Understanding ‘Instantiation’ within a Generically Dependent Continuant

[Anthony Petosa]

The BFO 2 documentation states ‘instantiation’  is a relation holding between particulars & universals and is expressed by the ‘instance_of’ relation and its inverse ‘has_instance.’ For continuants, c instance_of C at t means a particular continuant entity c instantiates the universal C at t. Similarly, for occurrents, p instance_of P means a particular occurrent entity p instantiates the universal P. It does not explicitly state that a particular must instantiate one and only universal. I suppose this accounts for the fact that not all BFO ‘categories’ are disjoint. The notable exceptions are the siblings Object, Fiat Object Part & Object Aggregate. For example, depending on the “ontological zoom,’ a particular may instantiate Object at one zoom level and Object Aggregate at another. Otherwise, I assume BFO intends that a given ‘particular’ always directly instantiates one and only one ‘universal.’

Examples:

·       this hammer instance_of Hammer

·       12:15:30 PM EDT today instance_of Temporal Instant

Generically Dependent Continuant means:
              b is a Continuant that g-depends on one or more other entities

b g-depends on c at t₁ means:
              b exists at t₁ and c exists at t₁
              & for some type B it holds that (c instantiates B at t₁)
              & necessarily, for all t (if b exists at t then some instance_of C exists at t)
              & not (b s-depends on c at t₁)

Domain: Generically Dependent Continuant

Range: Independent Continuant

“Specifically Dependent Continuants are subject to the axiom of non-migration – they cannot migrate from one bearer to another. Generically Dependent Continuants, in contrast, can in a sense migrate, namely through a process of exact copying with allows, for example, the very same information artifact to be saved to multiple storage devices...We can think of Generically Dependent Continuants, intuitively, as complex continuant patterns (complex qualities) of the sort created by authors or designers, or (in the case of DNA sequences) through the process of evolution. Further examples of Generically Dependent Continuants include: the chessboard pattern, the Coca Cola logo, the pattern of a traffic sign. Each such pattern exists only if it is concretized in some counterpart Specifically Dependent Continuant – the pattern of black and white squares on this wooden chessboard here before me; the pattern of red and white swirls on the label of this Coca Cola bottle; the pattern of paint on this traffic signboard.” [source: “Basic Formal Ontology 2.0 Specification and User’s Guide”, Smith, Barry (corresponding author), June 26, 2015, pp.63-64.]

This makes sense, but I have difficulty understanding how instantiation is treated by a Generically Dependent Continuant. In the g-depends on elucidation, how is it that “(c instantiates B at t₁)”? I asked ChatGPT.

<quote>
Prompt: The formal definition of BFO's Generically Dependent Continuant includes the phrase "c instantiates B at t1." How is it possible that c instantiates B at t1 and not that c instantiates C at t1?

Result: Great question! This touches on some subtle points in the Basic Formal Ontology (BFO) and its treatment of generically dependent continuants (GDCs), such as information content entities (ICEs).

The BFO Definition

In BFO, a generically dependent continuant (GDC) is something like a text, a digital file, or a gene sequence—something that can be "realized" in multiple bearers (e.g., a poem instantiated in many books).

The BFO definition (paraphrased) says:

"A GDC c is an instance of class C, and c instantiates B at t1."

Here, B is a generically dependent continuant universal (a type, like "poem"), and c is a particular (like "the copy of the poem in this book").

The Key Distinction

• C is the universal of which c is an instance (e.g., "CopyOfPoem").
• B is the universal that c instantiates at time t1 (e.g., "Poem").

Why "instantiates B" and not "instantiates C"?

• Instantiation in BFO is a relation between a particular and a universal.
• c is an instance of C (by the usual instance-of relation).
• But c instantiates B (not C) because B is the content or pattern that is realized in c.

Example

Suppose:

• B = "The Gettysburg Address" (the content universal)
• C = "DigitalFileOfGettysburgAddress" (the carrier universal)
• c = a particular digital file on your computer

Then:

• c is an instance of C (it's a digital file)
• c instantiates B (it realizes the content of the Gettysburg Address)

Why Not "c instantiates C"?

Because instantiation is about the content or pattern that is realized in the particular, not about the particular's own type. The type of the particular (C) is a different relation (instance-of).

• c is an instance of C (by virtue of being a digital file)
• c instantiates B (by virtue of realizing the content of the Gettysburg Address)

Summary Table

Relation          Universal          Particular          Example
instance_of    C                         c                          c is a digital file
instantiates    B                         c                          c realizes Gettysburg Address

In Short

• c instantiates B at t1: c (the particular) realizes the content B (the universal, e.g., "Gettysburg Address") at time t1.
• c is an instance of C: c is a member of the class of digital files (or whatever the carrier type is).
• c does not instantiate C: Instantiation is about the content (B), not the carrier type (C).

