IT-ontology. one more definition
alex.shkotin
Colleagues,
Before adding this definition to our glorious list https://ontologforum.org/index.php/Ontology(IT), please criticize it. I hope it will be useful.
Definition FTD26.
IT ontology is a formal theory that uses data.
◽
Explanation. Let's divide formal theories into three types:
- those that provide definitions of certain data, including methods for working with them. For example, any formalization of arithmetic, from Peano to Presburger and so on, allows for working with natural numbers.
- those that use data and consider its definitions to be known, such as virtually any applied ontology in OWL2, RDF(S), and other Semantic Web languages. For natural numbers, there is xsd:NonNegativeInteger.
- those that do not use any data, such as any formalization of Euclidean geometry, such as Geocoq.
The IT community has spontaneously adopted the inspiring term "ontology" for formal theories of the second type, and it's not customary to add "formal" to them.
The advantage of this definition over others (https://ontologforum.org/index.php/Ontology(IT)), including "specification of conceptualization," is that it takes us directly to mathematics, or more precisely, mathematical logic, and all we have to do is agree on what data is. Otherwise, we would need to define "specification" and "conceptualization," and so on.
For reference:
Definition FT26.
A formal theory is a finite system of interconnected axioms, definitions, rules of inference, theorems (hypotheses), and proofs.
◽
Note. If we put two unrelated theories together in one place, we will not get a new theory.
Alex
alex.shkotin
Chris Partridge
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Frank Guerino
Hi Alex,
Could you please provide more specifics about your phrase: “IT ontology is a formal theory that uses data.” I ask for this clarification because your statement 1) seems incomplete, and 2) it seems to stray from the “noun form” of how the word ontology is defined by all major dictionaries.
As a reminder and in advance of the dictionary definitions for the word Ontology that I provide further below, here are the explanations of Uncountable and Countable Nouns:
Uncountable Nouns (Mass Nouns): An uncountable noun refers to something that is viewed as a whole mass, a broad concept, or an abstract idea. It cannot be counted with numbers or split into individual pieces.
- Grammar Rules: You cannot make it plural (no "-s" at the end). You do not use "a" or "an" with it. You use words like "some" or "much."
- General Examples: Water, air, information, happiness, music.
- The "Ontology" Connection: When used philosophically, ontology is uncountable. It is an abstract field of study. You would say, "He/she is studying ontology," not "He/she is studying an ontology."
Countable Nouns: A countable noun refers to something that exists as a distinct, separate entity. It can be counted as individual items.
- Grammar Rules: It can be singular or plural. You can use numbers before it, and you can use "a" or "an" with the singular form.
- General Examples: Apple (two apples), car (three cars), book (a book).
- The "Ontology" Connection: When used in computer science, ontology becomes countable because it refers to a specific, digital map or document. You can build an ontology for a medical system, combine it with a second ontology, and end up with two ontologies.
The definitions of Ontology from the most notable dictionaries…
According to Merriam-Webster:
- Philosophical Definition (Uncountable Noun):
- A branch of metaphysics concerned with the nature and relations of being.
- A particular theory about the nature of being or the kinds of things that have existence.
- Technical / Systemic Definition (Countable Noun):
- (Does not list a computer science definition in its primary entry.)
Oxford English Dictionary / Learner's:
- Philosophical Definition (Uncountable Noun):
- A branch of philosophy that deals with the nature of existence.
- Technical / Systemic Definition (Countable Noun):
- (In computing) A list of concepts and categories in a subject area that shows the relationships between them.
Cambridge Dictionary:
- Philosophical Definition (Uncountable Noun):
- The part of philosophy that studies what it means to exist.
- Technical / Systemic Definition (Countable Noun):
- (Provides no technical/systemic definition but lists secondary corpus examples for computer systems, but the primary definition is strictly philosophical.)
- Formal Representation: Developing ontologies for standardizing engineering requirements, including modeling material-flow processes.
- System Automation: Utilizing ontologies to automatically evaluate requirement statement quality.
- Content Modeling: Defining core ontology classes through grammatical functions and representing domain discourse for semantic meaning.
- Design & Management: Extending existing plan ontologies, combining multiple ontologies, utilizing taxonomies as "lightweight" models, and implementing ontology managers.
Collins Dictionary:
- Philosophical Definition (Uncountable Noun):
- The branch of metaphysics dealing with the nature of being, reality, or ultimate substance.
- A particular theory about being or reality.
- Technical / Systemic Definition (Countable Noun):
- (In logic / British English entry) The set of entities presupposed by a theory.
