Kinship systems and inverse semigroups

Abstract

Inverse semigroups are introduced as a model for kinship structures. It is shown that semigroups are implied by the traditional anthropological law of uniform descent, and that inverses are suggested by the principle of reciprocity. A separation into a ‘surface’ and a ‘deep’ level of analysis was induced by viewing a kinship system as a partition on an underlying inverse semigroup. Some Omaha‐type kinship systems are decomposed into direct and semidirect products. Additional assumptions are made to deiive a theoretical similarity measure, which is then compared with a judged similarity task on Tenejapan Indians. The results of this preliminary experiment seem to be encouraging.