# Wiki source code of KAM - Kinship Algebra Modeller

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1 | [[image:KAESLogo|| style="float: right;margin-left:10px""]] | ||

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3 | {{box cssClass="floatinginfobox" title="**Contents**" width="330px"}} | ||

4 | {{toc start="2"/}} | ||

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7 | **Kinship** provides a link between biologically constituted and culturally constituted societies. Although we argue that kinship terminologies may well interface biology and culture, using formal and computational methods we refute the assumption that kinship is based on genealogical definitions of kin terms as the primitives of kinship systems. Rather, genealogical definitions of kin terms are entirely predictable when the kinship terminology is viewed instead as a system of cultural symbols. | ||

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9 | Kinship terminologies have an underlying logic that makes it possible for a terminology to be commonly shared among culture bearers despite imperfect learning and imperfect transmission of “kinship knowledge”. Though there has been over a century of intensive study of kinship systems and marriage rules, this work has not adequately addressed the nature and form of the underlying conceptual/cultural constructs that underlie the way cultural kinship constructs the other as having a symbolically defined relationship to self. | ||

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11 | The Kinship Algebra Modeller (KAM), helps to demonstrate this. KAM is a suite of computer programs, including the Kinship Algebra Expert System (KAES) that begins with informant information about relationships among kin terms and produces an underlying grammar for the kin terms as a system. We will further present results from a multi-agent simulation models to indicate an account for why kinship terminologies might tend to be describable by algebras, and why the resulting algebras are similar, even for apparently quite different kinship terminologies. We will also present some implications of these results for understanding the origins and propagation of human culture. | ||

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13 | (% style="color: rgb(0, 0, 0); font-family: Times; font-style: normal; line-height: normal; text-align: start;" %) | ||

14 | == Kinship Algebra Expert System (KAES) == | ||

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16 | (% style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; line-height: normal; text-align: start;" %) | ||

17 | 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. | ||

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20 | (% style="color: rgb(0, 0, 0); font-family: Times; font-style: normal; line-height: normal; text-align: start;" %) | ||

21 | === Kin Term Map === | ||

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23 | (% style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; line-height: normal; text-align: start;" %) | ||

24 | 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>>url:http://kaes.anthrosciences.net/akt.jpg]]. A kin term map displays the way kin terms, viewed as symbols in a linguistic or mathematical sense, are structurally interconnected. | ||

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26 | (% style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; line-height: normal; text-align: start;" %) | ||

27 | 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. | ||

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30 | 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. | ||

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33 | 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. | ||

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

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38 | (% style="color: rgb(0, 0, 0); font-family: Times; font-style: normal; line-height: normal; text-align: start;" %) | ||

39 | === Algebraic Model === | ||

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42 | 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>>url:http://kaes.anthrosciences.net/algebra.jpg]]) 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. | ||

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45 | The algebraic construction is based on a [[theory about the nature of kinship terminology structures>>url:http://kaes.anthrosciences.net/csac/SASci/kaes.tabs/Theory]]. The theory asserts that a kinship terminology structure may be generated using the following 5 steps: | ||

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48 | 1. construct a structure of ascending terms, all with the same sec marking (male, female or neutral), | ||

49 | 1. 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, | ||

50 | 1. 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, | ||

51 | 1. introduce affinal terms, and | ||

52 | 1. introduce rules for locally modifying the structure in (4) (for example, the rules for the Cousin terms in the AKT). | ||

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55 | === Genealogical Instantiation of the Algebraic Structure === | ||

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58 | 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>>url:http://kaes.anthrosciences.net/akt_gen.jpg]]) the prediction is 100% accurate, a level of accuracy in prediction normally associated only with the hard sciences! | ||

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62 | 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. | ||

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65 | (% style="font-size:1.2em;" %)**Kinship and Kinship Terminologies** | ||

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68 | Unraveling what constitutes kinship in human societies has been a central theme in anthropological theorizing ever since the publication by Lewis Henry Morgan of //Systems of Consanguinity and Affinity of the Human Family// in 1871. | ||

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71 | Early anthropologists became interested not only because of the appaent central role of kinship relationships in societies, but also because of the apparent commonalities between societies in the way they organised kin. Russ Bernard (2006) notes: | ||

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73 | (% cite="http://kaes.anthrosciences.net/csac/SASci/kaes.tabs/Bernard%202006%20p300." style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; text-align: start;" %) | ||

