ChaosBench-Logic: A Benchmark for Logical and Symbolic Reasoning on Chaotic Dynamical Systems

TL;DR

ChaosBench-Logic is a comprehensive benchmark designed to evaluate large language models' logical and symbolic reasoning capabilities on chaotic dynamical systems, revealing strengths and weaknesses in their reasoning skills.

Contribution

The paper introduces ChaosBench-Logic, a novel benchmark with diverse dynamical systems, annotated logic, and evaluation metrics to assess LLM reasoning in complex scientific domains.

Findings

LLMs achieve 91-94% accuracy on individual items

LLMs score 0% on compositional reasoning tasks

Dialogue accuracy varies from 53.1% to 75.5%

Abstract

Large language models (LLMs) excel at natural language tasks but remain brittle in domains requiring precise logical and symbolic reasoning. Chaotic dynamical systems provide an especially demanding test because chaos is deterministic yet often misinterpreted as randomness or complexity. We introduce ChaosBench-Logic, a benchmark that evaluates LLM reasoning across 30 diverse dynamical systems using a unified first-order logic (FOL) ontology. Each system is annotated with truth assignments for 11 semantic predicates, and 621 questions are generated across seven reasoning categories, including multi-hop implications, cross-system analogies, counterfactual reasoning, bias probes, and multi-turn dialogues. We define metrics for logical accuracy, implication consistency, dialogue coherence, and contradiction, and we release an open-source evaluation pipeline. Initial experiments show that frontier LLMs such as GPT-4, Claude 3.5 Sonnet, Gemini 2.5 Flash, and the open-source LLaMA-3 70B achieve 91-94% per-item accuracy, yet still score 0% on compositional items and exhibit fragile global coherence. Dialogue-level accuracy ranges from 53.1% (GPT-4 CoT) to 75.5% (LLaMA-3 zero-shot). ChaosBench-Logic provides a rigorous testbed for diagnosing such failures and a foundation for developing neuro-symbolic approaches that improve scientific reasoning in LLMs.