I would offer that, from these definitions, we can derive a somewhat more combined and comprehensive definition of “IT Ontology” to be (from Oxford’s & Collins’ definitions) a list of concepts and categories representing the set of entities in the subject area of Information Technology (IT) that shows and explains the relationships between them, supported by secondary corpus examples such as but not limited to Formal Representation, System Automation, Content Modeling, and Design & Management. (Further noting that no one person or group has ever been able to define the full list, set, set or structure due to its vastness and complexities.)
I would further offer that even this definition is too incomplete, as it does not cover key concepts like “forms, permutations, tenses, uses, rules, interactions, and anti-patterns,” which I personally believe should be explicit in the definition.
I hope this helps,
Frank
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Frank Guerino, Principal
The International Foundation for Information Technology (IF4IT)
http://www.if4it.com
1.908.294.5191 (M)
Guerino1_Skype (S)
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Alex Shkotin
Chirs,
Let me point to this passage from remarks on definition FTD26:
"The advantage of this definition over others (https://ontologforum.org/index.php/Ontology(IT)), including "specification of conceptualization," is that it takes us directly to mathematics, or more precisely, mathematical logic…"
The question you raised
"I would expect an IT Ontology to be executable, in the sense it should be capable of directly running on a computer - maybe even stored on a computer that could execute it in some way."
is applicable to any math object and procedure: Is that possible to keep them in computer and work with. And if we find a way we are happy. And yes, we can store and process IT Ontology in computers, as well as we can do this with natural numbers, and string of characters and pictures.
So, keeping in mind symbolic processing I think "formal theory" subsumes using computers to keep and process.
If you think we need this kind of note, please, give me one to add.
By the way I am adding the Note about derivation rules.
Alex
TEXT-2
PRELIMINARES
Definition FT26.
A formal theory is a finite system of interconnected axioms, definitions, rules of inference, theorems (hypotheses), and proofs.
terminology. The "derivation rule" is a SYNONYM to "rule of inference".
◽
Note about interconnection. If we put two unrelated theories together in one place, we will not get a new theory.
MAIN COURSE
Definition FTD26.
IT ontology is a formal theory that uses data.
◽
Explanation. Let's divide formal theories into three types:
- those that provide definitions of certain data, including methods for working with them. For example, any formalization of arithmetic, from Peano to Presburger and so on, allows for working with natural numbers.
- those that use data and consider its definitions to be known, such as virtually any applied ontology in OWL2, RDF(S), and other Semantic Web languages. For natural numbers, there is xsd:NonNegativeInteger.
- those that do not use any data, such as any formalization of Euclidean geometry, such as Geocoq.
The IT community has spontaneously adopted the inspiring term "ontology" for formal theories of the second type, and it's not customary to add "formal" to them.
The advantage of this definition over others (https://ontologforum.org/index.php/Ontology(IT)), including "specification of conceptualization," is that it takes us directly to mathematics, or more precisely, mathematical logic, and all we have to do is agree on what data is. Otherwise, we would need to define "specification" and "conceptualization," and so on.
Note about derivation rules. Usually a particular IT ontology does not keep derivation rules in. And we should read documentation, so called "semantics", or count on processing algorithms, so called "reasoners", directly.
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/CAMWD8MqLatx2qWmoHkawVnpiXfMdBbvkqr89coLvOv4M%2BdyXzw%40mail.gmail.com.
Alex Shkotin
Hi Frank,
It is very useful to keep definition separately from other text, like this
definition FG26
IT-ontology is a list of concepts and categories representing the set of entities in the subject area of Information Technology (IT) that shows and explains the relationships between them, supported by a secondary corpus.
◽
Note about "secondary corpus". secondary corpus examples such as but not limited to Formal Representation, System Automation, Content Modeling, and Design & Management. (Further noting that no one person or group has ever been able to define the full list, set, set or structure due to its vastness and complexities.)
END OF TEXT
I am ready to add your definition to our collection https://ontologforum.org/index.php/Ontology(IT) if you wish.
But I'm confused by the phrase "representing the set of entities in the subject area of Information Technology (IT)"—the subject area of IT-ontology could be any area where we have theoretical knowledge. This could include genomics (GENO), chemistry (ChEBI), and hundreds, if not thousands, of other sciences and technologies.
The basic idea is that if we have theoretical knowledge, we can formalize it.
This formalized knowledge is called ontology in IT.
It is important that we are not discussing all the terminology used in IT, but only how the term ontology is used in IT.
Thanks for your help,
Alex
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/2F23D32B-D878-410D-A79F-C48A6FB69CDC%40if4it.com.
Maxwell Gillmore
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Frank Guerino
Hi,
My interpretation of Chris’ statement about the ontology being “executable” (and I may be wrong about this) is that he’s implying that the ontology must be reified into some technology-consumable form for use within systems.
Consider that many businesses existed long before computers and the language they used before computers was that of an unformalized ontology that had yet to be formalized/reified for computer-related use.