74 | >In his work with the Murray Islanders (in the Torres Straits between Australia and Papua New Guinea) and then later with the Todas of southern India, W.H.R. Rivers developed the genealogical method - those ego-centered graphs for organizing kinship data that we take for granted today - as a way to elicit accurately and systematically the inventory of kin terms in a language (Rivers 1906, 1910, 1968 [1914]; and see Rivers's work in Volume VI of Haddon 1901-1935). | ||

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76 | (% cite="http://kaes.anthrosciences.net/csac/SASci/kaes.tabs/Bernard%202006%20p300." style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; text-align: start;" %) | ||

77 | >Anthropologists also noticed very early that, although kinship systems could be unique to each culture - which would mean that each system required a separate set of rules - they simply weren't. Alfred Kroeber showed in 1909 that just eight features were needed to distinguish kinship terms in any system: (1) whether the speaker and the kin referred to were of the same or different generations; (2) the relative age people who are of the same generation - older or younger brother, for example; (3) whether the person referred to is a collateral or a lineal relative; (4) whether the person referred to is an affinal or consanguineal relative; (5) whether the relative is male or female; (6) whether the speaker is male or female; (7) whether the person who links the speaker and the relative is male or female; and (8) whether the person who links the speaker and the relative is alive or dead. | ||

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79 | (% cite="http://kaes.anthrosciences.net/csac/SASci/kaes.tabs/Bernard%202006%20p300." style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; text-align: start;" %) | ||

80 | >Now, if you first choose whether to use or not use any of those eight features and then choose among the two alternatives to each feature, you can concoct 3^^8^^6,561 kinds of kinship systems. But, while there are some rare exceptions (the bilineal Yakö of Nigeria, the ambilineal Gilbert Islanders), most of the world's kinship systems are of one those familiar types you studied in Anthropology 101 - the Hawaiian, Sudanese, Omaha, Eskimo, Crow, and Iroquois types. Early anthropologists found it pretty interesting that the world's real kinship systems comprised just a tiny set of the possibilities. Ever since the work of Morgan and Kroeber and Rivers, a small, hardy band of anthropologists has tried to determine if these systems are associated with particular political, economic, or environmental conditions (Leach 1945; Alexander 1976; Lehman 1992; Houseman and White 1998; Kronenfeld 2004). | ||

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83 | >This interest in classifying kinship systems led to methods for discovering sets of terms in other domains, like kinds of foods, things to do on the week- end, kinds of crime, bad names for ethnic groups, dirty words, names for illnesses, etc. Note that none of these is about people's preferences. Asking people people to tell you "which animals do you think make good pets" is very different from asking them to "list animals that people here keep as pets" (Borgatti 1999:117). | ||

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85 | (% style="text-align:right" %) | ||

86 | ((( | ||

87 | [[Bernard 2006>>url:http://www.amazon.com/gp/product/0759108692/qid=1149741818/sr=1-1/ref=sr_1_1/002-5843225-7994446?s=books&v=glance&n=283155||target="_blank"]] p300 - //Research Methods in Anthropology// 4^^th^^ edition. AltaMira Press. | ||

88 | ))) | ||

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91 | === Kinship Terminologies === | ||

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94 | All societies have a means for identifying or labeling some set of relationships between an individual and other individuals that is expressed linguistically through a set of terms known as a //kinship terminology// . | ||

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97 | Kinship terminologies often cannot be fully translated from one language into another as the relationships that are recognized in one society may not have an exact counterpart among the relationships recognized in another society. (//American Kinship Terminology versus Shipibo Kinship Terminology// ) | ||

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100 | The basis for the differences in the relationships that are recognized by different societies has been a source of contention in anthropological theorizing. Equally problematic has been identification of the basis for the particular relationships recognized within a given society. | ||

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103 | At one extreme is the presumption that the relationships linguistically identified through a kinship term are essentially biological in origin. | ||

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106 | A more middle-of-the-ground viewpoint has assumed that the kin terms are based on biological relationships but are given cultural expression that may deviate from their biological grounding. From this perspective kin terms are viewed as linguistic labels identifying the classification that the members of a society make of a genealogical space grounded in marriage and procreation. | ||

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109 | A third perspective, and the one underlying the KAES program, considers the kin terms to constitute a system of interconnected concepts, expressed through the kin terms and the conceptual interconnections among the kin terms. Structural properties arise, in this perspective, through the logic by which the structure is generated from a few primitive concepts. Thus a kinship terminology is a symbolic system that cannot be fully understood without reference to the way the system is generated as a conceptual construct. | ||

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112 | The differences among these three perspectives biological, genealogical and cultural are subject to verification and falsification as each perspective has quite different implications for the relations between persons that are identified via the kin terms making up a kinship terminology. | ||

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115 | The biological perspective implies that these relations should bear a close resemblance to the actual biological relatedness of individuals. | ||

