Conceptual blending addresses framing new concepts based on existing ones. Blending theory can be applied to a variety of areas, but the most popular in literature seems to be education in the sense of blended learning techniques. In this paper, the introductory part, the reference section, and the keyword and the definition in the abstract entirely refer to concept or conceptual theory, not theory blending as in the title--such a term sounds fictitiously as the one not existing in literature. However, the authors try to determine its meaning as “a subform of the general notion of conceptual blending with high relevance for applications in mathematics. ... This form of concept blending will consequently be referred to as theory blending.” Honestly, even this definition does not convince me of this topic, which according to the authors lacks an algorithmic account.

An overview of conceptual blending is presented from a historical perspective, but the focus is shifted to Goguen’s account on which the authors build their mathematical model. The cognitive linguistics examples, illustrating Goguen’s account that uses the web, unpacking, and topology principles, are interesting. The first one maintains the connections between the inputs and the blend; the next one reconstructs the inputs based on the blend; and the last one relies on similarities between the blend components and their input space equivalents. The proposed model is called heuristics-driven theory projection for which these three principles work as well. The left and right input spaces are axiomatized in first-order languages. The algorithm proposed consists of generalization, identification, blending, and relaxation.

It should be stressed that the evaluation is not compared with any other blending algorithms. In the summary, the authors highlight the simplicity of their approach when compared to Goguen’s account. As the work is not supported by working examples, I would recommend it to mathematicians only as it does not have much to do with computer science or linguistics.