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The kin term product calculations used by culture-bearers to compute kin relationships from kin terms without reference to genealogy are the basis for the structure of a kinship terminology and its underlying generative logic. The details of that logic account for differences in the structural forms for kinship terminologies. The structural form of the Polynesian kinship terminologies, like that of other classificatory (i.e., bifurcate merging) terminologies, derives from a structural logic in which a sibling term is a generating element. When a sibling term is a generating element, differences in the patterning of sibling terms arise from different ways in which structural logic for the reciprocity of sibling terms is implemented. These differences in implementation of sibling term reciprocity are used to construct, in analogy with a language tree, a kinship tree based on the different structures for sibling terms in the Polynesian terminologies. The kinship tree has two root structural forms for sibling terms. One structural form matches that for sibling terms in the Anuta, East Futuna, West Futuna, Luangiua, Nanumea, Takuu, Tikopia, and Tuvalu kinship terminologies. The other matches the structural form for sibling terms in the Pukapuka and Pileni terminologies. In contrast, the Proto-Polynesian terminology derived using the methods of historical linguistics has a root structural form for the sibling terms matching that found among the East Polynesian language kinship terminologies. These differences in analytical results are discussed and a possible way to reconcile them is developed.
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