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118 | The genealogical perspective implies that a terminology can only be understood through the criteria used to classify the possible genealogical relations between pairs of individuals. | ||

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121 | The cultural perspective implies that the terminology will have a structure whose features can be constructed or generated from a few, fundamental symbols and concepts along with a general process for the production of the structure for a kinship terminology. | ||

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124 | In brief, the biological perspective implies that the structure of a kinship terminology and its usage cannot be understood without reference to the biological relatedness of pairs of individuals. | ||

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127 | The genealogical perspective implies that the structure of a terminology should reflect the criteria by which a classification of a genealogical space is formulated. | ||

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130 | The cultural perspective implies that a kinship terminology should be a logically consistent structure, hence its features should be highly predictable from the logic of how the structure may be generated. | ||

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133 | Neither the biological perspective nor the genealogical perspective imply that kinship terminologies should be highly logical in terms of how they constitute a symbolic system. | ||

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136 | (% style="font-size:1.2em;" %)**Kinship Terminology Logic** | ||

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139 | The KAES program is designed to explore the logic underlying the way the kinship terms form a structured system of symbols (with symbols taken in a linguistic and mathematical sense). | ||

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142 | **//Kin Term Product//** | ||

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145 | The KAES program is based on the common ethnographic observation that individuals usually determine kin relations neither by identifying their biological pedigree nor their genealogical connectedness but by doing computations with kin terms. As the anthropologist Marshall Sahlins has noted with regard to Moala kinship: | ||

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147 | (% style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; text-align: start;" %) | ||

148 | >"… [kin] terms permit comparative strangers to fix kinship rapidly without the necessity of elaborate genealogical reckoning //reckoning that typically would be impossible// . With mutual relationship terms all that is required is the discovery of one common relative. Thus, if A is related to B as child to mother, //veitanani// , while C is related to B as //veitacini// , sibling of the same sex, then it follows that A is related to C as child to mother although they never before met or knew it.//Kin terms are predictable. If two people are each related to a third, then they are related to each other// " (Marshall Sahlins, 1962, //Moala: Culture and Nature on a Fijian Island// . Prentice-Hall, Englewood Cliffs, p. 155, emphasis added). | ||

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151 | Based on ethnographic observations similar to Sahlins comment about Moala kinship, we may define a kin term product informally as follows. Suppose one person (ego) properly refers to a second person (alter 1) by the kin term K, and alter 1 properly refers to a third person (alter 2) by the kin term L. The product of the kin terms K and L will be the kin term, M, if any, that ego properly uses for alter 2. | ||

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154 | For example, and with respect to the American/English Kinship Terminology (AKT), when ego refers to alter 1 by the kin term Aunt and alter 1 refers to alter 2 by the kin term Daughter, then ego (properly) uses the kin term Cousin to refer to alter 2. So the __product__ of the kin terms Daughter and Mother is the kin term Cousin in the AKT. | ||

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157 | We need to make a clear distinction here between //kin types// and //kin type products// , which have to do with genealogical relations, and //kin terms// and //kin term products// , which have to do with the conceptual system we refer to as a kinship terminology and the structure formed from relations linking kin terms via kin term products. Kin term products express the way in which the kin terms (viewed as linguistic symbols) form a system of symbols. In contrast, kin type products have to do with the way in which a genealogical relation can be constructed through concatenation of pairs of genealogical relations. | ||

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160 | More formally, we define a kin term products as follows: | ||

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162 | (% style="color: rgb(0, 0, 0); font-family: Times; font-size: medium; font-style: normal; text-align: start;" %) | ||

163 | >//Definition// : Let //K// and //L// be kin terms in a given kinship terminology, **T** . Let ego, alter1 and alter2 refer to three arbitrary persons each of whose cultural repertoire includes the kinship terminology, **T.** The kin term product of //K// and //L// , denoted //K o L// , is a kin term, //M// , if any, that ego may (properly) use to refer to alter2 when ego (properly) uses the kin term //L// to refer to alter1 and alter2 (properly) uses the kin term //K// to refer to alter2. | ||

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166 | **//Kin Term Map//** | ||

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169 | Kin term products are the basis upon which the analysis of a kinship terminology structure proceeds. One part of the KAES program deals with representing the structure of a kinship terminology based on kin term products. A diagram displaying the structure for kin terms based on kin term products is called a //kin term map// and is the beginning point for the analysis of the structure of a kinship terminology. (__Kin term map for the AKT__ ) | ||

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172 | **//Generating Terms//** | ||

