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A theory of cultural structures predicts the objects observed by anthropologists. We here define those which use kinship relationships to define systems. A finite structure we call a partially defined quasigroup (or pdq, as stated by Definition 1 below) on a dictionary (called a natural language) allows prediction of certain anthropological descriptions, using homomorphisms of pdqs onto finite groups. A viable history (defined using pdqs) states how an individual in a population following such history may perform culturally allowed associations, which allows a viable history to continue to survive. The vector states on sets of viable histories identify demographic observables on descent sequences. Paths of vector states on sets of viable histories may determine which histories can exist empirically.Keywords: quantum logic; groups; partially defined algebras; quasigroups; viable cultures Ethnographic FoundationThe structures described here and their consequences imply much of what may be predicted about empirical cultures. Anthropologists very often draw illustrations of structures using methods discussed here, but based on intuition, thus have little notion of what their commonly used diagrams might predict. While [1,2] defined mathematical means to describe the current and future demographic organization of lineage organizations, with empirical examples, we here specify the demography of kinship-based systems [3][4][5][6][7][8] with some related definitions in our Appendix A; and empirical examples in [9][10][11][12][13]. We follow the inspiration of [14]. In an empirical culture many other relations may also occur; we note some of those in our Part 7, Discussion at the end.Our notion of studying viable minimal structures-which are the smallest minimal cultural structures that can "reproduce" the ascribed social relations in one generation-follows from [15]. Our history describes how sustaining those relations allow the culture to reproduce the rules. Cultural rules describing histories may be stated in natural languages, which label the individuals in a descent sequence with a subset called a kinship terminology. Our term viable embodies what anthropologist Radcliff-Brown called "persistent cultural systems" ([10], p. 124). Radcliff-Brown and others often described histories using discrete generations, as do we. Empirical cultures are almost ubiquitously described by many anthropologists using viable histories, typically represented in an ethnography by its minimal structure. The nearly ubiquitous presence in ethnographies of viable histories implies they may be the only observed histories.An example is Figure 1 (whose source is [9]) which is an actual viable minimal structure of a history (that is, a persistent cultural system). The triangles in the illustration are males, the circles are females, descent moves in the downward direction, the labels are names used in the kinship terminology. The sign "=" means "marriage" between the two individuals attached to it; the "=" on the far right in the illu...

Holts S u m m i t , Missouri Descriptions w e d by ethnography can be embodied in a mathematical theory, yielding strong measurable inferences. This theory is interpreted and applied to an empirical example, to derive population measures from lineage descriptions. The theory is purely cultural in that it derives testable implications from social anthropological descriptions without w e of techniques from classical demography. The new techniques are not subsumed by 'general systems'' or statistical methods commonly taught, therefore implying these methods are fundamentally wrong. [social anthropology, mathematical theory, cultural theory, population measures]

This paper reports preliminary results on a new area of application of quantum structures, motivated by a reading of the 2004 monograph Reasoning in Quantum Theory. Ethnographers often describe a particular culture by describing rules of social relations that they assert characterize that culture. Viable cultures exist over periods of time, that is, over sequences of "generations". To embody this, we define a suitable set of objects and relations, and a structure on which cultural rules act as "operators" on a set of "configurations" on generations. This yields an MV-algebra of those operators. This implies that culture theory might be studied as an example of the theory of quantum structures.

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