May 2024 - CG - lists.cs.uni-kassel.de

by Jon Awbrey

Logical Graphs • Discussion 5 • https://inquiryintoinquiry.com/2023/08/28/logical-graphs-discussion-5/ Re: Logical Graphs • First Impressions • https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/ Re: Facebook • Daniel Everett • https://www.facebook.com/permalink.php?story_fbid=pfbid026jD3t75k69Wbs9q3qa… DE: Nice discussion. Development of icon-based reasoning. My Comment — As it happens, even though Peirce's systems of logical graphs do have iconic features, their real power over other sorts of logical diagrams (like venn diagrams) is due to their deeper symbolic character. Thereby will hang many tales to come … Regards, Jon cc: https://www.academia.edu/community/VjWX8L cc: https://mathstodon.xyz/@Inquiry/110967659414575933

2 months, 1 week

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Future Systems of the Past

by John F Sowa

Kingsley, Paul, List. As I said, I've been a mathematician from way back, and I consider designs that can be translated to and from other formats without loss of info to be functionally identical. But I also worked at IBM for 30 years, and I learned about all the pain and suffering caused by revisions and upgrades and supposed equivalences that aren't. As an extreme example, consider the IBM SAGE computer for the US Strategic Air Command in the 1950s, which was intended to detect and monitor all aircraft flying over North America. It weighed 250 tons and occupied one acre of floor space. See https://www.ibm.com/history/sage#:~:text=SAGE%20remained%20in%20service%20b…. When I joined IBM in the 1960s, I saw the actual engineering model in operation in Kingston, NY. It was used to test all software upgrades and fixes for the machines that were deployed at various installations. The software designs for SAGE in the 1950s were adapted to the airlines reservation system for American Airlines in the 1960s, which ran on the IBM 7094. Later that was upgraded for a System/360 version that included hotel reservations and car reservations. That system was so successful that all software systems by all competitors world wide adopted the same software conventions. Today, any reservations that anybody makes world wide are based on extensions of the design decisions that were made for that 250-ton monster of the 1950s. But the computer chip in your cell phone today has vastly more computer speed and storage capacity. However, the system design and data structures at each stage were upward compatible with the previous versions. Summary: The SAGE data structure designs are still buried deep inside the latest and greatest reservation systems today. The high-level design decisions last forever, but the details at the bottom change with every major upgrade. General principle: Implementation details are temporary. Logic is forever. John ---------------------------------------- From: "Kingsley Idehen' via ontolog-forum" <ontolog-forum(a)googlegroups.com> Hi Paul, On 5/30/24 6:09 PM, Paul Tyson wrote: John: thanks for the good explanation and your reasoned assessment of the W3C semantic stack. Kingsley: I agree with your points except regarding RDF/XML. Anyone who still is stuck on this needs to read the RDF/XML spec and understand the design principles and limitations, and then move on to other serializations that suit their needs and toolchains. Yes, but my point is that W3C spec publication issues have left confusing items in the public view that continue to either confuse people or reinforce long discarded confusion. I would advise against adopting any RDF toolchain that did not at least read RDF/XML, and preferably also write it, mainly to support integration with XML toolchain including XSLT, xquery, xproc, etc, enabling full integration of XML document corpuses with RDF datasets. Sorta. Our Virtuoso platform still makes extensive use of RDF/XML, right now, but completely outside the user's view. For a baseline example, a few dozen lines of XSLT will transform any xml document into its infoset RDF representation (in RDF/XML conveniently, slightly less so in another notation). Marry that up to other domain semantic data sources, and you have with very little effort created a linked data pool far more valuable than either the XML or the RDF by itself. From there, the sky's the limit for expanding and exploiting your linked data. (Not to say there aren't other ways to do this, but none so easy using ready-to-hand tools and existing data sources.) Yes, but that isn't the front-door of RDF i.e., its an implementation detail. I generally discourage narratives that lead to the misconception that XML is a mandatory requirement regarding RDF :) Kingsley Regards, --Paul

6 months

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Precursors Of Category Theory

by Jon Awbrey

Precursors Of Category Theory • 1 • https://inquiryintoinquiry.com/2024/05/25/precursors-of-category-theory-1-a/ All, A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. My notes on the project are still very rough and incomplete but I find myself returning to them from time to time. Preamble — ❝Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor” from Carnap (“Logische Syntax der Sprache”), and “natural transformation” from then current informal parlance.❞ — Saunders Mac Lane • “Categories for the Working Mathematician” Resources — Precursors Of Category Theory • https://oeis.org/wiki/Precursors_Of_Category_Theory Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy Survey of Precursors Of Category Theory • https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-… Regards, Jon cc: https://www.academia.edu/community/VWY2Qq cc: https://mathstodon.xyz/@Inquiry/112502692087155139

