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

Re: [ontolog-forum] Philosophical Implications of Gödel and Turing/Church

by John F Sowa

Michael, The word 'understand' is a vague word that has no formal definition of any kind. In any specific example, it's essential to replace it with a statement of the operations that had been performed. MDB: ChatGPT ... can understand Turtle but it seems to understand natural language definitions better. Short summary: LLMs process patterns of symbols. Their most reliable applications map strings of symbols (in natural or artificial languages) to strings of symbols in other languages. Those are not perfect, but they are the most reliable because they do the least amount of processing. But they do nothing that remotely resembles what humans do when they "understand" the source and target languages. The more steps in the processing, the more unreliable the results. Translation is the most reliable because the source and target patterns are very closely related. LLMs can also be used to find information when a pattern in a question has a more distant relation to a pattern in the target that is found. That kind of search is more reliable the closer the search pattern is to the pattern that is found. But LLMs don't do any evaluation. If a search pattern has a closer match to bad data than good data, the bad data will be retrieved. The most spectacular, but also the most unreliable applications of LLMs search for a pattern that does some kind of transformation and then apply that transformation to some source data to produce some target data. People often call these transformations "reasoning". But the kind of reasoning should be called "guessing" or "hypothesis" or "abduction". Humans who understand what LLMs do can often find them very useful because they are sufficiently knowledgeable about the subject that (1) they recognize bad guesses and ignore them; and (2) they do further tests and checks to evaluate the answers before using them. There is much more to say about the details. But never, ever use the words 'reasoning' or 'understanding' for what LLMs do. However, it may be permissible to use the word 'reasoning' for a hybrid system that uses symbolic methods for deduction and evaluation of the results that LLMs find or generate. And most of all, it's best to reject , discard, or ignore any publication that claims LLMs are approaching a human level of understanding or reasoning. I have never seen any article about artificial general intelligence (AGI) that has any insight whatsoever into human intelligence. John PS: Penrose wrote some excellent books on physics. When he wanders outside of his level of expertise, his ideas may be interesting -- or not. ---------------------------------------- From: "Michael DeBellis" <mdebellissf(a)gmail.com> Sent: 9/26/24 11:41 AM As we know there is a large and subtle discussion around Penrose thesis. I am not in it. I am sure that there should be a forum for this topic. And your question "Why do we have to accept the "indisputable validity" of these statements that lie outside the scope of P?" is to RP not to me. Sorry. Alex, no need to apologize. Although I'm starting to wonder how subtle the discussion really is. I'm starting to suspect this is a case of the emperor having no clothes (ironic given the title of one of Penrose's book). Specifically, 95% of the people who read Penrose's book don't have the capability to understand Godel at all, and of the 5% that can at least somewhat grasp Godel (most of us) even fewer (like Paolo Mancosu, the guy at Berkeley who taught a class I audited a long time ago on Godel, Turing, etc.) who are the real experts aren't interested enough to point out obvious errors. For example D. Hilbert wrote the axiomatic theory of Euclid's geometry. Do we have formalization? No I don't quite understand that. Isn't an "axiomatic theory" a formalization? But our robots are waiting for them. One of the ironies of this whole discussion IMO is that in some circumstances (LLMs) it is now easier to communicate to software agents using natural language than formal language. I still need to do a lot more work on this but so far that is what I'm finding in my work with ChatGPT, it says it can understand Turtle but it seems to understand natural language definitions better. One of the things I plan to work on is a simple generator to generate basic NL descriptions of classes, properties, and axioms. It shouldn't be hard. If something like this exists I would appreciate a pointer How many theories outside math are formalized? One of the philosophers in the Vienna circle, think it was Carnap, thought that we SHOULD formalize other disciplines of science and attempted to do that for physics. I've always thought one of the reasons he failed was because to create such a complex model required some kind of tool. For a while I even thought it might be possible to do with OWL. I actually tried but it was soon apparent that 1) I don't know physics well enough and 2) Even if I did (here I'm in violent agreement with John Sowa) OWL wasn't powerful enough for this kind of model. Michael On Wed, Sep 25, 2024 at 1:11 AM Alex Shkotin <alex.shkotin(a)gmail.com> wrote: Michael, As we know there is a large and subtle discussion around Penrose thesis. I am not in it. I am sure that there should be a forum for this topic. And your question "Why do we have to accept the "indisputable validity" of these statements that lie outside the scope of P?" is to RP not to me. Sorry. And any discussion outside some theory, which should be definitely pointed to concrete theory, is just mind to mind games. In Linguistics there are a lot of theories fighting. For example D. Everett has one theory and N. Chomsky has another. Outside scope on any theory we just gymnastics the mind. Why not! But the challenge is to formalize one or another existing theory 🎯 For example D. Hilbert wrote the axiomatic theory of Euclid's geometry. Do we have formalization? No 😂 How many theories outside math are formalized? 0. But our robots are waiting for them. By the way topic of truth values is one of the subtle in math logic 👍 Everyone, who has created a formal ontology, formalized some theoretical knowledge. From what theory? Where is this theory expressed? How to justify his formalization by this theory? We can always verbalize formalization and then must find in this particular theory a justification or ask experts. Theory first, robots second 🏋️ Alex

