[PEIRCE-L] Diagrams and structures
Alex, Those things were done and published years ago. They are not research issues, and there is nothing controversial about them. They were published in an official ISO standard. The latest version was published in 2018, but it is more complex, and the subset that was defined in 2007 is the only version that has been implemented and used: ISO/IEC standard 24707 for Common Logic. Even more important, it can be downloaded for free: http://standards.iso.org/ittf/PubliclyAvailableStandards/c039175_ISO_IEC_24707_2007(E).zip The ISO standard for Common Logic specifies the core semantics in an abstract syntax that is independent of any readable notation of any kind. Then it states that any concrete syntax (linear or diagrammatic) that has a formally defined mapping to the abstract syntax may be called a dialect of Common Logic. Then three different concrete syntaxes are specified in the Appendices: (1) Common Logic Interchange Format (CLIF), which has a LISP-like syntax: (2) Conceptual Graph Interchange Format (CGIF); and (3) an XML-based notation (XCL). In that standard, the core semantics is formally equivalent to Peirce's existential graphs. The formal name for the notation is "core CGIF", but I use the name EGIF (Existential Graph Interchange Format) because the core can be mapped to and from the graphic notation for EGs. Anything stated in the full CLIF or CGIF or XCL dialects can be mapped to CGIF and then to the core EGIF. The mappings are defined in that standard. For more details about the full graph notation plus extensions, see the peer-reviewed research publication in the International Journal of Applied Logics: Sowa, John F. (2018) Reasoning with diagrams and images, http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf . That issue of the journal contains several articles presented at a conference in Bogota, Columbia. My article is the second one. It defines an extension to EGs that also supports mappings to and from images. But before reading all those formal publications, I recommend the slides from the talk that I presented at the European Sematic Web Conference in 2020: https://jfsowa.com/talks/escw.pdf . These slides present a simpler overview, which may help smooth the way toward the more detailed formalism. They also contain more links to other publications and presentations that can add useful background. See the links at the bottom of most slides, and the suggested readings in the last slide. John From: "Alex Shkotin" John, For me the next steps are -to find axiomatic theories of EG, CG in your egtut.pdf [0] or other papers. -wait for development of [1]. -to continue with E2HOL [2] where we need algorithms: string is input, graph or diagram is output. I am happy we align our terminology. Alex [0] https://jfsowa.com/pubs/egtut.pdf [1] https://inquiryintoinquiry.com/2023/09/15/logical-graphs-formal-development-1/ [2] https://www.researchgate.net/publication/366216531_English_is_a_HOL_language_message_1X _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Diagrams and structures
Alex, Both dictionaries I quoted (and others I did not bother to quote) make a very clear distinction between structures (as patterns that exist independently of what anybody may think or say about them) and diagrams (as patterns that people or animals or computers choose to represent for explaining or reasoning about structures). And thank you for the definition from Wikipedia, which makes exactly the same distinction and emphasizes that it goes back to prehistoric times (over 10 thousand years ago). Euclid and other geometers (more than 2,000 years ago) adopted diagrams for the foundation of mathematics, especially geometry -- and those diagrams are also used for reasoning and for applications in science, engineering, and architecture. And thank you for the three citations to the Stanford articles. The one on diagrams discusses the writings by C. S. Peirce, and it also cites two things by me: (1) My book on Knowledge Representation, published in 2000, and (2) an article I wrote in 2011, which was published in the journal Semiotica: https://jfsowa.com/pubs/egtut.pdf The article about the structure of scientific theories admits that humans may have discovered and stated the theories. But it focuses on the patterns in the theory that are independent of the scientists who discovered or stated them. Their primary example is Newtonian mechanics, but it ignores anything that Newton himself thought or did. I discusses only the mathematical patterns. Today, we know that the mathematical pattern of Newtonian mechanics is only approximately true about the universe. But the patterns implied by that theory exist (in a mathematical sense) independently of what we think about them. When considered as a mathematical formula and the collection of patterns implied by that formula, it is independent of what anyone may think about those patterns.. The article about structural realism admits that some people might consider structures as things that people built or imagined. But it also makes a case that the structures that are really real -- they exist independently of what anybody may think about them. In summary, the American heritage definition of diagram is as good as any and better than most: - A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole. - A graphic representation of an algebraic or geometric relationship. - A chart or graph. This implies that diagrams are chosen by humans for explanations and reasoning. Structures are patterns considered as existing by themselves. The processes that create the structures (human or non-human) are not relevant to their existence as structures. Unless anybody can find any better terminology for any application of ontology, I believe that this distinction is the best we have. John From: "alex.shkotin" IN ADDITION "A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment.[1] Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram." https://en.wikipedia.org/wiki/Diagram четверг, 14 сентября 2023 г. в 12:26:31 UTC+3, alex.shkotin: John, We can dive into a fascinating exploration of how the terms diagram and structure are used in everyday life. Meanwhile I decided to look into the Stanford Encyclopedia of Philosophy. And I was glad to find an article [1] that explained your approach to me. Unfortunately, the term structures does not have a separate article. But there is an article “The Structure of Scientific Theories” [2]. This is what I do to the best of my ability with an emphasis on formalization. After all, before formalizing a theory, it must be structured. However, there is an interesting article “Structural Realism” [3]. Alex [1] https://plato.stanford.edu/entries/diagrams/ [2] https://plato.stanford.edu/entries/structure-scientific-theories/ [3] https://plato.stanford.edu/entries/structural-realism/ чт, 14 сент. 2023 г. в 01:27, John F Sowa : Since I suggested that anybody who is trying to define anything should check the definitions in a good dictionary, I decided to take my own advice. See the attached defs.htm for definitions of the words 'diagram' and 'structure' in the American Heritage Dictionary and the Merriam Webster Dictionary. In general, I have found the American Heritage definitions and etymologies very good. They are usually clearer and more precise than the definitions in other dictionaries. But it's always useful to get a second or third opinion. An important distinction: A structure is a pattern in an entity of some kind. A diagram is a pattern that somebody draws
[PEIRCE-L] Diagrams and structures
Since I suggested that anybody who is trying to define anything should check the definitions in a good dictionary, I decided to take my own advice. See the attached defs.htm for definitions of the words 'diagram' and 'structure' in the American Heritage Dictionary and the Merriam Webster Dictionary. In general, I have found the American Heritage definitions and etymologies very good. They are usually clearer and more precise than the definitions in other dictionaries. But it's always useful to get a second or third opinion. An important distinction: A structure is a pattern in an entity of some kind. A diagram is a pattern that somebody draws or imagines as a representation or explanation of a pattern that somebody observed of found in some structure. Therefore, a diagram would be more likely to be the kind of pattern that some human or animal or computer would be likely to use to support reasoning or computation about a pattern of any kind. John Definition of diagram From American Heritage Dictionary: A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole. A graphic representation of an algebraic or geometric relationship. A chart or graph. From Merriam Webster Dictionary: A graphic design that explains rather than represents; especially a drawing that shows arrangement and relations (as of parts). a line drawing made for mathematical or scientific purposes. Definition of structure From American Heritage Dictionary: Something made up of a number of parts that are held or put together in a particular way. The way in which parts are arranged or put together to form a whole; makeup. The interrelation or arrangement of parts in a complex entity. From Merriam Webster Dictionary: The action of building; construction. Something (such as a building) that is constructed. Something arranged in a definite pattern of organization; leaves and other plant structures. Manner of construction; makeup. _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