Frank
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Frank Guerino, Principal
The International Foundation for Information Technology (IF4IT)
http://www.if4it.com
1.908.294.5191 (M)
Guerino1_Skype (S)
From: Ontolog Forum <ontolo...@googlegroups.com> on behalf of Maxwell Gillmore <maxwellr...@gmail.com>
Reply-To: Ontolog Forum <ontolo...@googlegroups.com>
Date: Saturday, June 13, 2026 at 6:29 AM
To: Ontolog Forum <ontolo...@googlegroups.com>
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/CAA3BDEB-57B9-45D1-A2E4-4BB82D285A89%40gmail.com.
Frank Guerino
Hi Alex,
You wrote: “But I'm confused by the phrase "representing the set of entities in the subject area of Information Technology (IT)"—the subject area of IT-ontology could be any area where we have theoretical knowledge. This could include genomics (GENO), chemistry (ChEBI), and hundreds, if not thousands, of other sciences and technologies.
The basic idea is that if we have theoretical knowledge, we can formalize it.
This formalized knowledge is called ontology in IT.” END OF TEXT
I agree with you and I think your assertion that the ontology could include hundreds, if not thousands, of other sciences and technologies is accurate and worth some discussion, as I do not know how you might want to represent this in your definition (if at all).
To make the conversation easier, let’s say there is a baseline IT-only Ontology that is founded on a baseline IT-only Taxonomy, which is the list of all things that are only specific to “generic” IT. Think a basic set of technical entities (e.g., Computers, Software, Databases, Applications, Networks, etc.). This Taxonomy-Ontology pair might be adequate for an IT-only company that just sells IT products and/or services.
However, you made the accurate point (using Genomics & Chemistry as examples) that the Taxonomy-Ontology pair could include entities from other such sets. I believe your point highlights the reality that there are (and always will be) industry-specific or domain-specific permutations of “IT.” For example (taking the word “entities” to mean data entities or things)…
- Generic IT Entities = Generic or “IT-only” IT, which uses an IT-only IT Ontology.
- This IT-only Ontology is used by humans to run the IT-only business and in systems to help enable this business.
- Generic IT Entities + Healthcare Payer Entities = Healthcare Payer IT, which uses a Healthcare Payer IT Ontology.
- This Healthcare Payer Ontology is used by humans to run the Healthcare Payer business and in systems to help enable this business.
- Generic IT Entities + Life Sciences & Pharmaceutical Entities (LS&P) = LS&P IT, which uses a LS&P IT Ontology.
- This LS&P Ontology is used by humans to run the LS&P business and in systems to help enable this business.
- Generic IT Entities + Financial Services Entities = Financial Services IT, which uses a Financial Services IT Ontology.
- This Financial Services Ontology is used by humans to run the Financial Service business and in systems to help enable this business.
- the possible permutations are seemingly endless when you think of all unique companies that require custom data and information sets.
- In the “Overview” section of the chapter, we see an image depicting two forms of the same IT-only Taxonomy (foundation for an IT-only Ontology).
- Further down in the “The taxonomy enables model scalability” section of the same chapter, there are three side-by-side Taxonomies, one for each of the industry-specific examples given above. This tries to depict the common IT-only taxonomy entities in grey and the industry-specific taxonomy entities in other colors.
So…
- When we speak of an “IT Ontology” that is in the philosophical uncountable noun form, I believe we are speaking in the abstract form of any one or all possible permutations (above).
- However, when we speak of an “IT Ontology” that is in the technical/systemic countable noun form, I believe we are (casually) assuming it must be only one of the above as it is clear that a Financial Services IT Ontology would be useless to a Healthcare Payer IT company that only cares about the Healthcare Payer language constructs.
In other words, there is 1) an abstract totalitarian concept of an IT Ontology and 2) each domain can have its own IT Ontology that drives its own unique Enterprise Model that allows both common and different knowledge constructs to be derived from it, based on both common and different data & information within each.
I believe the industry/domain-specific examples given above all fall into what I described earlier in the thread to be the secondary corpus examples that lead us to the reality that there is a baseline IT-only Ontology and there can be derived industry-specific or domain-specific IT Ontologies that sit on top of (or possibly inherit) the baseline IT-only Ontology. I do not know how or if this is worth capturing in your documented definition(s).
I suggest having and describing both a definition that addresses 1) the philosophical uncountable noun form and a definition that addresses 2) the technical/systemic countable noun form, as both are valid and may be of value to readers.
I look forward to your and the group’s thoughts and feedback about all this.
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/CAFxxROQb0d3YrD033Lbyj4Lm1QiNsKeQc8djGiP%3DjMW3rBnmEA%40mail.gmail.com.
