The Mathematics of Comparing Objects

`After reading two different crime stories, an artificial intelligence concludes that in both stories the police has found the murderer just by random.'' -- To what extend and under which assumptions this is a description of a realistic scenario?

The Complexity of Comparative Text Analysis -- "The Gardener is always the Murderer" says the Fourth Machine

There is a heated debate about how far computers can map the complexity of text analysis compared to the abilities of the whole team of human researchers. A "deep" analysis of a given text is still beyond the possibilities of modern computers. In the heart of the existing computational text analysis algorithms there are operations with real numbers, such as additions and multiplications according to the rules of algebraic fields. However, the process of "comparing" has a very precise mathematical structure, which is different from the structure of an algebraic field. The mathematical structure of "comparing" can be expressed by using Boolean rings. We build on this structure and define the corresponding algebraic equations lifting algorithms of comparative text analysis onto the "correct" algebraic basis. From this point of view, we can investigate the question of {\em computational} complexity of comparative text analysis.