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

by Jon Awbrey

Differential Logic • Overview • https://inquiryintoinquiry.com/2024/11/25/differential-logic-overview-a/ A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions. Indeed, one of the first lessons I learned when I set about implementing Peirce's graphs and Spencer Brown's forms on the computer is that 2‑dimensional representations of logic quickly become death traps on numerous conceptual and computational counts. Still, venn diagrams do us good service at the outset in visualizing the relationships among extensional, functional, and intensional aspects of logic. A facility with those connections is critical to the computational applications and statistical generalizations of propositional logic commonly used in mathematical and empirical practice. All things considered, then, it is useful to make as visible as possible the links between variant styles of imagery in logical representation — and that is what I hoped to do in the sketch of Differential Logic outlined below. Note. I'll give just the links to the main topic heads below. Please follow the link at the top of the page for the full outline. Introduction • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Introduction Cactus Language for Propositional Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_f… Differential Expansions of Propositions • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Differential_Expa… Propositional Forms on Two Variables • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Propositional_For… Transforms Expanded over Ordinary and Differential Variables • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expand… Field Picture • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Field_Picture Differential Fields • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Differential_Fiel… Propositions and Tacit Extensions • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Propositions_and_… Enlargement and Difference Maps • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Enlargement_and_D… Tangent and Remainder Maps • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Tangent_and_Remai… Resources — Logic Syllabus • https://inquiryintoinquiry.com/logic-syllabus/ Survey of Differential Logic • https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/ Regards, Jon cc: https://www.academia.edu/community/546xOz cc: https://www.researchgate.net/post/Differential_Logic_Overview

6 months, 3 weeks

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Differential Logic

by Jon Awbrey

Differential Logic • 1 • https://inquiryintoinquiry.com/2024/10/30/differential-logic-1-a/ Introduction — Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition that broad naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component governs the use of a “differential logical calculus”, that is, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse. Simple examples of differential logical calculi are furnished by “differential propositional calculi”. A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe. Such a calculus augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes. Resources — Survey of Differential Logic • https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/ Regards, Jon cc: https://www.academia.edu/community/lJX2qa cc: https://www.researchgate.net/post/Differential_Logic_The_Logic_of_Change_an…

6 months, 3 weeks

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Re: [ontolog-forum] Accelerating Knowledge Graph and Ontology Engineering with Large Language Models

by John F Sowa

Pascal, I just read your paper (cited below). I agree that LLM technology is good for finding important and valuable information. But as you know, there are serious issues about evaluating that information to avoid irrelevant, erroneous, or even hallucinogenic data. I didn't see much attention devoted to evaluation and testing. As I often mention, our old VivoMind company was doing large volumes of high-speed knowledge extraction, analysis, evaluation, and processing over 20 years ago. For a description of that system with some examples of large applications, see https://jfsowa.com/tallks/cogmem.pdf . The systems described there are just a small sample of the applications, since our customers do not want their data or methods publicized. I also noticed that you are using OWL for ontology. We use a high-speed version of Prolog, which is much richer, more powerful, and faster than OWL, which implements a tiny subset of the logic that Tim Berners-Lee had proposed for the Semantic Web. Some of our customers were among the sponsors of the IKRIS project, funded from 2004 to 2006, to support a much larger and more powerful version of what Tim BL had proposed. For an overview of IKRIS with links to some of the original publications, see https://jfsowa.com/ikl . The IKL technology does not replace LLM, but it is valuable for evaluating the results generated by LLM, detecting errors and avoiding irrelevant, erroneous, or even hallucinogenic data. When processing high volumes of data at high speed, human checking is not possible. High quality computer checking is necessary to eliminate 99% or more of the bad or even dangerous data. Human checking would only be required for the tiny percentage of data for which the computational methods are uncertain. For a more recent talk, see https://jfsowa.com/talks/eswc.pdf . John ---------------------------------------- From: "Pascal Hitzler' via ontolog-forum" <ontolog-forum(a)googlegroups.com> Given the currently ongoing ISWC2024 conference and all the discussions around this neurosymbolic topic: Link to our (with Cogan Shimizu) position paper on this: https://kastle-lab.github.io/assets/publications/2024-LLMs4KGOE.pdf The developments are really exciting! Pascal.