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CfP AIA Special Issue on Measuring Ontologies for Value Enhancement

by Polovina, Simon (BTE)

Hello, all. As a guest editor for this special issue, I welcome your submissions. Thanks! Simon URL: https://ojs.bonviewpress.com/index.php/AIA/SI_MOVE Aims and Scope The MOVE (Measuring Ontologies for Value Enhancement) is a community of academic researchers and industrial practitioners that aim to inspire research, discussion, and tools to achieve value from ontologies by measuring their impact in all fields. These measures would identify where there are gaps and overlaps within and across ontologies and the extent to which they are applied in multiple disciplines towards a holistic general ontology. Lead Guest Editor Rubina Polovina Systems Affairs, Canada Research Interests: Post-object-oriented modelling and AI Guest Editors Simon Polovina Department of Computing, Sheffield Hallam University, UK Research Interests: Business Computing and Enterprise Ontology Ivan Launders BT Global, UK Research Interests: Global Cloud Architecture Special Issue Information The contributions from researchers describing their original, unpublished research contribution on the following theme (but not limited to): ∙ Artificial Intelligence, General and Domain-Specific ∙ Case Studies or Histories ∙ Bringing Computer Productivity to Individual or Organisational Human Creativity ∙ Communication Theories and Practices ∙ Conceptual Graphs, Formal Concept Analysis, or Other Conceptual Structures ∙ Data Infrastructures ∙ Data, Information, Knowledge, and Wisdom Space ∙ Enterprise and Endeavour Architectures ∙ Ethical Theories and Moral Practices ∙ Government Services ∙ Industry or Third-Sector Applications ∙ Knowledge Graphs, Linked Data Graphs, or Enterprise Data Graphs ∙ Large Language Models ∙ Modelling Theories and Practices ∙ Ontology Theories and Practices ∙ Philosophical Foundations ∙ Neuroscience and Phycology Relevant to AI ∙ Semantics ∙ Semiotics ∙ Societal Adaption ∙ Systems Theories and Practices ∙ Value Inquiry ∙ Vocabularies, Taxonomy, and Ontology ∙ Web-Based, Cloud, Mobile, or Other Software Tools ∙ User Experiences ∙ Any Other Area Relevant to MOVE Manuscript Submission Information Submission deadline: May 31, 2025 Submissions that pass pre-check will be reviewed by at least two reviewers of the specific field. Free, fast publication and early access will be provided to all accepted papers. Journal Information Editor-in-Chief: Shivakumara Palaiahnakote, University of Salford, UK Frequency: Quarterly Submission to First Decision: 60 days Submission to Acceptance: 161 days Accept to Publish: 17 days Acceptance Rate: 18% eISSN: 2811-0854 © 2024 Bon View Publishing Pte Ltd. Dr Simon Polovina Department of Computing, Sheffield Hallam University, UK Profile<https://ontologforum.com/index.php/SimonPolovina> │ Email<mailto:S.Polovina@shu.ac.uk?subject=Enquiry>

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Formalizing vague information is a bad idea (was goedel and more

