Kinship Algebra Expert System (KAES)

The KAES program performs three major tasks: (1) building a kin term map, (2) constructing an algebraic model of the kin term map, and (3) mapping the algebraic model into a genealogical space, thereby producing predicted genealogical definitions of kin terms.

Kin Term Map

The KAES program provides the tools to construct a kin term map for a kinship terminology such as the kin term map for the American Kinship Terminology. A kin term map displays the way kin terms, viewed as symbols in a linguistic or mathematical sense, are structurally interconnected.

The connections between kin terms derives from the way kin relations are computed directly from kin terms. The product of two kin terms, K and L, is a kin term M (if any) that would be used by ego for alter 2 when ego properly refers to alter 1 by the kin term K and alter 1 properly refers to alter 2 by the kin term L. For example, for users of the American Kinship Terminology (AKT) if ego refers to a female by the kin term Aunt and she refers to a male by the kin term Son, then ego properly refers to that male by the kin term Cousin and so Cousin is the product of Daughter and Aunt in the AKT.

The kin term product connections in the kin term map are based on a small set of kin terms. These typically are the terms used to refer (at least) to members of ones' family.

In the KAES program the kin term map may be constructed directly as a graph, or it may be constructed in a table format (a Cayley Table) with the rows labeled by the kin terms of the terminology and the columns labeled by the terms used in constructing kin term products. A table entry is the kin term that arises (if any) when a product is taken of a row kin term with a column kin term.

The KAES program automatically links the graph and the table so that one can work interactively with the graph and the table.

Algebraic Model

The kin term map becomes the input for the algebraic modeling. The modeling proceeds by first reducing the kin term map to a simple form, then constructing a base model for the simplified form of the kin term map, and lastly expanding the base model by reversing the steps used to simplify the kin term map. The goal of the modeling is to construct an algebraic model (e.g., an algebraic model for the AKT) whose structural form is isomorphic to the structural form of the kinship terminology as expressed in a kin term map. The steps used in the production of the algebraic model then become the basis for viewing the kin term map as a structure that can be generated from a few, core concepts that give the kinship terminology its particular characteristics.

The algebraic construction is based on a theory about the nature of kinship terminology structures. The theory asserts that a kinship terminology structure may be generated using the following 5 steps:

1. construct a structure of ascending terms, all with the same sec marking (male, female or neutral),
2. construct an isomorphic structure of descending terms that will be reciprocals of the terms in the ascending structure, and combine the ascending structure and the descending structure into a single structure of terms all with the same sex marking,
3. introduce both male and female marked terms by either (A) introducing an isomorphic structure of terms with the opposite sex marking when the structure in (2) consists of male marked terms or of female marked terms, or (B) by bifurcating the terms in (2) into male marked and female marked terms when the terms in (2) are all marked as neutral,
4. introduce affinal terms, and
5. introduce rules for locally modifying the structure in (4) (for example, the rules for the Cousin terms in the AKT).

Genealogical Instantiation of the Algebraic Structure

The third part of the KAES program links an algebraic structure isomorphic to sets of genealogical kin types by first mapping the generating elements in the algebra to kin types and then mapping algebraic products to sets of kin types in accordance with the algebraic structure. This yields a mapping of the algebraic structure onto the genealogical space. When the algebraic structure is also isomorphic to the kin term map, the isomorphism between the algebraic structure and the kin term map, in conjunction with the mapping of the algebraic structure into a genealogical space, produces predicted genealogical definitions for all of the kin terms in the kinship terminology. For all terminologies considered to date (e.g., the American Kinship Terminology) the prediction is 100% accurate, a level of accuracy in prediction normally associated only with the hard sciences!

The ability to predict the genealogical definitions of kin terms has far reaching implications for our understanding of kinship terminologies and their relationship to how kin are culturally identified, in particular, and to the notion of culturally constructed conceptual systems, in general.