All models are wrong, but some are useful.

[John F Sowa]

Alex,

Every program on a digital computer is FORMAL.  It is impossible to write an informal program for a computer whose only commands are to insert, delete, move, and modify strings of bits.

The most difficult part of ontology is the analysis and understanding of the subject matter and determining what are the most significant parts that must be related to one another.  And it always begins with an INFORMAL understanding drawn with pictures and diagrams or stated in an informal natural language. 

That is the hardest, most difficult part of any project.  As soon as that part has been clearly expressed in pictures and/or language, the formal part becomes much,  much easier.

As an example, consider Einstein imagining a train going faster and faster until it approaches the speed of light.  That INFORMAL image was the key that led him to determine the primitive ideas and the various ways to relate them to one another.  Only AFTER he had identified the basic patterns and their relations in an informal movie in his head could he see the importance of the speed of light and its relationship to matter and energy:  Energy E equals the product of the matter m times the square of the speed of light c.

The informal image of the high-speed train comes first. Informal ontology (identifying the critical features E, m, and c) comes next.  And the formal equations that relate the parts come last.

Note the slogan in the title line.   The mental model of a high-speed train was certainly WRONG in the sense that there was no way that anybody could build such a train.  But is was USEFUL in helping Einstein determine what features were relevant, how to represent them, and how to think about the relationships.

The word 'think'  is important.  We must first think about the subject in pictures and diagrams.  That gives us the a vision of the relevant parts and relationships.  The next step is to translate those images to words related by informal sentences.  Formalization is the final step.

Ontology is a very early stage when the parts of the image or diagram are being identified.  That is an INFORMAL ontology.   The formal ontology comes at the end, after the theoretical work has been done, and it has been tested by experiments.  It is never the beginning.

John

 

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From: "Alex Shkotin" <alex.s...@gmail.com>

John,

Formalization, that is, the construction of formal theories and mathematical objects, structures as their models, is a very specific activity. Formalizers are not satisfied with even an axiomatic theory, for example, in the form in which Hilbert wrote it for geometry. And they will not rest until they write out all its axioms, definitions, theorems, proofs in some formal language: Isabell, Coq, HOL4 etc.

Surprisingly, this topic is close to our community, since the formal part is a significant innovation in our ontologies, without which they would be just explanatory dictionaries, reference books.

Usually our ontologies contain mainly theoretical propositions, but often, especially in the form of knowledge graphs, they also contain a bunch of facts, i.e. a model of the theory.

But the formalization approach is that some scientific or engineering text is taken and formalized.

For example, I can formalize your reasoning about building a bridge, or about banking.

However, usually a textbook or an article or an engineering report is taken.

One of the fundamental questions: what mathematical objects, systems of objects do we use as models of our theories and how do we connect them with reality. Of course, this is done with some practical purpose.

There are many interesting topics here.

Alex

[Alex Shkotin]

John,

Let's consider the classical process of cognition: from phenomenon to theory, its experimental verification and logical-mathematical notation.

Informal ontology uses a universal language intended for the phenomenology of matter. This language is deeply geometric, and it is not only about figures but also about their movement and change of shape, where it already serves for mechanics, namely in kinematics.

But our modern ontologies contain knowledge that is part of theories, and not just descriptions of phenomena incomprehensible to us.

Thus, they formalize theories, as you said "the theoretical work has been done".

It turns out that taking ontologies, for example, in OBO Foundry, we have to find out which theories are formalized there and where these theories are presented.

And why, in fact, was it not possible to formalize these theories directly? Without constructing quite large artifacts somewhere separately.

Let's take a textbook on genomics and formalize it.

This is the main idea of (PDF) Theory framework - knowledge hub message #1: only its basic units of knowledge are extracted from the theory: axioms, definitions,  theorems, and proofs. It is this treasure that is formalized. And this does not include any thought experiments, even Einstein's. Because there are so many talks, interpretations and popularizations around this treasure that formalizing it all would take a lot of time and effort. For example, here is how Grok talks about Einstein's early thought experiments [1].

Fortunately, there is no need to formalize everything.

Luckily (PDF) English is a HOL language message #1X

Alex

[1] https://grok.com/share/bGVnYWN5_5a71b5d4-6523-40d2-ae09-ff403c29f94f 

"What were Einstein's earliest thought experiments regarding the motion of bodies near the speed of light?

Einstein began contemplating the motion of bodies at speeds close to the speed of light as a teenager. His earliest thought experiment, conceived around the age of 16 (circa 1895), involved imagining himself chasing a beam of light. He pictured himself riding a bicycle or moving parallel to a light beam at the speed of light. According to classical physics, the light beam should appear stationary relative to him, like a standing wave. However, this contradicts Maxwell's equations, which state that electromagnetic waves (light) always propagate at the speed of light, c (approximately 300,000 km/s), in a vacuum, regardless of the motion of the source or observer.

This paradox led Einstein to question classical notions of time and space, ultimately contributing to the formulation of the special theory of relativity in 1905. Another related early thought experiment involved a mirror: if an observer moves at a speed close to c while holding a mirror in front of them, they should see their reflection normally, as light from their face reflects back to them. Yet, for a stationary observer, this would seem impossible without violating the principle of the constancy of the speed of light.

These ideas were foundational and preceded later thought experiments, such as the scenario with a train and lightning bolts, which illustrated the relativity of simultaneity.

"

пт, 5 сент. 2025 г. в 23:04, John F Sowa <so...@bestweb.net>:

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[John F Sowa]

Alex and Ravi,

Your notes get into many complex issues.  I don't have the time right now to go into detail, but I recommend the talk I presented at the 2020 European Semantic Web conference:  https://jfsowa.com/talks/eswc.pdf .

Slide 4 shows three "Layer Cakes":  (1) The original requirements by DAML in early 2000.  (2) The winning proposal by Tim Berners-Lee in October 2000,  (3) The final version in 2005.

If you notice, both #1 and #2 have a big double arrow for logic, which is called SWeLL (Semantic Web Logic Language) in #2.   But in 2005, that big arrow became a little green box.  SWeLL became Common Logic, and the little green box became OWL.

Slide 7 shows the mapping among all the logics.  The Hets toolkit (and other software) implements those mappings.

Slides 21 and later discuss the mappings to and from natural languages.

Slides 29 and later discuss metalangage (language about language) and metadata (data about data),

Slide 31 is a cartoon that illustrates the kinds of metalanguage.

Slide 34 discusses the transition from human perception to human cognition.  The following slides go into some detail about the neuropsychology,  They compare machine learning to human learning.

The latest AI work with LLMs goes beyond the older machine learning, but it is still very far from true human learning.  LLMs, by themselves, cannot do any of the logical reasoning in the previous slides.  It/s essential to combine LLMs with the logical methods described in the previous 33 slides.

Slides 53 and 54 talk about the future.  LLMs improve the mappings to and from natural languages.  But by themselves, LLMa are very flaky with reasoning,   Neurosymbolic hybrids are essential.  That is the most important research area today.

John