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 these tasks are intractable in general, that they remain intractable when the number of input tuples is bounded, and that they become solvable in polynomial time when the descriptions of the entities are small as well. The bounds we establish are tight. This enables local, incremental navigation of expansion graphs, supporting practical applications without requiring full graph construction.

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