6 months

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Some things provably suck (was Future Systems of the Past

by John F Sowa

Mike, we've discussed related issues before. I agree that pointless criticism does not solve problems. But some technologies really do suck. I believe that it's important to tell people (1) Why those technologies suck; (2) What other options are available; and (3) How they can make a transition from the worse to the better. But I also know that it's rarely possible to replace legacy software in the short term. Therefore, interim measures are often necessary. As I said in a previous note, I have been doing that for years. At IBM in the 1970s, I wrote a memo that had a strong influence on killing a bad project before the managers who were responsible for it had time to unfurl their golden parachutes. That memo saved IBM quite a few $$$, but it caused some highly placed managers to "hate my guts". Fortunately, my manager arranged for me to get me a transfer outside of their chain of command. M. Bergman: Please refrain from your incessant put-downs and dismissals of W3C semantic standards. No one is forcing you, or anyone else, to use it. I think the constant denigration speaks more to you than the standards. Short answer: When some method is provably worse than others, anybody who can show the proof has an obligation to show exactly how and why the situation can be remedied. Tim Berners-Lee had an excellent vision for the Semantic Web in his winning proposal in 2000. Unfortunately, he decided to allow voting by a huge W3C committee to make design decisions. The deciability gang (some very intelligent logicians who had no experience with practical computation) stacked the voting to enforce decidabiity. That derailed some much better projects, and installed a theoretical basis for OWL that destroyed Tim's vision. Please read "Fads and fallacies about logic" https://jfsowa.com/pubs/fflogic.pdf . In that article, I cited working systems that were far superior to anything based on OWL. I also showed theoretical reasons for an implemented alternative (not by me) that was simpler, easier to implement, easier to read and write, more efficient, and on a faster growth path to the future. As support for that article, Jim Hendler, who had written the original requirements for the proposal that Tim B-L won, agreed with me, liked the article I wrote, and approved it for publication. (At that time he was the editor of the IEEE journal in which it was published. First of all, I recommend the following overview of AI tools and theories for supporting applications of AI to practical applications of databases and knowledge bases. You don't have to believe anything I wrote. I recommend the following overview: Semantics for interoperable systems, https:/jfsowa.com/ikl That overview of systems from the 1980s to about 2018 contains 48 URLs to articles written by other people. I'm not asking you to believe anything I say. But I am asking you to review what many knowledgeable people have written in those citations. The most important part of that overview is the section on the IKRIS project (from 2004 to 2006) which was funded by a different branch of the US government from the one that funded the W3C project. The people who funded IKRIS were very unhappy that the W3C had adopted a direction that was far worse than what Tim B-L had proposed. When I wrote my fflogic article, my criticism was mild in comparison to the issues discussed and developed by IKRIS. The IKRIS project included quite a few very knowledgeable people who have contributed quite a few influential notes and talks to Ontolog Forum, (See the list of participants in some of the articles). It also includes people who developed the logic foundations for Common Logic and other important contributions. MB: John, you too often violate in my opinion Peirce's admonition to not block the way to inquiry. As I said before, there is much more to say -- mostly very constructive. But sometimes, a bit of destruction is necessary to clear the way of inquiry. Peirce himself did quite a bit of destruction along the way. In fact, many of his later writings destroyed or made major revisions to some of his earlier projects. John

6 months, 1 week

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History of the logical foundations for ontology (was Future directions...H

