The computer program Kinship Algebra Expert System (KAES) provides a graphically based framework for constructing, if possible, a generative algebraic model for the structure of a kinship terminology (the terms used to refer to one's kin). The algebraic modeling is based on a theory of kinship terminologies elaborated through writing the software program. The theory relates the properties and structure of kinship terminologies to an underlying logic that the KAES program helps uncover and model as a generative structure. The program then relates the structural logic of a kinship terminology modeled by the KAES program to a genealogical space based on genealogical tracing of kin relations. The KAES program demonstrates the surprisingly logical character of kinship terminologies and challenges the received view of the primacy of genealogical relations in defining cultural kinship through showing how genealogical definitions of kin terms can be accurately predicted in the terminologies considered to date.T he computer program, Kinship Algebra Expert System (KAES), is a graphical user interface application for investigating and modeling the structure of kinship terminologies and the ways in which these are instantiated (for further information and for downloading a copy of the application program, see Read & Fischer, 2005). It is based on a theory of kinship terminology structures elaborated through writing the KAES program. The program is an example of how a theory can be approached and evidence evaluated with respect to that theory to produce results that identify a future research trajectory rather than simply accounting for relations in a body of data. The results of research based on KAES will have far-reaching consequences for many other domains in the social sciences.The focus on kinship terminologies may strike many readers as a rather specialized and narrow application, especially following more than a decade in which the study of kinship has diminished in the curricula of major anthropology programs, only to be replaced by courses on gender and new reproductive technologies. However, KAES successfully implements a theory of kinship terminology structures that is fundamental to our understanding of the kinship basis through which a newborn person initially obtains social identity crucial throughout his or her life. In addition, by providing a fully worked out theory and model of one culturally constructed symbolic system (symbolic in the linguistic or mathematical and 43