tion of all geometric properties involved as well as just the topological ones, geographers can reinterpret, add to, and refine the conventional concepts in the methodology of uniform regional geography and provide it with a basis in logic." 
Many geographers at the time would push the concept logic form and notions from set theory further into geographic analysis and not just in the sense of a useful analogy. In a paper written for one of the classic compilations texts from early years mathematical geography called, The Philosophy of Maps, Warntz and others like Waldo Tobler, and William Bunge, would change not only the vocabulary used in analysis but would also alter the very form of its expression. In an article in the collection, called Some Elementary and Literal Notions About Geographical Analysis and Extended Venn Diagrams, Warntz would say that, "Maps showing regional classification can be regarded as logic diagrams. Mapping of sets is a general mathematical concept. Geographical mapping is merely a special case of this."  Warntz here sees almost a mereological or mereotopological relationship between the spatial extent of Venn diagrams and their isomorphic counterparts of geographic regions.
John VennIt is quite remarkable that the two systems of logic that Warntz draws on in this paper, Venn diagrams and existential graphs, are both visual and not symbolic logical systems. Most of the work done in logic during the 20th century has focused on symbolic systems with little research, at least until quite recently, on the heterogeneous reasoning of the type Warntz is advocating. He says that, "It is part of our purpose here to extend the use of such diagrams to the mapping of geographical regions by making use of properties already inherent in Venn diagrams but as yet unutilized... We intend to apply spatial properties literally to real spatial distributions on the earth's surface..."
Venn diagrams can grow to extremely complex forms depending on the number of sets one is dealing with and recent research on the use of logical diagrams has shown that Warntz was ahead of his time in thinking that the spatial and geometrical component of logical diagrams would be useful analogs for spatial maps. 
As stated above, Warntz' paper calls on the work of Charles Sanders Peirce (above) and his existential logic diagrams, which he sees as mappings from non-spatial sets to geographical maps. Looking at the complexity of Peirce's systems, there is both an alpha and beta form depending on the required complexity, one wonders how deeply Warntz explored the subject of existential graphs. An important aspect of these graphs that Warntz thought useful for regional geographic analysis was the fact that a logic diagram can be drawn as a two-dimensional figure with spatial relations that are isomorphic with the structure of some logical statement. This is very important if one is going to try to apply set theory of the type Warntz is envisioning here, simply because these spatial relations are usually of a topographic nature.Logic diagrams, especially the type developed by Peirce (simple examples shown above with a page frm Peirce's notebook below), stand in the same relation to the various logical algebras as maps of areas stand in relation to their particular algebraic functions; they are simply other ways of symbolizing the same basic structure. 
In much of what Warntz has to say here we are reminded of the long way we have come when talking about set theory, topology and the formal properties of spatial structures and their relationship to cartography. One only has to look at books like Varzi and Casati's, Parts and Places: the Structures of Spatial Representations (MIT, 1999)  to get a feel for how our language and conceptual grasp of these topics has improved since Warntz and others involved in the early development of computer cartography were experimenting with what at the time were radically new ideas.
The current project envisioned here, which grew out of my research for the 20th century volume of the History of Cartography, wi