The notion of a classification does not build in any assumptions about closure under the usual Boolean operations. It is natural to ask What role do the usual Boolean connectives play in information and its flow? This lecture takes an initial step toward answering this question. We will return to this question in later chapters as we develop more tools. It is not a central topic of the book, but it is one that needs to be addressed in a book devoted to the logic of information flow.

Actually, there are two ways of understanding Boolean operations on classifications. There are Boolean operations mapping classifications to classifications, and there are Boolean operations internal to (many) classifications. Because there is a way to explain the latter in terms of the former, we first discuss the Boolean operations on classifications.

Boolean Operations on Classifications

Given a set Φ of types in a classification, it is often useful to group together the class of tokens that are of every type in Φ. In general, there is no type in the classification with this extension. As a remedy, we can always construct a classification in which such a type exists. Likewise, we can construct a classification in which there is a type whose extension consists of all those tokens that are of at least one of the types in Φ.