal contexts.
Key Results
- gpt-4o with few-shot CoT achieves 93.95% accuracy, outperforming GPT-3.5-Turbo's 51.05%. Overall, few-shot CoT yields the highest mean accuracy of 76.33%. Increasing formula operators and events introduces challenges, with performance fluctuations observed but stability in few-shot CoT. Qualitative analysis uncovers three major failure issues: temporal semantics misalignment, context hypothesis detachment, and reasoning error amplification, especially in complex scenarios.
- Models demonstrate significant performance gaps in handling nested and multi-step temporal relations. The highest accuracy among models reaches nearly 94%, while the lowest hovers around 51%. The robustness of few-shot CoT suggests its potential as a reliable reasoning strategy. The analysis of errors indicates that models often misunderstand the precise timing of events, ignore contextual cues, or propagate initial mistakes, which hampers their reasoning accuracy in complex tasks.
Significance
This study pioneers the integration of formal logic, specifically LTL, into large-scale model evaluation, providing a systematic and scalable benchmark for temporal reasoning. It addresses the critical gap in assessing models’ abilities to handle complex logical relations over time, which is vital for applications like automated verification, planning, and event prediction. The insights into failure modes guide future model improvements, emphasizing the importance of logical and temporal understanding, thus advancing both theoretical research and practical deployment.
Technical Contribution
The core technical innovation lies in the automated pipeline that synthesizes challenging temporal reasoning tasks grounded in LTL, verified via NuSMV, ensuring logical correctness. This approach enables controlled variation of task complexity through operators and event counts, facilitating detailed performance analysis. It bridges formal verification techniques with large language model evaluation, offering a new paradigm for benchmarking reasoning capabilities in AI.
Novelty
This is the first work to systematically generate and evaluate large-scale temporal reasoning challenges based on LTL, integrating formal verification with natural language tasks. Unlike prior datasets relying on knowledge graphs or rule-based questions, this approach provides a rigorous, logic-based framework that captures complex temporal relations. The automatic challenge synthesis and verification process ensures high-quality, diverse tasks, marking a significant step forward in reasoning benchmarks.
Limitations
- The challenge generation relies on random graph sampling, which may not cover all real-world temporal scenarios, limiting ecological validity.
- Models still struggle with deeply nested or multi-layered temporal formulas, indicating room for improvement in logical reasoning capabilities.
- The current evaluation is static and task-specific; future work should incorporate dynamic, real-world temporal data and multi-modal inputs for broader applicability.
Future Work
Future directions include integrating reinforcement learning to enhance reasoning robustness, expanding the challenge set with more complex operators and real-world scenarios, and developing explainability tools to interpret model reasoning pathways. Additionally, exploring multi-modal temporal reasoning and applying this framework to real-world tasks like autonomous planning and event forecasting will be key to advancing AI’s temporal understanding.
AI Executive Summary
Temporal reasoning (TR) is fundamental for AI systems to understand and manipulate the relationships between events over time. Despite recent advances in large language models (LLMs), their ability to perform complex temporal reasoning remains limited, especially in scenarios involving nested or multi-step relations. Existing benchmarks often lack the formal structure needed to rigorously evaluate models’ understanding of temporal logic, creating a gap in assessing their reasoning capabilities.
To address this, the authors propose an innovative challenge generation pipeline based on Linear Temporal Logic (LTL), a formal language for expressing temporal relations. This pipeline automates the creation of diverse and logically valid TR tasks by generating random directed graphs representing event sequences, synthesizing LTL formulas with varying complexity, verifying their correctness via NuSMV model checker, and translating these into natural language problems. Using this approach, they constructed LTLBench, a dataset of 2000 challenges, and evaluated 12 prominent LLMs across five reasoning strategies.
Results reveal that the best-performing model, gpt-4o, reaches nearly 94% accuracy with few-shot chain-of-thought prompting, while the weakest, GPT-3.5-Turbo, scores just over 51%. The study highlights that increasing formula complexity and event count introduces significant challenges, causing performance fluctuations. Qualitative analysis uncovers three core issues: models often misinterpret temporal semantics, detach from contextual cues, and amplify initial reasoning errors, especially in complex tasks.
This work advances the field by providing a scalable, formal benchmark for temporal reasoning, emphasizing the importance of logical understanding in AI. It demonstrates that current models, despite progress, still face fundamental difficulties in handling intricate temporal relations, guiding future research toward more robust, logic-aware AI systems. The authors plan to extend this framework with multi-modal inputs and reinforcement learning techniques, aiming to develop models capable of sophisticated, real-world temporal reasoning.
