Kinship is a fundamental feature and basis of human societies. We describe a set of computational tools and services, and the logic that underlies these, 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 their logical consistency and implications. Not surprisingly, kinship terminologies are particularly amenable to formal representation. Researchers throughout the history of kinship studies have noted the logicality of kinship terminology systems. The logic is explored here through the kin term computations made by use...