Recognizing similarities among entities is central to both human cognition and computational intelligence. Within this broader landscape, Entity Set Expansion is one prominent task aimed at taking an initial set of (tuples of) entities and identifying additional ones that share relevant semantic properties with the former -- potentially repeating the process to form increasingly broader sets. However, this ``linear'' approach does not unveil the richer ``taxonomic'' structures present in knowledge resources. A recent logic-based framework introduces the notion of an expansion graph: a rooted directed acyclic graph where each node represents a semantic generalization labeled by a logical formula, and edges encode strict semantic inclusion. This structure supports taxonomic expansions of entity sets driven by knowledge bases. Yet, the potentially large size of such graphs may make full materialization impractical in real-world scenarios. To overcome this, we formalize reasoning tasks that check whether two tuples belong to comparable, incomparable, or the same nodes in the graph. Our results show that, under realistic assumptions -- such as bounding the input or limiting entity descriptions -- these tasks can be implemented efficiently. This enables local, incremental navigation of expansion graphs, supporting practical applications without requiring full graph construction.

翻译：识别实体间的相似性是人类认知与计算智能的核心任务。在此背景下，实体集扩展是一项重要任务，其目标是以初始的（多元组）实体集为基础，识别出与前者共享相关语义属性的更多实体——该过程可重复进行以形成更广泛的集合。然而，这种“线性”方法无法揭示知识资源中更丰富的“分类”结构。近期一种基于逻辑的框架提出了扩展图的概念：这是一种有根有向无环图，其中每个节点代表由逻辑公式标注的语义泛化，边则编码严格的语义包含关系。该结构支持基于知识库的实体集分类扩展。然而，此类图可能规模庞大，在实际场景中完全物化可能不切实际。为解决此问题，我们形式化了若干推理任务，用于检测两个多元组是否属于图中可比较、不可比较或相同的节点。研究结果表明，在现实假设下——例如限制输入规模或约束实体描述——这些任务可被高效实现。这使得扩展图能够进行局部增量式导航，在无需构建完整图结构的前提下支持实际应用。