John F Sowa
Sent: 6/13/26 6:27 AM
Alex Shkotin
Maxwell,
It's usual to spend some time and effort to understand each other.
I think you use "executable ontology" when we use "applied ontology", and you use "descriptive ontology" when we use "reference ontology" or "subject area ontology".
Anyway, please, give me an example of an executable ontology, and how to execute it.
And, Chris, your example would help me greatly.
I know one reference https://browse-export.arxiv.org/abs/2509.09775
But from my point of view the author uses "executable ontology" as a brand name, like Knowledge Graph is used by Oracle Corp.
Interesting talk!
Alex
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/CAA3BDEB-57B9-45D1-A2E4-4BB82D285A89%40gmail.com.
Alex Shkotin
Alex,
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Alex Shkotin
Frank,
Formalization needs to be considered separately. Formulas existed long before computers, and back then, the role of the processor was performed by humans.
I hope Chris and Maxwell will give us an example of an executable ontology. This is the simplest way to delve deeper into the concept: to use it in practice by presenting an entity that fits it.
Alex
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/2A78C391-13AB-42F2-BC75-918C32A07458%40if4it.com.
Alex Shkotin
Frank,
My spontaneous abbreviation "IT-ontology" turned out to be ambiguous. Please consider it equivalent to the abbreviation "ontology(IT)". What is the actual title of our collection https://ontologforum.org/index.php/Ontology(IT)
It stands for:
"ontology (used in the IT/computing sense, not the philosophical one)"
Here are other abbreviations AI suggests:
IT-sense ontology, ontology (IT-specific), computational ontology, ontology in the computing sense
And of course, there are many formal ontologies for various parts of the IT field.
I asked Deepseek, but I haven't verified the answer [1].
Sorry,
Alex
Alex Shkotin
Frank,
The IF4IT approach would be best addressed in a separate thread.
Alex
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/4A44C75D-F7A3-46FD-B281-383BC550BD17%40if4it.com.
Alex Shkotin
John,
The fact that we use multiple theories when discussing the geometry of a car and its parts should be discussed separately. This is one of the most important issues in applying theories in practice.
Since the Note about interconnection raised doubts and even denials, I decided to add a proof. This is now a lemma.
Lemma FT26_L1.
Let T1 and T2 be formal theories. If T1 and T2 are unrelated, then the union of T1 and T2 is not a formal theory.
Proof.
According to the definition of FT26, the union of T1 and T2 should form a single whole, but since these theories are unrelated, they do not form a single whole. They form two single wholes.
◻️
Similarly:
- two pencils placed side by side do not form a single pencil.
- two connected graphs, if unrelated, considered together do not form a connected graph.
Now the section on the proposed definition is as follows [1].
Thanks to our discussion, this section gets better and better,
Alex
[1]
MAIN COURSE
Definition FTD26.
IT ontology is a formal theory that uses data.
◽
Explanation. Let's divide formal theories into three types:
- those that provide definitions of certain data, including methods for working with them. For example, any formalization of arithmetic, from Peano to Presburger and so on, allows for working with natural numbers.
- those that use data and consider its definitions to be known, such as virtually any applied ontology in OWL2, RDF(S), and other Semantic Web languages. For natural numbers, there is xsd:NonNegativeInteger.
- those that do not use any data, such as any formalization of Euclidean geometry, such as Geocoq.
The IT community has spontaneously adopted the inspiring term "ontology" for formal theories of the second type, and it's not customary to add "formal" to them.
The advantage of this definition over others (https://ontologforum.org/index.php/Ontology(IT)), including "specification of conceptualization," is that it takes us directly to mathematics, or more precisely, mathematical logic, and all we have to do is agree on what data is. Otherwise, we would need to define "specification" and "conceptualization," and so on.
Note about derivation rules.
Usually a particular IT ontology does not keep derivation rules in. And we should read documentation, so called "semantics", or count on processing algorithms, so called "reasoners", directly.
PRELIMINARES
Definition FT26.
A formal theory is a finite system of interconnected axioms, definitions, rules of inference, theorems (hypotheses), and proofs.
terminology. The "derivation rule" is a SYNONYM to "rule of inference".
◽
Lemma FT26_L1.
Let T1 and T2 be formal theories. If T1 and T2 are unrelated, then the union of T1 and T2 is not a formal theory.
Proof.
According to the definition of FT26, the union of T1 and T2 should form a single whole, but since these theories are unrelated, they do not form a single whole. They form two single wholes.
◻️
Similarly:
- two pencils placed side by side do not form a single pencil.
- Two simply connected graphs considered together do not form a simply connected graph.