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175 | Although the kin term product is defined for any pair of kin terms, we quickly discover that certain kin terms play a central role in constructing a kin term map. For the AKT these are terms such as Mother, Father, and Parent and their reciprocals, Daughter, Son and Child. | ||

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178 | Other kin terms in the AKT can be constructed by taking products of these kin terms. For example, the kin term Grandfather = Father o Parent ( read: Grandfather is Father of Parent, or more completely, the kin term Grandfather is the result of taking the kin term product of the kin term Father with the kin term Parent), where this is a statement about the three symbols, Grandfather, Father and Parent. (The symbol o between Father and Parent indicates that we have a binary product (namely the kin term product) that maps a pair of symbols (in this instance, the Father, Parent pair) to another symbol (in this instance, to the symbol Grandfather).) | ||

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181 | Though this equation may look like a genealogical statement, nothing could be further from the meaning of this equation. The equation states that when ego properly refers to a person as Parent (and regardless of the actual genealogical connection, if any, between the two persons) and that person properly refers to a third person as Father (again, regardless of the actual genealogical connection between them, if any) then ego would properly refer to that third person by the kin term Grandfather (again, regardless of the actual genealogical relationship between them). Some of the persons in question might be adopted and so the actual genealogical relations that are involved are unknown; nonetheless the users of the AKT still know the proper usage of the terminology in cases of adoption by virtue of the conceptual relations that hold among the kin terms. | ||

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184 | (% style="font-size:1.2em;" %)**Criteria for Generating Terms** | ||

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187 | The kin term map is constructed by first deciding on the kin terms that will serve as the generating terms through which kin terms are linked to one another. The generating terms must account for the closest kin term linkages between a person and another person and so they will likely be some variant on the kin terms that can be transliterated as Mother, Father, (and possibly Parent) and their reciprocals, Daughter, Son, (and possibly Child). In addition terms that can be transliterated as Brother or Sister (or possible Older Brother, Younger Brother, etc.) will be generating terms in some terminologies but not in other terminologies. | ||

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190 | **//Kin Term Map as a Generated Structure//** | ||

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193 | The kin term map, even without any analysis, serves as an effective, graphical device for displaying the structural differences among kinship terminologies. Each terminology has its own structural form (or variant on a structural form for closely related terminologies) that expresses differences in the ways in which the kin terms of a terminology form a structure. | ||

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196 | The kin term map is more than just an effective, descriptive means to display the conceptual structure formed by the kin terms in a kinship terminology. An obvious question is whether the map can be generated from a few, simple structural properties and if so, does this account for the features of the terminology (such as the odd way in which the Aunt and Uncle terms in the AKT are used both for individuals linked genealogically to ego and for individuals who are linked to ego only through marriage). If the kin term map is the graph of a generative structure, then it follows that a kinship terminology is neither simply a representation of biological kin relations nor a classification of a genealogical space by criteria that lie outside of the kinship terminology. Instead, the kinship terminology is a cultural construct and the meaning of kin terms cannot be fully understood without reference to that construct and the logic underlying how it is generated. | ||

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199 | **//Generating Terms: Descriptive versus Classificatory Terminologies//** | ||

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202 | One of the key discoveries about terminology structures that has been obtained to date relates to the distinction Lewis Henry Morgan made between what he called Descriptive Terminologies versus Classificatory Terminologies (and despite the considerable debate about the validity of the distinction within anthropological theorizing about kinship terminological systems) relates to whether or not the Sibling kin terms are generating kin terms or are constructed from other kin terms. In the AKT, for example, the kin term Brother is constructed via Brother = Son of Parent (which can also be expressed via the two equations Brother = Son of Father or Brother = Son of Mother). The kin term map for the AKT is not consistent with a claim that the Sibling terms are generating terms for the terminology. | ||

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205 | In contrast, classificatory terminologies such as the Trobriand terminology or the Tongan terminology are found to be terminologies for which Sibling terms are generating terms. The analysis of the structure of these terminologies demonstrates that the kind of genealogical equations that have been used to define classificatory terminologies, namely f = fb and m = mz are a consequence of the structural implications that arise from including the Sibling kin terms among the generating terms for the terminology. | ||

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208 | (% style="font-size:1.2em;" %)**Algebraic Model for a Kin Term Map** | ||

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211 | The algebra part of Kinship Algebra Expert System refers to the use of algebraic concepts to model the structure of a kinship terminology as displayed through a kin term map. By //algebraic structure// is meant the structure that is formed when one has a set of symbols (for example, the kin terms making up a terminology), a binary product defined for all pairs of symbols in that set (for example, the kin term product for kin terms), including whether the binary product is associative (e.g., for the binary operation, +, the sum a + (b + c) is the same as the sum (a + b) + c; for kin terms the product K o (L o M) = (K o L) o M) or commutative (e.g., for the binary number operation, +, a + b = b + a; however, commutativity does not hold, for many kin term products; e.g. Son of Father is not the same as Father of Son) and certain equations that the binary product must satisfy. The equations give an algebra its particular structural form. | ||

