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The claim that extant terminologies are optimal solutions in a space of all possible terminologies depends on invalidly assuming any partition of a set of genealogical relations is a possible kinship terminology. Instead, kinship terminologies have a particular type of logical/formal structure that is generative with categories providing for classification that is reciprocal. As a consequence, all terminologies, extant or hypothetical, are optimal solutions in the sense this term is used in the claim made about kinship terminologies.

Kinship is a fundamental feature and basis of human societies. We describe a set of computational tools and services, the Kinship Algebra Modeler, and the logic that underlies these. These were developed to improve how we understand both the fundamental facts of kinship, and how people use kinship as a resource in their lives. Mathematical formalism applied to cultural concepts is more than an exercise in model building, as it provides a way to represent and explore logical consistency and implications. The logic underlying kinship is explored here through the kin term computations made by users of a terminology when computing the kinship relation one person has to another by referring to a third person for whom each has a kin term relationship. Kinship Algebra Modeler provides a set of tools, services and an architecture to explore kinship terminologies and their properties in an accessible manner.