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Maxwell Gillmore
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Maxwell Gillmore
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Chris Partridge
The question you raised
"I would expect an IT Ontology to be executable, in the sense it should be capable of directly running on a computer - maybe even stored on a computer that could execute it in some way."
is applicable to any math object and procedure: Is that possible to keep them in computer and work with. And if we find a way we are happy. And yes, we can store and process IT Ontology in computers, as well as we can do this with natural numbers, and string of characters and pictures.
So, keeping in mind symbolic processing I think "formal theory" subsumes using computers to keep and process.
I read as suggesting that "any math object and procedure" is formal. I think there are some gaps. As I understand it, most current mathematical procedures are formally gappy - not every step is proven. Hence interest in Lean and AI.
Much mathematical proof is given in a language other than predicate logic. I suspect some mathematicians would be happy to call this formal.
Much mathematical proof is in Latex, but this doesn't mean that it's content computer readable - though the file of course is.
Work done in Lean (or tptp) would, in my opinion, be content readable by computers.
So, I think Alex *from what he has said) assumes that it is maths we can store and process it in computers. I suspect the current state of affairs is more nuanced.
It also seems to me odd that there is a dearth of formal grammar standards for predicate logic (CLIF and tptp spring to mind as exceptions) - and how little these are used. I also find it interesting that there are few (or at least I have found few) examples of data structures for logic. I'm guessing one reason is that the problems are trivial.
One of the reasons this tickled my radar is that it links to a wider question about levels of digitalisation - see our outdated presentation ( https://www.academia.edu/89132134/Digitalisation_Levels - there has been a lot of subsequent work) - and the more specific questions about digitalisation in mathematics.
- a speech in which I verbally describe the ontology
- a paper where I write the ontology down
- a paper printed from a document on a computer
- a document on a computer
- a file on a computer where the ontology is stored in a data structure
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Frank Guerino
Hi Alex,
For your consideration in your fashioning of your definition, I respectfully present that an ontology (in the countable noun form) is not a pencil and not a graph but instead a description for how things like pencils and graphs can be reified and exist in computing memory/infrastructure.
- Given what we know about physics and chemistry, two pencils placed side by side can never be combined. The ontology describes how one or more pencils can exist and coexist. Rules within that ontology tell us that solids cannot easily be combined (but there are cases where we can do so, like smelting two distinct gold bars to combine them, thereby creating one common gold bar).
- However, two graphs placed side by side can, in fact, be combined… by a single common node. This is true even if the graphs exist distinctly in two separate computing memory spaces but have common instances. One very common example of this in industry is realized in Mergers & Acquisitions, where two separate companies with separate graphs to represent them decide to merge. Upon doing so, they will immediately have common nodes that will allow their two graphs to become one graph. A common node in any two graphs (e.g., a Vendor instance or a Parental Legal Entity instance) is a natural join point between them. The ontology describes how one or more graphs can exist or coexist. Rules with in that ontology tell us that graphs can easily be merged and combined, with rules for how to do so. This is proven when I have two graphs A->B->C and C->D->E. Each can coexist in separate or common memory spaces, and they can mean separate things with two distinct contexts. The join point of the two distinct graphs that allow them to naturally become one graph and create new meaning (while not losing the meaning of those two distinct contexts) is node C.
Since there is no computer in the world that contains the singular God-Graph as defined by a singular philosophical ontology (in the uncountable noun form), which contains all possible nodes and relationships, we all work with localized reified graph “instances” that are bounded by contexts and that take the form of patterns. I present it is these separate contexts and patterns that allow us to distinctly refer to separate ontology contexts, such as but not limited to: an IT Ontology, a Financial Services Ontology, a Farm Ontology, an English Language Ontology, a Chinese Language Ontology, etc. These contexts tell us the intent and boundaries of what is intended to be reified or what has been reified. In applied practice (e.g., Engineering or Computer Science) where things must be reified to test a theory (i.e., Theoretical Science), the distinction between each contextual type can be determined by comparing the contents of any one reified graph to the contents of any other reified graphs. This pattern supports the integrity of the ontology by allowing repeatable recreations/reifications of different and distinct graph instances that all follow the same rules across different computing infrastructures and that reinforce the ontological definition and its descriptions & rules. In other words, the proof that the design of the ontology is accurate happens when you 1) can repeatably create distinct working representations (i.e., reified instances) of it across separate and distinct computing spaces, such that 2) if we combine what is in multiple spaces, the pattern still holds.
If anyone believes this is incorrect, kindly present me with how and why, and with evidence to support so I may better understand.