7 months

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A cosmic speed limit?

by John F Sowa

Interesting question. John ____________________ There may be a cosmic speed limit on how fast anything can grow Alan Turing's theories about computation seem to have a startling consequence, placing hard limits on how fast or slow any physical process in the universe can grow https://www.newscientist.com/article/2454024-there-may-be-a-cosmic-speed-li… A newly proposed cosmic speed limit may constrain how fast anything in the universe can grow. Its existence follows from Alan Turing’s pioneering work on theoretical computer science, which opens the intriguing possibility that the structure of the universe is fundamentally linked to the nature of computation. Cosmic limits aren’t a new idea. While studying the relationship between space and time, Albert Einstein showed that nothing in the universe can exceed the speed of light, as part of his special theory of relativity. Now, Toby Ord at the University of Oxford is proposing a new physical limit based on computation. “I had the seed of this idea more than 20 years ago,” he says. “It would apply to any quantity you can directly measure, including mass, charge, energy, etc., and even more subtle things like the time intervals between a sequence of events.” . . .

7 months, 1 week

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Information = Comprehension × Extension • Comment

by Jon Awbrey

Information = Comprehension × Extension • Comment 1 • https://inquiryintoinquiry.com/2024/10/11/information-comprehension-x-exten… Re: Information = Comprehension × Extension • Selection 1 • https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-exten… All, Selection 1 ends with Peirce drawing the following conclusion about the links between information, comprehension, inference, and symbolization. ❝Thus information measures the superfluous comprehension. And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension. ❝I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of information.❞ (Peirce 1866, p. 467) At this point in his inventory of scientific reasoning, Peirce is relating the nature of inference, information, and inquiry to the character of the signs mediating the process in question, a process he describes as “symbolization”. In the interest of clarity let's draw from Peirce's account a couple of quick sketches, designed to show how the examples he gives of conjunctive terms and disjunctive terms might look if they were cast within a lattice‑theoretic framework. Re: Information = Comprehension × Extension • Selection 5 • https://inquiryintoinquiry.com/2024/10/09/information-comprehension-x-exten… Looking back on Selection 5, let's first examine Peirce's example of a conjunctive term — “spherical, bright, fragrant, juicy, tropical fruit” — within a lattice framework. We have the following six terms. t₁ = spherical t₂ = bright t₃ = fragrant t₄ = juicy t₅ = tropical t₆ = fruit Suppose z is the logical conjunction of the above six terms. z = t₁ ∙ t₂ ∙ t₃ ∙ t₄ ∙ t₅ ∙ t₆ What on earth could Peirce mean by saying that such a term is “not a true symbol” or that it is “of no use whatever”? In particular, consider the following statement. ❝If it occurs in the predicate and something is said to be a spherical bright fragrant juicy tropical fruit, since there is nothing which is all this which is not an orange, we may say that this is an orange at once.❞ (Peirce 1866, p. 470). In other words, if something x is said to be z then we may guess fairly surely x is really an orange, in short, x has all the additional features otherwise summed up quite succinctly in the much more constrained term y, where y means “an orange”. Figure 1 shows the implication ordering of logical terms in the form of a “lattice diagram”. Figure 1. Conjunctive Term z, Taken as Predicate • https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-1.jpg What Peirce is saying about z not being a genuinely useful symbol can be explained in terms of the gap between the logical conjunction z, in lattice terms, the greatest lower bound of the conjoined terms, z = glb{t₁, t₂, t₃, t₄, t₅, t₆}, and what we might regard as the natural conjunction or natural glb of those terms, namely, y, “an orange”. In sum there is an extra measure of constraint which goes into forming the natural kinds lattice from the free lattice which logic and set theory would otherwise impose as a default background. The local manifestations of that global information are meted out over the structure of the natural lattice by just such abductive gaps as the one we observe between z and y. Reference — Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982. Resources — Inquiry Blog • Survey of Pragmatic Semiotic Information • https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-info… OEIS Wiki • Information = Comprehension × Extension • https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension C.S. Peirce • Upon Logical Comprehension and Extension • https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm Regards, Jon cc: https://www.academia.edu/community/V91eDe

7 months, 2 weeks

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SAP HANA Cloud’s Knowledge Graph Engine for Business Context

by John F Sowa

Simon, I just wanted to add a note about history. From the Wikipedia page about Klaus Tschira: "After gaining his Diplom in physics and working at IBM, Tschira co-founded the German software giant SAP AG in 1972 in Mannheim, Germany." While he was at IBM, he read a copy of my Conceptual Structures book. He didn't use conceptual graphs, but he applied some of the topics in the book to the technology he used to found SAP. He later invited me to visit the research center he founded in Heidelberg. I recommended some issues about ontology, which led him to organize an invited conference on ontology at his center.. Various participants in that conference later subscribed to Ontolog Forum and worked on ISO standards projects for Common Logic and ontology.. This is one of many reasons why the 60+ years of symbolic AI is ESSENTIAL for practical and non-hallucinogenic applications of LLMs. John ---------------------------------------- From: "Polovina, Simon (BTE)' via ontolog-forum" <ontolog-forum(a)googlegroups.com> Hi all! Connecting the Facts: SAP HANA Cloud’s Knowledge G... - SAP Community may interest you. Combining knowledge graphs with LLM as a commercial product by the business computing market leader, SAP. Simon Dr Simon Polovina Department of Computing, Sheffield Hallam University

