This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of learning in education on all levels. From one point of view he was behind his times because in the 1960's semantic analysis was passe in academic circles having been replaced by modern linguistics (Smith, 2004, Chomsky, 1968). On the other hand, Upton could be considered ahead of his time because of the emergence of the importance of semantics and formal logic in computer science and other disciplines (Auwera, 2008; Hoenig; 2008; Yamashiro, 2006, Ma, 2004; Ploux, 2003, Lakoff, 1978). The purpose of this analysis is to determine if the reduction of Thinking Maps (TMs), based on Upton's semantic theory to mathematical expressions can give insight into why they have been so successful for learning. In this paper, the question is not if these maps work, but why and how they work. It is suggested that a formal analysis of a set of maps proven to work, David Hyerle's semantic maps ( 1996, 2004, 2006, 2009), will clarify and determine reasons behind their effectiveness. This analysis will help in the better understanding of the use of visual diagrams in teaching and other areas. It is also suggested that this understanding of the why and how of semantic maps will help in the design interactive eLearning software. (Contains 8 figures.)