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214 | For kinship terminologies we have the following basic algebraic machinery: | ||

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217 | 1. we have a set of symbols the terms making up the kinship terminology | ||

218 | 1. we have a binary product defined over those symbols the kin term product, including 0 as a symbol indicating that the product does not yield a kin term; e.g., Father o Father-in-law = 0 in the AKT since there is no kin term representing the product Father o Father-in-law | ||

219 | 1. the binary product is associative the kin term product is associative, except in certain special cases that are dealt with in the analysis on an individual basis. | ||

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222 | An algebraic system satisfying (1) (3) is known in the mathematical literature as a semigroup. | ||

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225 | The equations that are used when modeling a kinship terminology are used to introduce structural properties that characterize kin terms. These properties refer to kinds of kin terms such as: (1) a Sibling kin term, S, where S o S = S, (2) a Spouse kin term, Sp, where Sp o Sp = Self (with Self a symbol representing the concept of self, a concept fundamental to any kinship terminology), and so on. The equations also express relations between kin terms such as reciprocity of kin terms, where L is the reciprocal term for K implies that either K o L = Self or L o K = Self, or properties such as Spouse of Parent = Parent in the AKT, and so on. These structural equations are generated automatically by the KAES program as the analysis progresses. | ||

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228 | (% style="font-size:1.2em;" %)**General Model for the Structure of a Kinship Terminology** | ||

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231 | The following is a hypothesized, general process by which a kinship terminology is generated. | ||

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234 | 1. A //structure of ascending kin terms// , all with the same sex marking, is constructed based on an ascending generating term such as Mother if the terms are to be marked female, Father if the terms are to be marked male, and Parent if the terms are to be neutral. Included in this ascending structure is an identity term that be designated Male Self, Female Self or Self, depending on whether the ascending terms are marked male, female or are neutral. By an identity term is meant a term I such that for any kin term __K, K o I = I o K = K__ . The identity term will be designated by the symbol Self (with or without a sex marker) on the grounds that a concept of self is both universal and necessary for there to be a kinship terminology; that is, all terminologies must make a distinction between self and other, whether or not there is a linguistic symbol representing the concept self in the kinship terminology. | ||

235 | 1. A structure of descending kin terms is constructed from the structure of ascending kin terms by making an isomorphic copy of the ascending kin term structure and then a //larger algebraic structure// made up of both ascending kin terms and descending kin terms and cross products between ascending and descending kin terms is formed. Included here is the structural equation that makes an ascending kin term call it P and its isomorphic kin term call it C into reciprocal kin terms, namely, __P o C = Self__ . | ||

236 | 1. Terms with the other sex marking, or bifurcation of neutral kin terms into male marked and female marked kin terms, occurs next. (A) When the kin terms constructed in steps (1) and (2) are already sex marked, then terms of the opposite sex are constructed by taking an isomorphic copy of the structure generated in steps (1) and (2). The isomorphic copy will be a structure of kin terms with the opposite sex. The original structure and this isomorphic structure are combined together, along with appropriate structural equations, to make a new, larger structure consisting of terms marked with both sexes. (B) When the kin terms constructed in steps (1) and (2) are all marked neutral, then each kin term is bifurcated into two kin terms marked as male and female terms. Appropriate structural equations that relate male kin term and female kin term products are introduced as appropriate. | ||

237 | 1. Affinal kin terms are introduced next, along with appropriate equations that express the properties of affinal kin terms. | ||

238 | 1. Rules are identified that refer to ways that portions of the overall structure are locally modified. For example, in the AKT not all kin terms are marked as either male terms or female terms according to the Sex Marking Rule: A kin term, K, is marked neutral when the product of K with a spouse term is not a kin term. Another rule in the AKT identifies the way in which Cousin kin terms may be further distinguished according to properties such as ith Cousin or ith Cousin j-times Removed. These rules relate to ways in which the //overall structure// is modified for cultural reasons and are not modifications necessary for a terminology to have the structure of a kinship terminology. | ||

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241 | (% style="font-size:1.2em;" %)**Criterion for the Validity of a Structural Model** | ||