7 months, 4 weeks

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Re: [ontolog-trustee] Trying to develop a proper useful topic for the 2025 summit

by John F Sowa

Gary, The word 'limits" sounds negative. That is why I recommend a positive way of describing the distinction of continuous and discrete representations. 1. The mapping to and from the world depends of continuous representations, such as differential equations and an ope-ended variety of technologies for mapping information about the world for many kinds of applications. 2. Various kinds of diagrams and graphs represent discrete models of the world and things in it. Mappings of those representations to and from computable forms may use various kinds of formal logics. 3. Natural languages can represent anything that humans experience, think, plan, do, or intend to do. Therefore, they should be able to represent anything and everything in #1 and #2.at any level of precision or approximation. The top two lines describe the continuous and discrete. The third line shows how and why people can describe both sides while using their native language. An important point about using NLs for discussing formal topics: : Every textbook on logic defines the subject by sentences in some NL. Therefore it is possible (but not easy) to talk precisely about formal methods. However, it is too easy to slip into vagueness. The exercise of mapping NLs to a forma logic forces humans to be absolutely precise. But many people don't know how to do that. Therefore, it's important to develop interactive tools to aid in the translation. John. ---------------------------------------- From: "Gary Berg-Cross" <gbergcross(a)gmail.com> Sent: 10/18/24 1:48 PM To: ontolog-trustee(a)googlegroups.com Cc: ontolog-forum <ontolog-forum(a)googlegroups.com>, CG <cg(a)lists.iccs-conference.org> Subject: Re: [ontolog-trustee] Trying to develop a proper useful topic for the 2025 summit With John's points as background I suggest that the way to frame a workable summit topic would be to explore the current and likely limits to useful formalization. Gary Berg-Cross Potomac, MD 240-426-0770

8 months

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Two sides of representation (was Tools for modeling in first-order logic

by John F Sowa

Alex, I have been trying in many different ways to explain why your proposal, if accepted, would be the DEATH of science. Fortunately, no expert in any branch of science would accept it. The following slide from https://jfsowa.com/eswc.pdf explains the issues: Your proposal is a plan for relating discrete models, as represented by the diagram in the center, to formal notations, such as first-order logic or variations. By itself that is a good idea. But it ignores the much more difficult left side of the diagram. Physics is the most fundamental of the sciences. Physicists do NOT use formal logic to express their theories. They use many dimensional differential equations. Those theories represent a CONTINUOUS universe and everything in it. As I have been trying to explain, vagueness in natural language is not bad. It's ESSENTIAL in order to relate, explain, and communicate information about the world, our relationships to the world, and our actions in, on, and about the world and everything in it. As engineers say, all those explanations are false in general, but they can be made as precise as required within a level of tolerance that is appropriate for the application. That fact is the reason why systems such as WordNet. Roget's Thesaurus. and ordinary dictionaries are useful for analyzing and reasoning with and about NL information. By being vague, those systems can accommodate the vague statements that occur in all NL documents and communications. Any attempt to map vague statements to FOL or other logic is guaranteed to be false UNLESS the error bounds are explicitly stated and accommodated. If the error bounds are unknown, it's much better to preserve the NL source unchanged. In conclusion, I recommend the eswc.pdf slides. Since they were presented in 2020, they do not mention LLMs. But every sentence derived from NL statements is vague, and the context and information about error bounds is lost. Therefore, no statements derived by LLMs can be trusted unless the error bounds of the source data are known. if the sources are unknown, some system of evaluation is essential. Otherwise, anything LLMs produce must be considered as hypotheses that must be tested and evaluated by some method that uses the above diagram as a prerequisite and guide. John ---------------------------------------- From: "alex.shkotin" <alex.shkotin(a)gmail.com> John, The theory framework and task framework are proposed to be global: one for all and crowdsourced. Having a hypothesis in the former or a task without solution in the latter, anybody around the World can propose her solution. It would be checked by algorithms and, if the answer would be OK, added to the framework. This is how science and technology should concentrate their knowledge on the Internet era. Any R&D community from Wolfram Foundation to the lab of enthusiasts can start a framework. Welcome. And after some time OMG or ISO will release a standard ⚗️ Alex

