MV-Algebra for Cultural Rules

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. The author acknowledges Dick Greechie in appreciation for the many comments he offered on this paper and on the development of this line of research. Useful comments of an unidentified reviewer helped clarify results. Only the author is responsible for any errors, and for the ideas asserted. This paper was delivered at the meetings of the International Quantum Structures Association, IQSA-Malta 2006.