My best,
Frank
--
Frank Guerino, Principal
The International Foundation for Information Technology (IF4IT)
http://www.if4it.com
1.908.294.5191 (M)
Guerino1_Skype (S)
From: Ontolog Forum <ontolo...@googlegroups.com> on behalf of Alex Shkotin <alex.s...@gmail.com>
Reply-To: Ontolog Forum <ontolo...@googlegroups.com>
Date: Sunday, June 14, 2026 at 6:33 AM
To: Ontolog Forum <ontolo...@googlegroups.com>
Cc: CG <c...@lists.iccs-conference.org>
Subject: Re: [ontolog-forum] Re: IT-ontology. one more definition
John,
To view this discussion visit https://groups.google.com/d/msgid/ontolog-forum/CAFxxROTMvkiS6Oxw7aMSQfi-tEQrC9HNs6VxcovXeA_wzE9T7w%40mail.gmail.com.
Frank Guerino
Hi John,
Regarding your statement: “There is no formal way to distinguish an IT ontology from a farming ontology or an ontology for designing automobiles. Some basic axioms may be identical. The only difference would be in some special-purpose axioms for an application.”
I understand and agree with your point and present that it is, at a minimum, such axioms we refer to when we say: a Pharmacy Ontology, a Healthcare Payer Ontology, etc. We provide such labels as identifiers to prove and compare. However, I present that such labeled axioms cross the line into “scoped realizable contexts” that can be realized and measured as separate instantiated constructs (e.g., multiple distinct graphs built in separate computer memory infrastructures) to prove:
- the theories of ontology (in the uncountable noun form) and
- the realizability of an ontology (in the countable noun form).
I present that using the rules of a correctly defined ontology we can do two things to prove the ontology’s accuracy:
- We can successfully build (in computer memory) two separate and distinct realizable instances of a Pharmacy Ontology and a Healthcare Payer Ontology. Each has the same structure but different elements and labels. By nature of their existence as two distinct instances with different measurable and comparable internal elements (such as the types of things in them), they can coexist, be compared to prove they are different, conform to a context, and they can each separately prove the theorems and rules of the ontology definition. What they contain that can be compared helps reaffirm the scope/context of each.
- A point here is that there is a formal way to distinguish between two separate contextual ontologies by the comparison of the elements they are intended to instantiate and contain (pre-synthesis) or by the actual instantiated elements they do contain (post-synthesis).
- We can take both separate and different instances and combine them according to clear rules that would also be part of the same ontology, to create a new super-structure that still conforms to the ontology. The Pharmacy and Healthcare Payer companies can merge, resulting in their graphs combining. The resulting new graph still conforms to the rules of the ontology. This realization further reaffirms the ontology.
I suggest this notion that each instance, separately or combined, proves the design of the ontology is exactly what I’d expect to prove that the design of the ontology is correct. In other words…
- The realized existence of structure A, by itself and which is different than B, proves the accuracy of the ontology.
- The realized existence of structure B, by itself and which is different than A, proves the accuracy of the ontology.
- The realized existence of structure A combined with structure B into a new super-structure still and further proves the accuracy of the ontology.
- NOTE 1: This also still applies if you take A or B and split them into sub structures that conform to the ontology.
In all cases, the distinctly labeled contexts of “A”, “B”, and “A combined with B” are uniquely identifiable and remain distinct while never straying from the ontology that describes them.
I hope this helps clarify where I’m coming from. Please let me know if you think I’m wrong in any way and why.
My best,
Frank
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Frank Guerino, Principal
The International Foundation for Information Technology (IF4IT)
http://www.if4it.com
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From: Ontolog Forum <ontolo...@googlegroups.com> on behalf of John F Sowa <so...@bestweb.net>
Reply-To: Ontolog Forum <ontolo...@googlegroups.com>
Date: Saturday, June 13, 2026 at 11:55 AM
To: Ontolog Forum <ontolo...@googlegroups.com>
Cc: CG <c...@lists.iccs-conference.org>
Subject: Re: [ontolog-forum] Re: IT-ontology. one more definition
Maxwell, Alex, Chris,
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Alex Shkotin
Maxwell,
Thanks for the clarification. I think I understand your terms.
Am I correct in understanding that
-using your terms: a descriptive ontology can very well be executable.
-or not using your terms: "an ontology that describes a particular business domain" can very well be "an ontology over which a reasoner can be run."
I think Description Logics was named that way for a reason.
Of course, for "an ontology that describes a particular business domain," there is a direct term, "domain ontology."
Algorithmic processing methods for formal ontology can be quite diverse, and reasoner is only one of them. Another is, for example, proving algorithms such as those developed for Isabelle/HOL.
I think by descriptive you mean an ontology written in natural language (a document), possibly interspersed with mathematical and other formulas. For me, this is documentation for a formal ontology, which will largely be included in it in the form of comments and annotations. There's a crucial issue here about the current form of theoretical knowledge and how we formalize it.
But theoretical knowledge lies outside of IT; in IT, we merely formalize it. And this formalization is called ontology (IT).
