We propose a calculus for kinship and affinity relationships that generates the classification of Dravidian terminologies proposed by Dumont (1953 and 1958) in the form given to them by Trautmann (1981). This calculus operates on the language D* of words for kinship and affinity, endowed with rules that select amongst the words in D* a sub-set of words in canonical Dravidian form. We prove that these rules generate uniquely the Dravidian structure (as in Trautmann's model B), and we demonstrate that that Trautmann's model B is the correct version of his model A. We discuss the meaning of the anticommutative structure of D*, and finally point to a generalization of the proposed calculus allowing its rules to be seen in the more general Iroquois context.

The goal in constructing this artificial language is not to construct a grammar for a subset of natural languages. In other words, the artificial language of kin terms built by means of symbols B, Z, F, M, S and D is not intended as a grammar that would generate strings having syntactical or phonetic similitude with strings in any natural language, even in the restricted domain of kinship. This would have been a linguistic problem, not a problem in cultural theory. The formal language K* is a means to construct a genealogical space endowed with a very simple structure. The basic hypothesis is that kinship terminologies in natural languages are distinguished in the way they classify the paths in the genealogical space. To describe these actually existing classifications is a task of empirical research. The task of the theory is to construct a theoretically-based classification of the genealogical space that should reproduce the empirically given classification, or some relevant feature of it.