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244 | An algebraic model for a kinship terminology is a valid model for that terminology if, and only if, the algebraic model is isomorphic to the kin term map representation of the kinship terminology. Not all conceivable kin term maps can be validly represented by an algebraic model. //Success in formulating a valid algebraic model for a kinship terminology// identifies the basis by which the terminology structure can be logically generated in accordance with the general model for the construction of a kinship terminology. | ||

245 | |||

246 | |||

247 | Properties of the algebraic model are properties that arise from the logic of how a kinship terminology can be generated and do not require reference to properties outside of the terminology for their existence. For example, the algebraic model that validly represents the AKT has the property that Spouse o Aunt = Uncle and Spouse o Uncle = Aunt, hence the lack of terms marked with the suffix -in-law such as Aunt-in-law or Uncle-in-law is a consequence of the logic underlying the generation of the AKT as a kinship terminology structure. | ||

248 | |||

249 | |||

250 | Rules that are introduced in Step 5 identify structural properties that are not necessary for the structure to have the structural form of a kinship terminology, hence they are properties that may have been introduced for reasons extrinsic to the terminology structure, per se. | ||

251 | |||

252 | |||

253 | In other words, the analysis distinguishes between properties of the terminological structure that are necessary for the structure to be complete and consistent as a kinship terminology structure and properties that are parts of the terminology but are not necessary for its completeness and consistency, hence are likely to have origin for reasons extrinsic to the generative logic of the kinship terminology structure. | ||

254 | |||

255 | |||

256 | (% style="font-size:1.2em;" %)**Instantiation of the Symbolic Structure** | ||

257 | |||

258 | |||

259 | The algebraic model of a kinship terminology structure consists of abstract symbols and the relations among these symbols as determined by equations and other properties guiding the generation of the symbolic structure. These abstract symbols are //culturally instantiated// in terms of the individuals to whom the symbols may be properly refer when using the kinship terminology to identify kin relationships between individuals. A primary instantiation is through genealogical concepts and is obtained by identifying the instantiation of the generation terms in the algebraic structure. The generating terms are instantiated using kin types underlying the construction of a genealogical space. A male marked kin term used in the construction of the ascending structure is instantiated with the kin type, father; more precisely, with genealogical father. The reciprocal male marked kin term in the descending structure is instantiated with the kin type, genealogical son, and so on. | ||

260 | |||

261 | |||

262 | **//Predicted Genealogical Definitions of Kin Terms//** | ||

263 | |||

264 | |||

265 | Once the generating terms have been instantiated with genealogical kin types, then the instantiation of all other terms can be worked out from the instantiation of the generating kin terms and the algebraic structure by identifying algebraic products with products of sets of kin types. For example, Grandfather has the instantiation {genealogical father} x {genealogical father} = {genealogical fathers father} since Grandfather = Father o Father and Father has the instantiation {genealogical father}. | ||

266 | |||

267 | |||

268 | This process of instantiation of the generating terms and construction of the instantiation of all other kin terms based on the algebraic structure leads to a predicted set of genealogical definitions of kin terms. | ||

269 | |||

270 | |||

271 | For all terminologies considered to date, the predicted genealogical definitions match with 100% accuracy the genealogical definitions elicited by anthropologists using the perspective that the genealogical definitions are the primary data for the analysis of kinship terminologies. (//Predicted AKT Kin Term Definitions// ) | ||

272 | |||

273 | |||

274 | The KAES analysis demonstrates that those definitions are not the primary data for the analysis of the properties of kinship terminology structures, but derived definitions that are predicted from the way in which the terminology is generated as a structure. | ||

275 | |||

276 | |||

277 | Instantiation is not limited to genealogical instantiation. Instead, instantiation depends upon cultural rules for mapping abstract symbols to individuals and can be based on other criteria such as adoption or other means by which individuals are incorporated with in the conceptual structure of a kinship terminology. | ||

278 | |||

279 | |||

280 | **//Metaphoric Instantiation of Kin Terms//** | ||

281 | |||

282 | |||

283 | The constraint imposed by the algebraic structure on instantiation lies in the structural properties of a kinship terminology that are mapped onto individuals through the process of instantiation, such as instantiation must be consistent with the reciprocity of kin terms, and the generative properties of the kinship terminology structure. The latter implies that kin term products must also map over to individuals under the cultural rules of instantiation,. Thus an adopted child is not only a Child vis-à-vis the adopting parents, but the adopted child has the appropriate kin term relationship to other individuals in the kinship domain of the adopting parents. This contrasts with instantiation of individual kin terms that does not carry over to other kin terms, such as the use of the kin terms Aunt and Uncle by users of the AKT in an honorific sense; e.g. the use of the Uncle and Aunt terms for the friends of ones parents. The distinction between the more extended and the more limited forms of instantiation provides a more formal way to express what has sometimes been referred to as metaphoric usages of kin terms. | ||