by John F Sowa

Alex, We have to make a clear distinction of (1) Historical developments, (2) Particular implementations, (3) Logical foundations, (4) Practical usage and development. Alex: Description Logic is a theoretic basis for OWL2 - the most used formal language for ontologies. If we consider point #1, the type hierarchy for DLs was specified by Aristotle with his syllogisms, which are more readable today than any current implementation of OWL (Point #2). There are four rules (A I E O), which can be expressed in Greek, English, or any other natural language. These rules have been widely used for centuries, and they are a highly readable notation for the OWL hierarchy: A: Every S is P. (S is the subject, and P is the predicate) I: Some S is P. E; No S is P, O: Some S is not P. For an introduction and examples, see slides 25 to 30 of https://jfsowa.com/talks/patolog1.pdf . For theoretical issues (Point #3), see slides 26 to 33. The Stoic logicians introduced Greek sentence patterns (#2 and #3) for assertions in a subset of first-order logic. In the 14th century, Ockham introduced a more complete range of sentence patterns in Latin that could represent the full expressive power of first-order logic (#3 and #4). His notation was very readable (by anyone who could read Latin or its translation to English and other languages). But he didn't have all the reasoning methods of modern FOL for proving the expressive power. In addition to the type hierarchy, Brachman and Fikes (1979) wrote a paper about KL-ONE (Knowledge Language 1), which consisted of a terminology (T-Box) for the equivalent of Aristotle's syllogisms, and a notation for assertions (A-Box). This covers points #1, #2, #3, and #4 as a superset of OWL4. Anything and everything that can be represented in OWL2 can be represented in KL-ONE, or in Latin according to Ockham's Summa Logicae. But the Greek and Latin versions or their translation to modern languages had the same advantage as KL-ONE: The full expressive power of first-order logic. And by the way, C. S. Peirce was familiar with all the logic methods by the ancient Greeks and the medieval Latins. He took pride in having the largest collection of medieval manuscripts on logic in the Boston area (which included the Harvard libraries). When he specified his versions of logic, he was familiar with all the earlier options. By comparison, however, OWL2 was a major step BACKWARDS from the Greeks, the Latins, and KL-ONE by the hopelessly misguided idea that decidabiity was important. It just made the notation more complex, harder to read, harder to write, harder to implement, and much less expressive. Recommendation for OWL3: An upward compatible version that allows any statements in Turtle or other notations plus any statements in pure and simple first-order logic. That means that all current implementations can continue to be used without change. The user notation can be a highly readable controlled natural language, such as ACE. This gives us the best of all options #1, #2, #3, and #4 -- plus upward compatibility with current implementations. John PS: Since the word 'sowa' means owl in Polish, this version of OWL3 would rescue my totem animal from the ignominy of a horrible version of logic. That's another plus. ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> John, Description Logic is a theoretic basis for OWL2 - the most used formal language for ontologies. And at the very beginning they distinguished theoretical and factological (aka structural) propositions. Axioms and assertions in their terminology. What we need on the way to formal theoretical knowledge is a pattern for formal definitions and formal proofs. Like this here definition

6 months, 1 week

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Representing, Learning, Reasoning, and Applications (was Andrew Ng