by John F Sowa

Alex, Please reread my note below. For a subject that cannot be formalized, the practice of formalization is not just a waste of time -- It is a BAD IDEA. Any formalization will make it say something that is guaranteed to be false. Therefore, people who understand the issues will reject whatever you produce, and people who don't understand the issues will mistakenly use your false results. John ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> John, What a nice day to read this "Chuck's sentence is true about science and technology: "My hypothesis is that the language of science, technology, and mind is HOL." " There are a lot of details to discuss later. But the main direction is to formalize theories we already have in "science, technology, and mind" Thank you, Alex сб, 21 сент. 2024 г. в 23:55, John F Sowa <sowa(a)bestweb.net>: Alex and Chuck, I strongly agree on the importance of formal logic, but I must also add that the overwhelming majority of information that we must deal with comes from perception and natural languages. There is no simple, general, dependable, and trustworthy method for mapping those sources to and from any version of logic. 'There are good approximations, but none of them are as precise and dependable as any version of logic. Chuck's sentence is true about science and technology: "My hypothesis is that the language of science, technology, and mind is HOL." But the human mind is far more general than anything that can be mapped to and from HOL by any known or imagined technology that can be processed by any kind of computerized system that is known or proposed or imagined. In fact, I would add that the reasoning by your pet dog or cat is beyond what can be done with HOL. In fact everybody's favorite nematode C. elegans has only 303 neurons. Scientists have detected and mapped its complete connectome -- every connection of every neuron. But they are unable to predict or simulate its behavior, There is much more to say about these issues, but there is one serious warning: Any formal ontology about the world is limited by the methods for mapping language and perception to any kind of logic. I sympathize with the concerns that Chuck mentions and links to. But I am very well aware of the need for serious work on methods of detecting, correcting, and working around the limitations. Anybody who doesn't recognize and include such methods will be doing more harm than good. For more about these issues, see https://jfsowa.com/ikl That rather short web page has links to many important publications that discuss these issues. I strongly urge people to browse some of them. John

1 month, 3 weeks

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Re: [ontolog-forum] goedel and more

by John F Sowa

Mike, I agree that those two questions are extremely difficult questions about physics, and nobody knows how to anwer them. But that is not a question about mathematical logic, which Mihai Nadin was discussing in his note below. For the first question, you could start by writing an equivalent in an Englishy kind of logic: 1. For every x of type "law of nature" for every time t, law x is consistent at time t. That is a rather simple statement in logic, but nobody would know how to answer it by any possible experiment short of examining every region of the universe for all eternity. The second has the same limitation. It's a simple statement in logic that cannot be answered without testing it in every location of the universe at all points in time.:, 2. For every x of type "law of nature" for every y of type "region of the universe", x is applicable at y. John ---------------------------------------- From: "Mike Bergman" <mike(a)mkbergman.com> Hi John, OK; I'll bite, and give you two. See below. On 9/21/2024 5:09 PM, John F Sowa wrote: I agree with the note below. But nobody but a logician who has studied advanced issues in logic knows how to state an undecidable proposition, I would challenge anybody to find a single undecidable proposition in any branch of science or engineering or economics or politics or any field other than advanced mathematics. - "The laws of nature are consistent across time" (the counter was a favorite of Peirce) - "The laws of nature are universally applicable across all regions of the universe." Thanks, Mike I won't deny that a professional logician might contrive an undecidable proposition about some subject matter in any of those fields. But I will predict with almost absolute certainty that no professional in that field would understand it. And even if the logician could explain that proposition to somebody in that field, I predict with almost absolute certainty that the professional in that field would consider it irrelevant or even ridiculous. And by the way, if anybody could contrive such a proposition, I would be delighted to see it. Please send it to the list, state the proposition in English, translate it to some version of logic, prove that it is indeed undecidable, and find a professional in that field who would consider it significant. I seriously doubt that anybody could do that, but I'd be happy to be proven wrong. John ---------------------------------------- From: "Nadin, Mihai" <nadin(a)utdallas.edu> Sent: 9/20/24 5:39 PM To: "ontolog-forum(a)googlegroups.com" <ontolog-forum(a)googlegroups.com> Subject: [ontolog-forum] goedel and more Discussing Penrose is justified. BUT: the focus should be on Goedel. Allow me to repeat my advice: read the paper, i.e. his proof. Read also Turing, i.e. his proof for the Hilbert challenge. Against my better judgment, I am suggesting one of my papers: https://www.researchgate.net/publication/314424008_The_Intractable_and_the_… (in my book https://link.springer.com/book/10.1007/978-3-031-43957-5 this is discussed in detail) But I am not reacting to recent opinions only for the sake of pointing to my work. The thing that concerns me regarding the discussion is expressed as …and perhaps some day someone will somehow prove things that are unprovable according to GT/C Let us agree that science is not only about what is possible, but also about what is not possible. Squaring the circle—anyone? Just to give an example. Within the number construct we are using, there is PI)—no need to redefine it here. As long as we stick to the numbers used currently in order to represent our measuring (quantitative aspects) of reality, the doubling of the cube and trisecting the angle will remain impossible because of how we defined . NOT even the not yet invented new forms of computation will do it. Goedel discovered for a well-defined aspect of mathematics that consistency and completeness are not possible. Those using the outcome of his proof owe it to him to understand what the meaning of this is. Doubt is good (Dubito ergo sum), on the assumption that is grounded in knowledge. Get if from the source. Mihai Nadin https://www.nadin.ws https://www.anteinstitute.org Google Scholar