It turns out that every formula in a formal ontology has a natural language counterpart somewhere in the theoretical literature, which serves as its justification.
Many OWL2 ontologies require a reference to the document and the specific location within it where this counterpart is located.
And we find ourselves in a situation where every important theoretical statement is written in several languages, some of which are formal and have reasoners and other processors.
Here [1] is my favorite example of formalization. Incidentally, AI claims that this knowledge is inexpressible in OWL2.
Alex
[1] I21 axiom
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Alex Shkotin
Maxwell,
I propose a broader approach to this topic: we take some theoretical knowledge and examine how formalizable it is. I took graph theory and formalized the first chapter of a treatise. This took quite a long time, and the result is presented as an example of filling out a theoretical framework [1].
The approach here is as simple as it gets: take any document, from a textbook to corporate documentation, and formalize it. Incidentally, in some organizations, calling formalization an ontology is dangerous, as one of the speakers at OS-26 told us.
Alex
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Alex Shkotin
Chris,
I'm glad you delved into mathematics, as a formal theory is a mathematical object and quite complex.
I'll quote a working definition from the section on defining ontology(IT) [1].
Definition FT26.
A formal theory is a finite system of interconnected axioms, definitions, rules of inference, theorems (hypotheses), and proofs.
terminology. The "derivation rule" is a SYNONYM to "rule of inference".
◽
Let me clarify my text based on yours. I am quoting your text in its entirety, with an indent, and my explanations without an indent in <> brackets.
YOUR TEXT
I have replied to the last email in the thread, so we have continuity.
Firstly a reply to Alex, that should hopefully illustrate my concerns.
<This is the beginning of my email citation>
The question you raised
"I would expect an IT Ontology to be executable, in the sense it should be capable of directly running on a computer - maybe even stored on a computer that could execute it in some way."
is applicable to any math object and procedure: Is that possible to keep them in computer and work with. And if we find a way we are happy. And yes, we can store and process IT Ontology in computers, as well as we can do this with natural numbers, and string of characters and pictures.
So, keeping in mind symbolic processing I think "formal theory" subsumes using computers to keep and process.
<the end of my email citation>
I read as suggesting that "any math object and procedure" is formal.
<This suggestion is not correct. Maybe I should put a question mark at the end of the "Is" sentence like this "Is that possible to keep them in computer and work with?" but look at the next sentence: "And if we find a way we are happy." I hope this shows that this is not always the case.
The topic of "any math object and procedure" is subtle and I know at least three mind structures there: intuitionistic (Brouwer), constructive (Markov), classical (Kholmogorov and any mathematician working with these particular objects with these particular procedures).
And your discussion below is a great topic, but is too much generalization of a tiny topic of structure and features of one class of constructive math objects - formal theories.>
I think there are some gaps. As I understand it, most current mathematical procedures are formally gappy - not every step is proven. Hence interest in Lean and AI.
Much mathematical proof is given in a language other than predicate logic. I suspect some mathematicians would be happy to call this formal.
Much mathematical proof is in Latex, but this doesn't mean that it's content computer readable - though the file of course is.
Work done in Lean (or tptp) would, in my opinion, be content readable by computers.
So, I think Alex *from what he has said) assumes that it is maths we can store and process it in computers.
<For me this is an open question and Wolfram's great project is a way to study it. But in any way I think we cannot keep all natural numbers in the computer. So if somebody think about set of natural numbers as the object of her study she cant say in my computer I have it.>
I suspect the current state of affairs is more nuanced.
It also seems to me odd that there is a dearth of formal grammar standards for predicate logic (CLIF and tptp spring to mind as exceptions) - and how little these are used.
I also find it interesting that there are few (or at least I have found few) examples of data structures for logic. I'm guessing one reason is that the problems are trivial.
<"data structures for logic" what is it?>
One of the reasons this tickled my radar is that it links to a wider question about levels of digitalisation - see our outdated presentation ( https://www.academia.edu/89132134/Digitalisation_Levels - there has been a lot of subsequent work) - and the more specific questions about digitalisation in mathematics.
<Great topic but too much semantics for my taste. And I am for formalization in mathematics. As formalized may be put in the computer.
Well, below you are back to ontology and, please, read it substituting "formal theory" instead.>
My point was not to somehow draw a boundary outside of which there are no ontologies. It was more to make a distinction about the level of digitalisation of the ontology.
So, If I produce an ontology, perhaps using logic
a speech in which I verbally describe the ontology
a paper where I write the ontology down
a paper printed from a document on a computer
a document on a computer
a file on a computer where the ontology is stored in a data structure
In the first four cases, if we assume that for the logic and informal, agreed format is used, then for me they are not 'executable', in the sense that a computer cannot directly run computation over the content - as content.