by John F Sowa

Ravi, Michael, List, Ravi: I think of myself as a student of this amazing concept of Ontology which most in the west have learned from Aristotle and Greeks. So do I. In fact, Aristotle and the Stoics specified an excellent replacement for OWL. Aristotle organized his categories in a hierarchy that can be represented by the hierarchy part of OWL (the best and most useful part of OWL). The four sentence types for his logic (A, I, E, O) specify the operations for reasoning with and about the hierarchy. Then the Stoics specified if-then rules for stating constraints and performing inferences with and about the hierarchy and related information. Although they didn't have full FOL, their if-then rules were later extended to full FOL by the medieval logicians. Ockham had specified full FOL in the 14th century, but stated in a version of Latin. That combination would have been equivalent to KL-ONE (by Brachman and Fikes in 1973). They coined the term T-Box (Terminology box) for the hierarchy and A-Box (Assertion box) for the equivalent of FOL. Since they did not restrict their specifications by decidability, their T-Box plus A-Box would be equivalent to "good OWL" -- i.e. OWL without the limitations of decidability. Unfortunately, Brachman later listened to the decidability gang who inflicted decidabilit . That was a major step backward from the middle ages. The following point is fundamental to knowledge representation of any kind, especially applications of ontology: Michael DB: The main point I was trying to make in the meeting is IMO right now there is a large disparity between the ML people and the Semantic side and my impression is the ML people barely know we still exist. I don't know how to address that but I think it is worth thinking about some potential joint work with ML leaders like Ng and people from Ontolog in the future. One of the great strengths of Ontolog Forum is an issue that many (most?) theoreticians ignore: How do you use logic to do anything useful? Many excellent theoreticians don't have any experience in practical applications. I admit that was my outlook when I was studying math & logic. But at IBM, my first job was in a mathematical analysis group, where we had to solve problems for which the engineers didn't have the training. So I had to learn a great deal about their problems and about practical computational methods for solving them. That was excellent on-the-job training for which I had to educate myself. Michael: I think it is worth thinking about some potential joint work with ML leaders like Ng and people from Ontolog in the future. But it's important to recognize the goals and interests of any people you invite. You may have learned a great deal about linguistics by talking with Chomsky. But it's unlikely that Chomsky would take much interest in studying any problems you may have. (I know quite a few people who have been badly bruised or burned by Chomsky because they dared to modify his theories in order to deal with practical problems.) Re Andrew Ng: I have read some of his writings, and I agree that they're good. But as you said in your note, "the ML people barely know we [ontologists] still exist. I don't know how to address that." For some background on the history of AI, I recommend an article from 1983: Krypton: A Functional Approach to Knowledge Representation, https://web.stanford.edu/class/cs227/Readings/KryptonAFunctionalApproachToK… They discuss the issues and some of the historical developments. Looking backwards from today, I would summarize the issues in three parts: 1. An ontology specified as a hierarchy (tree or lattice). This would correspond to Aristotle's hierarchy with his four rules for specifying and reasoning with and about it. It would also correspond to the T-box. 2. Constraints on the hierarchy specified in full FOL instead of the subset in OWL specified by Turtle or other notations. 3. Assertions in a database of SQL, object-oriented DB, or RDF assertions anywhere on the WWW. Then add the constraint that #1 has priority over #2 in case of any contradictions, and #2 would have priority over assertions in #3 that come from a DB (SQL or object-oriented). For assertions that come from anywhere else, there may be good reasons for giving them higher priority, but that would depend on the sources and the circumstances. John ---------------------------------------- From: "Michael DeBellis" <mdebellissf(a)gmail.com> What message do you think ANdrew Ng would give to our summit in a paragraph? Ravi, I honestly don't know. There have been a couple presentations where I thought that semantic technology was highly relevant to what he was talking about. One of them was on improving ML systems by better training data. He spent a lot of time talking about the point that the best way to increase the accuracy of an ML system was not just increasing the amount of the data but increasing the quality of the data. That was a topic where I thought Semantic technology could be especially relevant in many ways. Defining data integrity constraints with SHACL and throwing out data that violates those constraints as well as using OWL models to better understand the data and using the ontology to evaluate specific elements (i.e., instances in a knowledge graph) to again determine if certain examples are probably the result of errors. Also, do identify trends in the data that might help provide better structure to the ML models. I've thought about reaching out to professor Ng. In the past I've done that with a few well known academics like Chomsky and I usually get very favorable responses. Several years ago I had some amazing detailed discussions with Chomsky about issues related to ethics, linguistics, and theory of mind. But Ng is very much in demand by various businesses as well as being a respected academic and my feeling is he probably gets swamped with so many random emails from undergrads learning ML that he's less likely to reply. The main point I was trying to make in the meeting is IMO right now there is a large disparity between the ML people and the Semantic side and my impression is the ML people barely know we still exist. I don't know how to address that but I think it is worth thinking about some potential joint work with ML leaders like Ng and people from Ontolog in the future. Michael On Fri, May 24, 2024 at 12:00 AM Ravi Sharma <drravisharma(a)gmail.com> wrote: Micheal Yes A couple of speakers did talk about specific roles and use of Agents, but including Fall series on LLMs and Ontologies and current Summit 2024, their mention has been not too often. What message do you think ANdrew Ng would give to our summit in a paragraph? I will try to look at the link as well. Thanks. Regards.Ravi

6 months, 1 week

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Survey of Precursors Of Category Theory

by Jon Awbrey

6 months, 1 week

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Future directions for ontology (was paper by Dean Allemang; Juan Sequeda

