Alex,
Formally defined existential graphs (EGs) and conceptual graphs (CGs) are precisely defined mathematical notations. In fact, CGIF (Conceptual Graph Interchange Format) is defined as an ISO standard representation of Common Logic. Therefore, any or all notations of the Semantic Web can be expressed in terms of CGs.
Furthermore, Peirce's EGs are formally equivalent to the Core subset of Common Logic. Therefore, anything specified in Common Logic can be mapped to a subset of CGIF, which I sometimes call EGIF. But I now prefer a simpler notation called CLIP, which can be translated to and from EGIF or CGIF.
However, Peirce began to define an extended version of EGs, which he called Delta graphs. Unfortunately, he had an accident for which the physician treated him with so much morphine that he was unable to do any serious work for six months. After that he was dying from cancer. But his various writings in the last few years of his life indicate what he planned to do with those extended graphs. From the hints he wrote, I specified an extension I call Generalized EGs (GEGs).
These GEGs can include arbitrary images (even continuous images) as parts. Your examples could be represented as GEGs. But the kinds of images they contain might include arbitrarily complex continuous fragments, which would require an uncountable amount of math to specify.
And thanks for the citation of the article: Images, diagrams, and metaphors: Hypoicons in the context of Peirce’s sixty-six fold classification of signs* PRISCILA FARIAS and JOA˜ O QUEIROZ Images, diagrams, and metaphors: Hypoicons in the context of Peirce’s sixty-six fold classification of signs* PRISCILA FARIAS and JOA˜ O QUEIROZ
I haven't had a chance to read it in detail, but it looks like something I should cite in my article.
John
From: "Alex Shkotin" <alex.shkotin@gmail.com>
John,
Thank you for the very useful description of Peirce's approach. But my question was about the diagrams you develop now. For me, a conceptual graph is a math object. And I think you are developing some extension of CG to get more modeling power.
Alex
