Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical reasoning and critical for practical LLM agents and decision-making systems. However, evaluating LLMs as effective rule-based executors and planners remains underexplored. In this paper, we introduce LogicGame, a novel benchmark designed to evaluate the comprehensive rule understanding, execution, and planning capabilities of LLMs. Unlike traditional benchmarks, LogicGame provides diverse games that contain a series of rules with an initial state, requiring models to comprehend and apply predefined regulations to solve problems. We create simulated scenarios in which models execute or plan operations to achieve specific outcomes. These game scenarios are specifically designed to distinguish logical reasoning from mere knowledge by relying exclusively on predefined rules. This separation allows for a pure assessment of rule-based reasoning capabilities. The evaluation considers not only final outcomes but also intermediate steps, providing a comprehensive assessment of model performance. Moreover, these intermediate steps are deterministic and can be automatically verified. LogicGame defines game scenarios with varying difficulty levels, from simple rule applications to complex reasoning chains, in order to offer a precise evaluation of model performance on rule understanding and multi-step execution. Utilizing LogicGame, we test various LLMs and identify notable shortcomings in their rule-based logical reasoning abilities.

Negation is a fundamental linguistic phenomenon that can entirely reverse the meaning of a sentence. As vision language models (VLMs) continue to advance and are deployed in high-stakes applications, assessing their ability to comprehend negation becomes essential. To address this, we introduce NegVQA, a visual question answering (VQA) benchmark consisting of 7,379 two-choice questions covering diverse negation scenarios and image-question distributions. We construct NegVQA by leveraging large language models to generate negated versions of questions from existing VQA datasets. Evaluating 20 state-of-the-art VLMs across seven model families, we find that these models struggle significantly with negation, exhibiting a substantial performance drop compared to their responses to the original questions. Furthermore, we uncover a U-shaped scaling trend, where increasing model size initially degrades performance on NegVQA before leading to improvements. Our benchmark reveals critical gaps in VLMs’ negation understanding and offers insights into future VLM development. Project page available at https://yuhui-zh15.github.io/NegVQA/.