by John F Sowa

João, Thanks for that reference. It's one more article that emphasizes the importance of ontology and knowledge graphs (KGs) for detecting and correcting the errors and hallucinations of LLMs. It's an example of the "Future directions" that are necessary to make LLMs reliable. By themselves, LLMs make two important contributions to AI: (1) They are very good for translating natural languages and formal notations to other languages and notations. (2) They are very good at generating hypotheses (guesses). Unfortunately. LLMs cannot do reasoning. They can find and apply methods of reasoning, but they are unable to do their own reasoning to evaluate the relevance and accuracy of any results (guesses) that they generate. The article by Allemang and Sequeda shows how to use KGs to evaluate and correct the output from LLMs. Following is Figure 1 from their article: This shows how they use GPT-4 to generate answers, which they check against an ontology. If they detect errors, they go back to GPT-4 and repair the LLM output, which they continue checking until the results are consistent with the ontology and an SQL database. To represent information, they use a version of Knowledge Graphs (KGs) that can support full first-order logic. Other notations for FOL could also be used. Peirce's existential graphs have been extended to support conceptual graphs and the ISO standard for Common Logic. They can support any reasoning by any version of KGs. See below for the abstract and URL of the article. Note that their methods improved the accuracy of LLMs from 16% to 54% by using KGs. With ontology, they obtained 18% more correct answers and 8% "I don't k now." That leaves 20% wrong answers. 100% correct answers is probably unattainable, but the system should answer "I don't know" for anything it does not know. Even without more data, more and better ontology and reasoning should enable it to answer "I don't know" for the remaining 20%. John _______________________________________ From: "João Oliveira Lima" <joaoli13(a)gmail.com> Hi, Yesterday the paper below was published on Arxiv, which may be of interest to this group. Joao Title: Increasing the LLM Accuracy for Question Answering: Ontologies to the Rescue! Authors: Dean Allemang, Juan Sequeda https://arxiv.org/pdf/2405.11706 Abstract: There is increasing evidence that question-answering (QA) systems with Large Language Models (LLMs), which employ a knowledge graph/semantic representation of an enterprise SQL database (i.e. Text-to-SPARQL), achieve higher accuracy compared to systems that answer questions directly on SQL databases (i.e. Text-to-SQL). Our previous benchmark research showed that by using a knowledge graph, the accuracy improved from 16% to 54%. The question remains: how can we further improve the accuracy and reduce the error rate? Building on the observations of our previous research where the inaccurate LLM-generated SPARQL queries followed incorrect paths, we present an approach that consists of 1) Ontology-based Query Check (OBQC): detects errors by leveraging the ontology of the knowledge graph to check if the LLM-generated SPARQL query matches the semantic of ontology and 2) LLM Repair: use the error explanations with an LLM to repair the SPARQL query. Using the chat with the data benchmark, our primary finding is that our approach increases the overall accuracy to 72% including an additional 8% of "I don't know" unknown results. Thus, the overall error rate is 20%. These results provide further evidence that investing knowledge graphs, namely the ontology, provides higher accuracy for LLM powered question answering systems.

6 months, 1 week

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Transformations of Logical Graphs • Discussion

by Jon Awbrey

Transformations of Logical Graphs • Discussion 1 • https://inquiryintoinquiry.com/2024/05/22/transformations-of-logical-graphs… Re: Laws of Form • https://groups.io/g/lawsofform/topic/transformations_of_logical/105927945 Mauro Bertani • https://groups.io/g/lawsofform/message/3204 Dear Mauro, The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations. Logical Graphs • First Impressions • https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/ Logical Graphs • Formal Development • https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development… Additional Resources — Logic Syllabus • https://inquiryintoinquiry.com/logic-syllabus/ Survey of Animated Logical Graphs • https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs… Survey of Semiotics, Semiosis, Sign Relations • https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign… Regards, Jon cc: https://www.academia.edu/community/laAADa cc: https://mathstodon.xyz/@Inquiry/112486421005431283

6 months, 1 week

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Transformations of Logical Graphs

by Jon Awbrey

Transformations of Logical Graphs • 1 • https://inquiryintoinquiry.com/2024/05/05/transformations-of-logical-graphs… Re: Interpretive Duality in Logical Graphs • 1 • https://inquiryintoinquiry.com/2024/04/22/interpretive-duality-in-logical-g… Re: Mathematical Duality in Logical Graphs • 1 • https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-g… All, Anything called a “duality” is naturally associated with a transformation group of order 2, say a group G acting on a set X. Transformation groupies generally refer to X as a set of “points” even when the elements have additional structure of their own, as they often do. A group of order two has the form G = {1, t}, where 1 is the identity element and the remaining element t satisfies the equation t² = 1, being on that account self‑inverse. A first look at the dual interpretation of logical graphs from a group-theoretic point of view is provided by the Table below. Interpretive Duality as Group Symmetry • https://inquiryintoinquiry.files.wordpress.com/2021/02/peirce-duality-as-gr… The sixteen boolean functions f : B × B → B on two variables are listed in Column 1. Column 2 lists the elements of the set X, specifically, the sixteen logical graphs γ giving canonical expression to the boolean functions in Column 1. Column 2 shows the graphs in existential order but the order is arbitrary since only the transformations of the set X into itself are material in this setting. Column 3 shows the result 1γ of the group element 1 acting on each graph γ in X, which is of course the same graph γ back again. Column 4 shows the result tγ of the group element t acting on each graph γ in X, which is the entitative graph dual to the existential graph in Column 2. The last Row of the Table displays a statistic of considerable interest to transformation group theorists. It is the total incidence of “fixed points”, in other words, the number of points in X left invariant or unchanged by the various group actions. I'll explain the significance of the fixed point parameter next time. Regards, Jon cc: https://www.academia.edu/community/l7jBGO

6 months, 2 weeks

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CG May 2024