ASPIRE is a general-purpose neural inference model for semantic inference and prediction on heterogeneous structured data. To address the challenges of real-world data, which often presents in diverse and disjoint forms with diverse schemas, inconsistent semantics, and no fixed feature order, it combines a permutation-invariant set-based transformer with a semantic module that learns feature dependencies across datasets by integrating natural language descriptions, dataset metadata, and contextual examples. It accepts an arbitrary set of feature-value pairs and supporting examples, aligns the meaning between disjoint tables, and makes predictions for a given target. After training, it generalizes to new inference tasks without further tuning. It not only delivers robust results across a variety of benchmarks but also naturally supports cost-conscious active feature acquisition in open-world environments, selecting beneficial features under test-time budget constraints on arbitrary, unseen datasets.