<We should be more specific here: "a computer… directly run computation over the content" means we have an algorithm to process content as a knowledge - another great topic!>
Of course, with OCR and speech recognition and LLMs, it might be easy to convert the format of these to stage 5. (And it might eventually become so easy we don't need the distinction).
<another subtle topic. And in my experience translating from natural language to formal is an act of art, where an output of any algorithm including LLMs must be verified. Except special cases like "domain specific natural languages".>
I also think that much data, with its 'formalised' data structure is a candidate for being an ontology - whether it has a top ontology or is written in a semantic web language.
<But here you touched upon a topic that I only hinted at in the phrase "all we have to do is agree on what data is". And classified as a kind of formal theories: "those that provide definitions of certain data, including methods for working with them. For example, any formalization of arithmetic, from Peano to Presburger and so on, allows for working with natural numbers.">
Hope my point is a bit clearer.
<me too🤝>
As an appendix to this long letter let me add another one [1]
What do you think right now about
"IT ontology is a formal theory that uses data."?
Thanks,
Alex
[1]
Definition FTD26.
IT ontology is a formal theory that uses data.
◽
Explanation. Let's divide formal theories into three types:
- those that provide definitions of certain data, including methods for working with them. For example, any formalization of arithmetic, from Peano to Presburger and so on, allows for working with natural numbers.
- those that use data and consider its definitions to be known, such as virtually any applied ontology in OWL2, RDF(S), and other Semantic Web languages. For natural numbers, there is xsd:NonNegativeInteger.
- those that do not use any data, such as any formalization of Euclidean geometry, such as Geocoq.
The IT community has spontaneously adopted the inspiring term "ontology" for formal theories of the second type, and it's not customary to add "formal" to them.
The advantage of this definition over others (https://ontologforum.org/index.php/Ontology(IT)), including "specification of conceptualization," is that it takes us directly to mathematics, or more precisely, mathematical logic, and all we have to do is agree on what data is. Otherwise, we would need to define "specification" and "conceptualization," and so on.
Note about derivation rules.
Usually a particular IT ontology does not keep derivation rules in. And we should read documentation, so called "semantics", or count on processing algorithms, so called "reasoners", directly.
PRELIMINARES
Definition FT26.
A formal theory is a finite system of interconnected axioms, definitions, rules of inference, theorems (hypotheses), and proofs.
terminology. The "derivation rule" is a SYNONYM to "rule of inference".
◽
Lemma FT26_L1.
Let T1 and T2 be formal theories. If T1 and T2 are unrelated, then the union of T1 and T2 is not a formal theory.
Proof.
According to the definition of FT26, the union of T1 and T2 should form a single whole, but since these theories are unrelated, they do not form a single whole. They form two single wholes.
◻️
Similarly:
- two pencils placed side by side do not form a single pencil.
- Two simply connected graphs considered together do not form a simply connected graph.
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Alex Shkotin
Frank,
Humanity has long and persistently studied nature and itself, and this activity is called scientific. As a result, we have theoretical knowledge in one form or another and have ways to apply it "in practice." In your text, the term "ontology" could easily be replaced with "theory" in the vast majority of places. Moreover, we usually have one or another science that needs to be applied in your examples.
For example,
you: "The ontology describes how one or more pencils can exist and coexist. Rules within that ontology tell us that solids cannot easily be combined (but there are cases where we can do so, like smelting two distinct gold bars to combine them, thereby creating one common gold bar)."
usually:"Physics describes how one or more pencils can exist and coexist. Rules within Physics tell us that solids cannot easily be combined (but there are cases where we can do so, like smelting two distinct gold bars to combine them, thereby creating one common gold bar)."
And then arise a concrete question: in which form theoretical knowledge exists in one or another science and technology? Is that possible to formalize this knowledge, maybe partially? What advantages will this formalization give us?
From this approach you just use special terminology and it's of course up to you.
But, please, look at other terminology. Where we have.
Definition FTD26.
IT ontology is a formal theory that uses data.
◽
Using this classical approach we are not talking about "an IT Ontology, a Financial Services Ontology, a Farm Ontology, an English Language Ontology, a Chinese Language Ontology, etc." We are talking about theoretical knowledge in and about "IT, Financial Services, agriculture, an English Language, a Chinese Language, etc." These are enormous! Can we formalise it?
That's the question.
We may discuss in depth the topic in my favorite undirected graph theory where may be I must write my proposition more carefully:
Let G1, G2 are two simply connected graphs without common nodes then the union of this graph is not simply connected.
I put it into the section this way: "Two simply connected graphs without common nodes considered together do not form a simply connected graph."
Thank you!
IMHO you use the term ontology where it is usual to use the term theory or name of concrete science.
My best,
Alex
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