To close the gap between LLM-based agents and humans in planning and reasoning, agents need large-scale, diverse environments for continuous learning—yet building such environments is itself prohibitively expensive. We present C-World, an environment creation system that enables users to build agent environments on demand. We define a complete agent environment through four components: an Action Space of 5,571 format-unified tools across 204 common applications, a Task Distribution engine that synthesizes long-horizon workflows with wild constraints, a Transition Function implemented as a state controller that injects realistic failures and perturbations, and a Reward Signal combining verifiable metrics with LLM-based judgment. C-World operates in two modes: a realistic mode grounded in live API execution, and a synthesized mode powered by the World Engine, which approximates tool behavior without live service access, enabling scalable environment creation—including environments for domains and tools that do not yet exist in the real world. Evaluation of nine state-of-the-art LLMs reveals that planning ability is uniformly strong but execution remains the bottleneck, and that constraint following—not tool invocation—is the dominant failure mode. The World Engine achieves Spearman 𝜌 = 0.883 ranking correlation with real execution, and fine-tuning on just 1,170 C-World trajectories outperforms baselines trained on 119k samples, demonstrating C-World’s dual value as a rigorous evaluation environment and a scalable data engine. Our code and data are available at https://ziqiao-git.github.io/C-World/.

The logical information contained in text isof significant importance for logical reasoning.Previous approaches have relied on embeddingtext into a low-dimensional vector to capturelogical information and perform reasoning inEuclidean space. These methods involve constructing special graph architectures that matchlogical relations or designing data augmentation frameworks by extending texts based onsymbolic logic. However, it presents two obvious problems. 1) The logical informationreflected in the text exhibits uncertainty that isdifficult to represent using a vector. 2) Integrating logical information requires modeling logical operations (such as ∪, ∩, and ¬), while onlysimple arithmetic operations can be performedin Euclidean space. To address both the problems, we propose Beta-LR, a probabilistic embedding method to capture logical information.Specifically, we embed texts into beta distribution on each dimension to eliminate logical uncertainty. We also define neural operators thatenable interpretability and perform logical operations based on the characteristics of the betadistribution. We conduct experiments on twodatasets, ReClor and LogiQA, and our Beta-LRachieves competitive results. The experimentsdemonstrate that our method effectively captures the logical information in text for reasoning purposes. The source code is available athttps://github.com/myz12138/Beta-LR.