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Re: [ontolog-forum] goedel and more

by John F Sowa

I agree with the note below. But nobody but a logician who has studied advanced issues in logic knows how to state an undecidable proposition, I would challenge anybody to find a single undecidable proposition in any branch of science or engineering or economics or politics or any field other than advanced mathematics. I won't deny that a professional logician might contrive an undecidable proposition about some subject matter in any of those fields. But I will predict with almost absolute certainty that no professional in that field would understand it. And even if the logician could explain that proposition to somebody in that field, I predict with almost absolute certainty that the professional in that field would consider it irrelevant or even ridiculous. And by the way, if anybody could contrive such a proposition, I would be delighted to see it. Please send it to the list, state the proposition in English, translate it to some version of logic, prove that it is indeed undecidable, and find a professional in that field who would consider it significant. I seriously doubt that anybody could do that, but I'd be happy to be proven wrong. John ---------------------------------------- From: "Nadin, Mihai" <nadin(a)utdallas.edu> Sent: 9/20/24 5:39 PM To: "ontolog-forum(a)googlegroups.com" <ontolog-forum(a)googlegroups.com> Subject: [ontolog-forum] goedel and more Discussing Penrose is justified. BUT: the focus should be on Goedel. Allow me to repeat my advice: read the paper, i.e. his proof. Read also Turing, i.e. his proof for the Hilbert challenge. Against my better judgment, I am suggesting one of my papers: https://www.researchgate.net/publication/314424008_The_Intractable_and_the_… (in my book https://link.springer.com/book/10.1007/978-3-031-43957-5 this is discussed in detail) But I am not reacting to recent opinions only for the sake of pointing to my work. The thing that concerns me regarding the discussion is expressed as …and perhaps some day someone will somehow prove things that are unprovable according to GT/C Let us agree that science is not only about what is possible, but also about what is not possible. Squaring the circle—anyone? Just to give an example. Within the number construct we are using, there is PI)—no need to redefine it here. As long as we stick to the numbers used currently in order to represent our measuring (quantitative aspects) of reality, the doubling of the cube and trisecting the angle will remain impossible because of how we defined . NOT even the not yet invented new forms of computation will do it. Goedel discovered for a well-defined aspect of mathematics that consistency and completeness are not possible. Those using the outcome of his proof owe it to him to understand what the meaning of this is. Doubt is good (Dubito ergo sum), on the assumption that is grounded in knowledge. Get if from the source. Mihai Nadin https://www.nadin.ws https://www.anteinstitute.org Google Scholar

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Re: goedel and more

by John F Sowa

Alex and Chuck, I strongly agree on the importance of formal logic, but I must also add that the overwhelming majority of information that we must deal with comes from perception and natural languages. There is no simple, general, dependable, and trustworthy method for mapping those sources to and from any version of logic. 'There are good approximations, but none of them are as precise and dependable as any version of logic. Chuck's sentence is true about science and technology: "My hypothesis is that the language of science, technology, and mind is HOL." But the human mind is far more general than anything that can be mapped to and from HOL by any known or imagined technology that can be processed by any kind of computerized system that is known or proposed or imagined. In fact, I would add that the reasoning by your pet dog or cat is beyond what can be done with HOL. In fact everybody's favorite nematode C. elegans has only 303 neurons. Scientists have detected and mapped its complete connectome -- every connection of every neuron. But they are unable to predict or simulate its behavior, There is much more to say about these issues, but there is one serious warning: Any formal ontology about the world is limited by the methods for mapping language and perception to any kind of logic. I sympathize with the concerns that Chuck mentions and links to. But I am very well aware of the need for serious work on methods of detecting, correcting, and working around the limitations. Anybody who doesn't recognize and include such methods will be doing more harm than good. For more about these issues, see https://jfsowa.com/ikl That rather short web page has links to many important publications that discuss these issues. I strongly urge people to browse some of them. John ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> Chuck, welcome on board. The more we formalize the better for World. As this is a way to check LLMs and other algorithms in use. And please share that "The status of this document is RFC (Request For Comments). It keeps a number of ideas to discuss. Abstract. Following the idea of R. Montague (RM for short) "English is a formal language" we will give examples of constructing operator expressions for sentences in the English language. For comparison of approaches, the examples are taken from the text [PTQ] by R. Montague. This makes it possible to compare operator bracket expressions with the author's constructions later." Alex сб, 21 сент. 2024 г. в 15:39, Chuck Woolery <chuck(a)igc.org>: Alex, Thank you for this paragraph... My hypothesis is that the language of science, technology, and mind is HOL. And when we have a framework for theories of mathematical logic, it will be the primary source for referencing any definitions, theorems, and proofs. We have the beginnings of a framework for undirected graph theory. Incidentally, we also need a framework for tasks, problems. Alex With your permission I will be sharing it with other in my blog posts attempting to bring sanity to a world where religious, economic, and political words can mean damn near anything. Cw Chuck Woolery, Former Chair United Nations Association, Council of Organizations 315 Dean Dr., Rockville, MD 20851 Cell:240-997-2209 chuck(a)igc.org

