Greg and Alex, I agree that graph structures support algorithms that are more flexible than the typical operations with predicate calculus. I also agree that it's important to support methods that deal with approximations or "fuzzy" kinds of truth values. There has been a huge amount of theoretical and practical R & D 0n these issues in the past 50 years. GS: The subject of pattern logic is developed over several illustrated webpages and culminates in the topic of "decisions" which represents a novel theory of propositional truth grounded in the structure of interpreted patterns. This expanded theory of truth encompasses both the typical truth values, as well as intermediate degrees of certainty and contradiction. I don't know the details of your system, but from your notes, I believe that you have a more advanced system than the so-called ":semantic web stack" that is based on the 2005 "layer cake". But as I have said many times, the "decidability gang" destroyed the vision and specifications in the winning proposal by Tim Berners-Lee in 2000. The so-called "Semantic Web Stack" of 2005 was a pale shadow of what Tim B-L had proposed. In 2003, another branch of the Federal Gov't saw that the Semantic Web was headed in the wrong direction, and they funded a much more advanced and more ambitious project called IKRIS. See https://jfsowa.com/ikl/ . It was funded for two years (2004 to 2006) and it included some of the most advanced AI projects and researchers from industry and Academia. Arun Majumdar and I were just two of the many researchers involved. Unfortunately, there were some cutbacks in gov't funding in 2005, and neither the IKRIS project nor the SW project were continued. For a survey of developments from the late 1970s to 2011, see Semantics for Interoperable Systems, documents collected and related by John Sowa, https://jfsowa.com/ikl/ . You don't have to believe me. I wrote the overview, but I include links to the original R & D articles by everybody I mention in the reviews. I also have more reviews and publications, but this is enough for now. John ---------------------------------------- From: "gregsharp73" <gregsharp73(a)gmail.com> The requested pattern logic primer can be found here: https://patternslanguage.com/pattern-logic The subject of pattern logic is developed over several illustrated webpages and culminates in the topic of "decisions" which represents a novel theory of propositional truth grounded in the structure of interpreted patterns. This expanded theory of truth encompasses both the typical truth values, as well as intermediate degrees of certainty and contradiction. For a discussion of why a cyclic pattern language is an improvement over linear formal languages and offers an approach to making the meaning in natural language accessible to computation see the following article: https://patternslanguage.com/articles/f/a-cyclic-pattern-language Thanks, Greg On Sunday, February 16, 2025 at 9:39:21 AM UTC-7 Alex Shkotin wrote: Just small Sunday's evening addition: If we put brackets we get this (∄(Philosopher) ⊇ ∂(Person)) i.e. we have two unary modifiers (∄ ∂) of unary predicates (concepts) into something that can be modified by the binary operator ⊇ to create a proposition. Very interesting. вс, 16 февр. 2025 г. в 14:42, alex.shkotin <alex.s...(a)gmail.com>om>: by the way " ∄Philosopher ⊇ ∂Person" [1] is not a FOL, but HOL like this ∃p:unary_predicate, ∃x:Person p≠Philosopher ∧ p(x) [1] https://patternslanguage.com/articles/f/unifying-logic-traditional-premises… пятница, 14 февраля 2025 г. в 17:29:39 UTC+3, Gregory Sharp: ꓱPhilosopher ⊇ ∂Person is a label given to the central occasion of a 9 occasion pattern that follows the general form of a logical statement. This particular statement is analogous to an Aristotelian I-premise which can be rendered in English as "some person is a philosopher". The general form of a logical statement requires quantification of both of its terms and a copula. The copula here is called "predication". There are three other copulas. The concept philosopher is existentially quantified. The concept person is partially quantified. There are two other quantifiers used in the analogous Aristotelian system. They are universal and non-existential quantification. There are six additional quantifiers in pattern logic. The four copulas and ten quantifiers set the boundaries for pattern logic "proper" in the ADEPT LION "first consideration" which encapsulates the "grammar" of the broader pattern language. The second consideration is the vocabulary and the third consideration is the syntax. From the standpoint of pattern logic, "wife" is a concept, or a non-logical term. Greg On Fri, Feb 14, 2025, 4:28 AM Alex Shkotin <alex.s...(a)gmail.com> wrote: Just FYI: "17.02.2025, jointly with S.I. Adian seminar Alexei Miasnikov (Stevens Institute of Technology): First-order classification, non-standard models, and interpretations In this talk I will focus on three things: 1. First-order classification: in particular, how one can describe ALL groups which are first-order equivalent to a given one. 2. Non-standard models of groups: in particular, I will describe non-standard models of the finitely generated groups with decidable or recursively enumerable (or arithmetic) word problems and explain how they naturally appear as non-standard Z-points of the general algebraic schemes. 3. Theory of interpretations: it seems a new rich theory is emerging right now. I will show several interesting results based on interpretations." https://www.mathnet.ru/eng/conf876 Enjoy, Alex