8 months

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Re: [ontolog-forum] Tools for modeling in first-order logic - making conceptual/ontological models in FOL

by John F Sowa

Alex, Before you make any proposals about methods of formalizing anything, please study the work that the international organizations have been doing for many years. I worked with some of those organizations as a representative of IBM (30 years ago), and later when I was working with some start-up companies. They have some very good people working on those standards, and the specifications they produce are actually IMPLEMENTED in working systems. They are much more than email notes, which people delete after a few days. Alex: whether it will be a language from the DOL family or Python is the choice of enthusiasts. No. Emtjusiasts are amateurs. Some of them may be very intelligent amateurs, but anything they do vanishes when they get bored with it. DOL is an professional standard by the Object Management Group (OMG), and it supports other standards by International Standards Organisation (ISO), and the Semantic Web. Those organizations develop standards that are adopted and implemented by professionals for software that is used by thousands or even millions or billions of people. Following is a reference from my previous note. I urge you to follow the links to the work by PROFESSIONALS in slides 8 to 11 of https://jfsowa.com/talks/eswc.pdf John ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> JFS:"To Alex: There is no need for you (or anybody else) to lean Python. With the DOL standard, any syntax that conforms to the ISO standard for Common Logic can be automatically translated to and from any syntax that can express FOL or many subsets and supersets of FOL. That includes OWL, Turtle, UML, and even TPTP (Thousands of Problems for Theorem Provers)." The situation is just the opposite. Formalization of a unit of knowledge (in this case, two theorems) can be placed in the framework of the theory (exactly this one!) in any language. The main thing is that there are enthusiasts who undertake to formalize this particular theory in this particular formal language. And whether it will be a language from the DOL family or Python is the choice of enthusiasts. The beauty of formalizing a unit of knowledge is that they are usually small (definitions can be several sentences long), of course, except for proofs that can take up terabytes (but in this case it's initially formal). The main thing is that the new unit is consistent with those already in the framework. This structure of the framework of the theory is known but not simple........

8 months

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Re: [ontolog-forum] Tools for modeling in first-order logic - making conceptual/ontological models in FOL