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Pragmatic Cosmos

by Jon Awbrey

Pragmatic Cosmos • 1 • https://inquiryintoinquiry.com/2024/09/21/pragmatic-cosmos-1-a/ Re: Michael Harris • Not About Fibonacci • https://mathematicswithoutapologies.wordpress.com/about-the-author/ • https://mathematicswithoutapologies.wordpress.com/2016/06/09/not-about-fibo… I have often reflected on the interminglings of the main three normative sciences. In one of my earliest meditations I saw Beauty, Goodness, and Truth as the intersecting circles of a Venn diagram, with the “summum bonum” the central cell. As far as our ability to approach our object from our origin without, perfect knowledge of the Good would require us to know all the consequences of our contemplated actions while perfect knowledge of the True would require us to know all the axiom sets which never beget a contradiction. As far as I could tell, and as far as I could see deciding with the empirical tests and theorem provers I could morally and mathematically envision devising, the above two tasks exceed the talents of mortal humans and all their technological extensions. But when it comes to Beauty, our form of being appears to have an inborn sense to guide us on our quest to the highest good. That way through beauty to our ultimate goal I called the “human‑hearted path”. Regards, Jon cc: https://www.academia.edu/community/Lpz0q7 cc: https://mathstodon.xyz/@Inquiry/113175621041124276

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Logical Graphs • Discussion

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

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Logical Graphs • Formal Development

by Jon Awbrey

Logical Graphs • Formal Development 1 • https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development… Recap — A first approach to logical graphs was outlined in the article linked below. Logical Graphs • First Impressions • https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-… That introduced the initial elements of logical graphs and hopefully supplied the reader with an intuitive sense of their motivation and rationale. Formal Development — Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. The next order of business is to give the precise axioms used to develop the formal system of logical graphs. The axioms derive from C.S. Peirce's various systems of graphical syntax via the “calculus of indications” described in Spencer Brown's “Laws of Form”. The formal proofs to follow will use a variation of Spencer Brown's annotation scheme to mark each step of the proof according to which axiom is called to license the corresponding step of syntactic transformation, whether it applies to graphs or to strings. Resources — Survey of Animated Logical Graphs • https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs… Regards, Jon cc: https://www.academia.edu/community/ld361R cc: https://mathstodon.xyz/@Inquiry/113129787112676868

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Logical Graphs • First Impressions

by Jon Awbrey

Logical Graphs • First Impressions 1 • https://inquiryintoinquiry.com/2024/08/30/logical-graphs-first-impressions-… Moving Pictures of Thought — A logical graph is a graph‑theoretic structure in one of the systems of graphical syntax Charles S. Peirce developed for logic. Introduction — In numerous papers on qualitative logic, entitative graphs, and existential graphs, C.S. Peirce developed several versions of a graphical formalism, or a graph‑theoretic formal language, designed to be interpreted for logic. In the century since Peirce initiated their line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph‑theoretic structures. The posts to follow explore the common basis of those formal systems from a bird's eye view, focusing on the aspects of form shared by the entire family of algebras, calculi, or languages, however they happen to be viewed in a given application. Resources — Logical Graphs • https://oeis.org/wiki/Logical_Graphs Futures Of Logical Graphs • https://oeis.org/wiki/Futures_Of_Logical_Graphs Propositional Equation Reasoning Systems • https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems Charles Sanders Peirce • Bibliography • https://mywikibiz.com/Charles_Sanders_Peirce • https://mywikibiz.com/Charles_Sanders_Peirce_%28Bibliography%29 Regards, Jon cc: https://www.academia.edu/community/V1Eowd cc: https://mathstodon.xyz/@Inquiry/113051725984818777

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CG September 2024