Many kinship terminologies can be modeled as inverse semigroups. This is especially true of Omaha-type kinship systems and is illustrated here with the Fox consanguineal (or “blood”) relatives. The semigroup operation comes not from the composition of relations, but from a more symbolic, or linguistic, operation. For example, a man’s brother’s brother reduces symbolically to his brother, even though in the composition of relations a man’s brother composed with brother would also include the man himself. The semigroup for the Fox system can be further specified to be an inverse semigroup, which is characterized in terms of their idempotent elements and as a web of the even more specific bicyclic semigroups.