This chapter focuses on Charles S. Peirce's insights into relational logic and the diagrammatic or graphical nature of the relationship between the knowing subject and known object. It argues that major benefits of a diagrammatic approach to ubiquitous computing system in the digital economy would derive from the application of pedagogical technologies based on the very computational techniques, networks, and applications that would be studied and analysed in a course focusing on drivers of the digital economy. More diagrammatic approaches to category theory have come to the fore, especially for representing transition systems. Category theory or topos theory is the chosen mathematical framework for teaching formal computation. Teaching along these Pragmatic lines would encourage students to think about information and communication technologies and Business Information Systems from a strategic perspective informed by an understanding of contemporary and evolving computational technologies. More generally, semantic technologies, sometimes described under the rubric of cognitive computing, are a rapidly growing field within artificial intelligence.