284 | |||

285 | |||

286 | == A Kinship Parable[1] == | ||

287 | |||

288 | |||

289 | //Dwight Read (UCLA)// | ||

290 | |||

291 | |||

292 | Eager Graduate student (EG for short), tired of taking courses that seemed only to be interested in navel gazing asked himself in confusion, after one of his classes. “Surely there must be something better!” A fellow graduate student suggested that he attend the Summer Workshop on Quantitative Methods and Modeling.[2] EG went to the workshop and learned about semantic domains and cultural consensus analysis.[3] | ||

293 | |||

294 | |||

295 | EG then went to the field to apply what he had learned in the Workshop. He quickly made friends with the men in his village and discovered they had 6 terms Tabu, Tama, Luta, Tuwa, Bwada and Latu that they used to refer to males. EG decided to see how the terms relate to each other as a semantic domain. So he set up a series of frames of the form: “If I use ~_~_~_~_~_~_ to refer to X, and X uses ~_~_~_~_~_~__ to refer to Y, then I should use ~_~_~_~_~_~_~_~__ to refer to Y.” This worked extremely well and he got back statements such as “If I refer to X as Bwada and X refers to Y as Tama then I refer to Y as Tama”. | ||

296 | |||

297 | |||

298 | EG put all of his data into neatly drawn tables. Then he applied the ideas of cultural consensus analysis and discovered a high degree of concordance among his informants. This was, indeed, a cultural domain. | ||

299 | |||

300 | |||

301 | Armed with his field data, EG went back to Research University to talk with Prof. Silverback. Prof. Silverback looked at EG’s notes and tables and asked EG: “Don’t you realize you have been getting kin terms? EG said “No. What are kin terms?” Prof. Silverback rolled his eyes upward and thought to himself: “Why should EG know about kin terms? We no longer teach classes on kinship and some of my fellow anthropologists have said that there is no such thing as kinship.” Prof. Silverback asked EG if he had used the genealogical method[4] for getting information on what the terms mean. EG looked puzzled. Prof. Silverback explained: “When you elicit kin terms, you need to find out from your informants the kin terms you can use for your genealogical relatives, beginning with genitor and genetrix.” | ||

302 | |||

303 | |||

304 | “Even if they don’t have a term for genitor,” he told EG, “insist on them telling you what term to use for the person who is one’s genitor, and similarly for genetrix.[5] Without that information we can’t analyze the 6 terms you have written down.” EG was genuinely puzzled and asked “Why can’t we just treat these 6 terms as part of a semantic domain and analyze them just like any other semantic domain?” Prof. Silverback smiled, for he knew that EG was referring to his work on semantic domains. | ||

305 | |||

306 | |||

307 | Prof. Silverback then told EG that he had gotten a new computer program, called Kinship Algebra Expert System (KAES),[6] that might be able to do something with his 6 terms. Prof. Silverback thought, though, that it was hopeless since EG did not have the genealogical definition of any of these terms. | ||

308 | |||

309 | |||

310 | Prof. Silverback turned on his computer and told EG that they had to make a kin term map showing the linkages among the terms based on the information he had elicited from his friends. After drawing the kin term map on the computer screen, Prof. Silverback pressed the Analyze button and several windows appeared. EG looked at the first window labeled Graph and said with amazement: “Even though I did not ask the women about terms, on one side of the graph are the 6 terms I elicited, and on the other side are 6 more terms that look like they should be the terms used by females!” | ||

311 | |||

312 | |||

313 | The computer now showed a list of terms and the set of genealogical positions that would be included under each term. “Amazing!” said EG. “How did the computer figure out that all of these terms and their genealogical definitions? I couldn’t even get anyone to provide a term that meant genitor!” | ||

314 | |||

315 | |||

316 | A new screen appeared with the graph of an idealized genealogy with ego at the center and a kin term listed for each position in the genealogy. It was Prof. Silverback’s turn to express amazement, for he had been sure that nothing would come of trying to analyze EG’s 6 terms. “This is remarkable! We have the complete terminology right before us, along with the genealogical definition of each kin term. But how can this be?” he wondered to himself. “EG did not get ask about genealogical definitions and did not ask anyone about the terms they use for genitor or genetrix. All he did was ask them about how the 6 terms relate to each other in the form of triadic frames.” | ||