Deep Analysis
Background
Temporal reasoning (TR) has long been a critical aspect of AI, enabling systems to understand the sequence and timing of events. Early work, such as Shoham and Goyal (1988), established the formal foundations with temporal logics. Kripke's (1963) structures provided the semantics for modal and temporal logics, facilitating formal verification. Recent efforts, including datasets like YAGO11k (Dasgupta et al., 2018) and the Test of Time benchmark (Fatemi et al., 2024), aimed to evaluate models on event order, frequency, and duration. However, these datasets often lack the capacity to test complex logical compositions and nested relations, limiting their scope in assessing models’ reasoning depth. As large language models (LLMs) grow in capability, there is a pressing need for benchmarks that can rigorously evaluate their understanding of formal temporal relations, especially in scenarios requiring multi-step, nested reasoning, which is essential for applications such as automated planning, event prediction, and verification.
Core Problem
Despite progress, current LLMs still struggle with complex temporal reasoning, especially when relations involve multiple operators or nested formulas. Existing benchmarks often focus on surface-level understanding or simple event sequences, failing to challenge models with formal logical structures. This gap hampers the development of models capable of reasoning about intricate temporal dependencies in real-world applications. Designing a comprehensive, scalable, and logically rigorous benchmark remains an open challenge. Additionally, verifying the correctness of generated challenges and ensuring they reflect real-world complexity pose significant hurdles, necessitating a systematic approach that combines formal verification with natural language processing.
Innovation
The core innovation of this work is the development of an automated challenge synthesis pipeline grounded in LTL, which systematically generates diverse, logically valid temporal reasoning tasks. Key components include: 1) random directed graph generation to model event sequences; 2) an adapted LTL formula synthesis algorithm to create complex temporal formulas; 3) NuSMV model verification to ensure logical correctness; 4) natural language translation for human evaluation. This integrated approach ensures high-quality, scalable challenge creation, bridging formal verification with large-scale model evaluation. The pipeline allows controlled variation of complexity via operators and event counts, enabling detailed performance analysis and failure mode identification, which was previously difficult with manual or rule-based datasets.
Methodology
- �� Generate random directed graphs representing event sequences, with nodes as events and edges as temporal relations.
- �� Use an improved Zhu (2021) algorithm to synthesize LTL formulas with specified operator counts, incorporating unary (X, F, G) and binary (∧, ∨) operators.
- �� Convert event graphs and formulas into NuSMV code, defining initial states, transitions, and LTL specifications, then verify their correctness.
- �� Translate the event relations and formulas into natural language descriptions, forming the challenge prompts.
- �� Construct the LTLBench dataset with 2000 tasks, varying complexity by adjusting event and operator counts, and evaluate 12 models with five reasoning strategies.
- �� Analyze performance metrics (accuracy) and conduct qualitative error analysis to identify failure modes such as semantic misalignment, context detachment, and error propagation.
Experiments
The evaluation involved 12 models, including GPT series, Qwen, DeepSeek, and others, tested across five reasoning methods: direct prompting, zero-shot CoT, few-shot CoT, self-consistency, and least-to-most. The dataset comprised challenges with fixed and varied complexity levels, manipulating event and operator counts. Metrics focused on accuracy, with detailed analysis of performance fluctuations. Additional ablation studies examined the impact of increasing formula operators and events on model performance. Qualitative analysis involved inspecting reasoning steps, identifying common failure patterns, and understanding the underlying causes of errors, especially in complex formulas. The experimental setup aimed to validate the robustness of the challenge pipeline and the models’ reasoning capabilities under different complexity conditions.
Results
The highest accuracy was achieved by gpt-4o with few-shot CoT at 93.95%, while GPT-3.5-Turbo with least-to-most scored 51.05%. Across models, few-shot CoT consistently outperformed other methods, with an average accuracy of 76.33%. Increasing formula operators and event numbers caused performance fluctuations, but few-shot CoT remained relatively stable, indicating robustness. Qualitative analysis revealed three main failure issues: temporal semantics misalignment, context hypothesis detachment, and reasoning error amplification. These issues were more pronounced as task complexity increased, highlighting the need for models to better understand and manage complex logical structures in temporal reasoning.
Abstract
Temporal Reasoning (TR) is a critical ability for LLMs to understand and reason over temporal information and relationships between events. To study the TR ability in LLMs, prior works provide different ways for evaluating various aspects of TR ability. In this work, we propose an alternative perspective for evaluating TR ability by leveraging Linear Temporal Logic (LTL), and develop a pipeline to automatically synthesize challenges for assessing the TR ability of LLMs. Based on this pipeline, we construct a dataset, namely LTLBench, consisting of $2000$ TR challenges, and benchmark 12 LLMs across 5 different methods. Furthermore, we conduct additional experiments to investigate the impact of increasing the number of formula operators and events on both LLM performance and the complexity of TR problems. We also perform qualitative analyses of their reasoning processes and the effects of varying the number of events and formula operators, which reveal 3 main issues in their temporal reasoning processes and the unexpected performance changes observed as problem complexity increases. We expect this work to provide valuable insights into the TR ability of LLMs.