This article supplements the previously published object theory, which established multigenerational kinship composition information as the substantive content of genealogical documents, by addressing the formal definition of keizu and keifu—a dimension systematically neglected in prior scholarship. A comprehensive examination of existing definitions reveals that virtually all prior research suffers from critical deficiencies: conflation of the two terms as synonyms, circular definitions that collapse into tautologies or contradictions upon substitution, and the absence of any formal criteria distinguishing one term from the other. 　In response, this article proposes original formal definitions grounded not in the presence or absence of genealogical lines but in the mode of expressing kinship relations: whether non-linguistic (diagrammatic) or linguistic. Accordingly, keizu is defined as a document (including digital data) in which the principal kinship relations are expressed non-linguistically through diagrammatic means, while keifu is defined as an oral or written record (including digital data) in which kinship relations are expressed exclusively through language. Integrating these formal definitions with the previously established substantive definition, the article fixes both concepts as academic terms within Genealogical Science, and introduces an operational principle—modeled on analogous usage in Japanese administrative law—to address cases where a document's title diverges from its formal characteristics.

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