317 | |||

318 | |||

319 | By now Prof. Silverback was almost visibly shaken. “Is it possible that kin terms provide a conceptual system that is not simply a classification of sets of kin types? Could it be that while people do trace out genealogical linkages, it is also true that the kin terms form a separate conceptual system, with its own internal logic, one that is more basic than the definition of kin terms using genealogical kin types? Is it really possible to predict correctly the genealogical definitions of kin terms?” | ||

320 | |||

321 | |||

322 | After EG left, Prof. Silverback hurried to his bookshelf and pulled out a dusty back issue of the American Anthropologist.[7] “I know that I have seen that terminology before,” Prof. Silverback said to himself. “Yes. Here it is. Let’s see. Here is the list of kin terms in the article along with their genealogical definitions, just as they should be listed. Surely it cannot be the case that the KAES program actually generated the complete terminology and all of the genealogical definitions of the kin terms.” Prof. Silverback checked the computer generated definitions against the terms in the article and exclaimed, “It’s exactly the right list! Must be pure coincidence, or a lucky guess, for some of the definitions are bizarre.” Prof. Silverback was looking at the genealogical definition of Tabu given in the article – ff, fm, mf, mm, mmb, fz, fzh, fzd, fzdd, ss, sd, ds, dd, man’s zds, man’s zdd, woman’s bs, woman’s bd, man’s wife’s brother son, man’s wife’s brother’s daughter, woman’s mbs, woman’s mbd, woman’s mmbs, and woman’s mmbd. “Now how could the KAES program ever figure out that list?” Prof. Silverback mumbled to himself. “Let’s see what is on the computer screen for Tabu –ff, fm, mf, mm, mmb, fz…” By this point Prof. Silverback was beginning to feel very uncomfortable, as if he was faced with a fact that he was desperately trying to hide from himself. “…, fzh, fzd, fzdd…” he stammered, slowly realizing that there was no difference between the list on the screen and the list in the article, except that the screen included other, more distant genealogical positions not mentioned in the article. Quickly, and almost as if in desperation, Prof. Silverback turned to the other terms. “Surely there must be one disagreement someplace!” When Prof. Silverback reached the end of the list without finding any errors he sank back into his chair and spoke as if to someone. “But this can’t possibly be! We’re talking about people, not machines! Machines may be predictable, but people aren’t. Kinship has to do with flesh and blood, real people, not cold symbols and mathematical-like relations.[8] There must be at least one error in here someplace!” Prof. Silverback kept looking at the screen and slowly it began to dawn on him. “Maybe this is telling us something fundamental about human cognition and something about what we mean by culture. Maybe this is even telling us something about what it means to be human!” With that thought, Prof. Silverback turned off the computer, then turned out the lights, and left his office, a puzzled smile on his face. | ||

323 | |||

324 | |||

325 | 1 Research sponsored in part by NSF Subcontract Y702129 (Biocomplexity Proposal). | ||

326 | |||

327 | |||

328 | 2 NSF Summer Institute for Research Design and Methods in Cultural Anthropology | ||

329 | |||

330 | |||

331 | 3 Romney, A. Kimball, Susan C. Weller, and William H. Batchelder. (1986) Culture as Consensus: A Theory of Culture and Accuracy. American Anthropologist 88: 313-338 | ||

332 | |||

333 | |||

334 | 4 Rivers. W.H. R. 1910, The Genealogical Method of Anthropological Inquiry. Sociological Review 3:1-12. | ||

335 | |||

336 | |||

337 | 5 “I was able to make the natives understand very thoroughly that I wanted the ‘proper father’” Rivers, W. H. R. 1900, A Genealogical Method of Collecting Social and Vital Statistics. Journal of the Royal Anthropological Institute 3:74-84. | ||

338 | |||

339 | |||

340 | 6 KAES program discussed in Read, D. and C. Behrens. 1990. KAES: An Expert System for the Algebraic Analysis of Kinship Terminologies. J. of Quantitative Anthropology 2:353-393; see also Read, D. 2001 What is Kinship? In The Cultural Analysis of Kinship: The Legacy of David Schneider and Its Implications for Anthropological Relativism, R. Feinberg and M. Ottenheimer eds. University of Illinois Press, Urbana. Pp. 78-117. KAES Program initially written in Turbo Pascal by Dwight Read and Cliff Behrens. Rewritten in Java by Michael Fischer in conjunction with Dwight Read. Copy of the Java version may be obtained from the author or from Michael Fischer (M.D.Fischer@ukc.ac.uk). | ||

341 | |||

342 | |||

343 | 7 American Anthropologist 1965 67(5) Part 2: 142-185. | ||

344 | |||

345 | |||

346 | |||

347 | 8 Paraphrase of an anonymous reviewer comment on a manuscript, 2001 |