by John F Sowa

Chris P, Chris M, and Alex, There is no reason why you need to standardize on one specific notation for everybody. The ISO standard for Common Logic was designed with an ABSTRACT SYNTAX, which allows any number of concrete syntaxes, linear or diagrammatic. Since Python is a procedural language, I'm sure that some data-like subset of Python was used to represent the data model. Ideally, that subset should be designed to conform to the CL abstract syntax. In fact, the DOL standard by the Object Management Group supports translation among an open-ended variety of concrete syntaxes. To Alex: There is no need for you (or anybody else) to lean Python. With the DOL standard, any syntax that conforms to the ISO standard for Common Logic can be automatically translated to and from any syntax that can express FOL or many subsets and supersets of FOL. That includes OWL, Turtle, UML, and even TPTP (Thousands of Problems for Theorem Provers). I discussed those options in my ESWC slides, for a talk at the 2020 European Semantic Web Conference. See the references in slides 8 to 11 of https://jfsowa.com/talks/eswc.pdf Those four slides and the references they contain, answer the basic questions. But you can continue to read more slides and references for more background information. Bit remember that slides 8 to 11 are sufficient to support FOL. John _________________________________________ From: "Chris Partridge" <partridge.csj(a)gmail.com> @chris_mungall - apologies if you answered earlier, but what 'format' are you using to input the FOL axioms? TPTP? CLIF? (The reason I'm asking is we did some work a while ago and we found it useful to have a more human-readable input format - we went with CLIF using an EBNF grammar approach to read - converted to an internal model then output in whatever format needed - often TPTP for e.g. Vampire. One of the design questions that came up was what was the best way to consume (effectively unstructured) text FOL 9e.g. a csv) at scale - and then what a common data structure that could output a variety of formats would look like.)On Fri, 11 Oct 2024 at 19:32, Chris Mungall <cjmungall(a)lbl.gov> wrote: Thanks Alex! To be clear, the reasoning is typically not done in Python. Python acts as the glue. Many developers use Python to specify data-models, but these data models are usually accompanied by complex procedural code for both validation and inference. The idea is to use Python syntax to encode FOL axioms for these data models (not dissimilar to using OCL with UML, or a rules language alongside Frames), and then to seamlessly run reasoners/solvers directly from Python (although these are carried out by integrations, e.g. clingo, souffle, Prover9, Z3). I chose the paths/graphs examples because it's familiar to both ordinary developers and is a staple of datalog documentation, but of course more sophisticated theories are possible. On Fri, Oct 11, 2024 at 1:53 AM alex.shkotin <alex.shkotin(a)gmail.com> wrote: Chris, Never heard that reasoning can be done in Python. Too bad I don't know Python. I'll do it and make a line for it in the ugraph theory framework when I get to paths. Path has a rather subtle definition. And path is an entity on its own where your Path is actually a predicate of path existence. And following [GNaA] 1.3 we have to define "walk" first, then "trail", and then "path" as a property of sequence of vertices and nodes. And your two axioms are theorems in ugraph theory. We have a polymorphic predicate adjacent where you use Link. With definition: rus Пусть v1, v2 - две вершины. v1 смежна v2 еите v1 и v2 являются различными и концевыми вершинами некоторого ребра. eng Let v1, v2 be two vertices. v1 is adjacent to v2 iff v1 and v2 are distinct end vertices of some edge. yfl declaration adjacent func(TV vertex vertex) (v1 v2) ≝ (v1≠v2) & (∃e:edge(U) enp(v1 e) and enp(v2 e)). Calculation on the model of logical formulas is clear to me. Especially if we specify how to encode quantifiers, but I'll definitely look at reasoning. Very interesting! Alex [GNaA] Graphs, Networks, and Algorithms. M. N. S. Swamy, K. Thulasiraman. Wiley, 1981. четверг, 10 октября 2024 г. в 04:40:01 UTC+3, Chris Mungall: Most developers these days are familiar with Python. I have been tinkering with an approach that allows existing Python data models (expressed using pydantic, sqlmodel, sqlalchemy, or linkml) to be enhanced with arbitrary FOL axioms. There are integrations with FOL solvers, and also with datalog and ASP engines (for programs that have the requisite expressivity), and soon OWL reasoners. There is also some preliminary LLM integration too. Comments welcome: https://py-typedlogic.github.io/ On Wed, Oct 9, 2024 at 12:42 AM 'Knowledge representation' via ontolog-forum <ontolo...(a)googlegroups.com> wrote: What user-friendly* tools capable of handling full first-order logic do you know? What tools can you build a conceptual model, ontology in FOL? What is a stack for: translating natural language sentences into FOL and then FOL to a computable language? If you refer to a particular FOL computable language, such as KIF, CL, or otherwise, what tools can easily help make an ontology formalized in the given langauge? (for all questions: in an ontology-neutral way = without committing to any ontology. So no tools that force the user to use the terms of some ontology) *For non-technical / non-computer scientists. Thanks -- All contributions to this forum are covered by an open-source license. For information about the wiki, the license, and how to subscribe or unsubscribe to the forum, see http://ontologforum.org/info --- You received this message because you are subscribed to the Google Groups "ontolog-forum" group. To unsubscribe from this group and stop receiving emails from it, send an email to ontolog-foru...(a)googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/ac5c66d7-6ea7-4554-9cad-507…. -- All contributions to this forum are covered by an open-source license. For information about the wiki, the license, and how to subscribe or unsubscribe to the forum, see http://ontologforum.org/info --- You received this message because you are subscribed to the Google Groups "ontolog-forum" group. To unsubscribe from this group and stop receiving emails from it, send an email to ontolog-forum+unsubscribe(a)googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/22a5fd29-f005-40f5-bcdd-202…. -- All contributions to this forum are covered by an open-source license. For information about the wiki, the license, and how to subscribe or unsubscribe to the forum, see http://ontologforum.org/info --- You received this message because you are subscribed to the Google Groups "ontolog-forum" group. To unsubscribe from this group and stop receiving emails from it, send an email to ontolog-forum+unsubscribe(a)googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/CAN9Aifs6%3Dqnga%3DH%3D0rw-… contributions to this forum are covered by an open-source license.For information about the wiki, the license, and how to subscribe or unsubscribe to the forum, see http://ontologforum.org/info --- You received this message because you are subscribed to the Google Groups "ontolog-forum" group. To unsubscribe from this group and stop receiving emails from it, send an email to ontolog-forum+unsubscribe(a)googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/CAMWD8MrFo2LNNPa9f0fi6BegQK….

8 months

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