References:

• BFO 2.0 Specification, Section 2.3.2
• Arp, Smith, Spear. Building Ontologies with Basic Formal Ontology, 2015.

In summary:

"c instantiates B at t1" means that the particular c realizes the content B at time t1. "c is an instance of C" means c is a member of the class C (the carrier type). Instantiation is about the content, not the carrier type.
</quote>

Note: I should have worded the prompt to read “The formal definition of BFO's Generically Dependent Continuant is based on the g-depends on elucidation, which includes the phrase…” However, I don’t think this would have resulted in a significantly different result.

ChatGPT claims that ‘instance of’ and ‘instantiation’ have different meanings. Also, if it is true that a “particular c realizes the content B at t1,” where BFO 2’s ‘realizes’ relation has Process as its domain and Realizable Entity as its range, then instantiation is only limited to realizable entities. How does a particular realize ‘content B’ (a GDC particular) at time t1, when the BFO ‘realizes’ relation only holds between Process and Realizable Entity? Should not an object of the ‘realizes’ relation only be either a Role, a Disposition or a Function and nothing else?

This is a bit confusing. Can anyone clarify this? Thank you.

[Pierre Grenon]

Hi Anthony, 

It looks like you found a typo -- 'instantiation' should read 'instance_of' in the elucidation. The document uses the former (name) in English and the latter (symbol) in formal expressions. 

With many thanks and kind regards,

Pierre

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[Pierre Grenon]

*instantiates*

[Werner Ceusters]

As a start, you should also take the BFO-FOL axioms into account and not just the definitions and elucidations. Also, at all times, use the appropriate time-indexing for the relations that are defined and axiomatized that way. You should tell that to ChatGPT too. Furthermore, if what you printed above is output from ChatGPT, toss it, because it misses the mark. 

Some specific points:

1) particulars typically instantiate a multitude of universals at the same time: the blackness of my shirt instantiates now black, and color, and SDC

2) The triad object, fiat object part and object aggregate has nothing to do with zooming, but with changes that can occur so that my left pinky which instantiates fiat object part now, will instantiate object at a time that it is chopped off.  
3) BFO does not enforces a particular to 'directly instantiate ' (I assume you mean the most determinate universal in some hierarchy) precisely one universal: my bent sine instantiates now both the universal spine and the universal disorder.

4) Re your prompt: "The formal definition of BFO's Generically Dependent Continuant includes the phrase "c instantiates B at t1." How is it possible that c instantiates B at t1 and not that c instantiates C at t1?"  --> Nowhere in the def it is said that c cannot instantiate C at t. If by "The Gettysburg Address" you mean that what was once spoken and now is concretized in different places then it is not a universal but a particular !!! I am sure that the SDCs in which it is concretized s-depend on ICs not all of which instantiate the same collection of universals. The only requirement is that particular c on which b g-depends must be an instance of independent continuant. Which one doesn't matter, and it may be distinct at distinct times.

Hope this clarifies.

W

[wceusters]

(Shorter version since my longer one seems not to have gone through)

ChatGPT is confused in understanding the elucidation. Nothing in the g-depends elucidation says that c cannot instantiate C at t. Actually, at t, it doesn’t matter whether c even exist as at that time, b may g-depends on a particular distinct than c.

 

W

This is a bit confusing. Can anyone clarify this? Thank you. --

[Anthony Petosa]

Thank you for the replies. Allow me to respond to specific points:

• >> *instantiates*
  Pierre,  the g-depends on elucidation already uses 'instantiates' in that part of the elucidation to which I referred, namely '(c instantiates B at t₁)'. Are you referring to something else?

• >> "Furthermore, if what you printed above is output from ChatGPT, toss it, because it misses the mark.   "
  

• Werner, how specifically does it miss the mark?

• >> "The triad object, fiat object part and object aggregate has nothing to do with zooming, but with changes that can occur so that my left pinky which instantiates fiat object part now, will instantiate object at a time that it is chopped off."
  

• Of the three I was talking about Object & Object Aggregate with respect to ontological zooming. For example, in one model, H2O (unable to subscript the '2'), is treated as an instance of Molecule, which in turn specializes Object. Within the same model, '1 pint of pure water' is treated as an instance of Object Aggregate and has one or more H2O Molecule instances as members. In another equally valid view of the world, H2O is treated as an Object Aggregate, and Hydrogen & Oxygen, specializations of Atom, are treated as Objects. At the instance level, 'this H2O molecule' has as members exactly two Hydrogen atom instances and one Oxygen atom instance. The reason BFO does not assert Object & Object Aggregate to be disjoint is to account for the possibility that two or more models that are true about the part of reality they each represent but at different levels of granularity will not result in a logical fallacy. If this scenario occurred and Object & Object Aggregate were asserted to be disjoint, then an OWL 2 DL reasoner would complain that an H2O instance cannot be a member both of a type and its complement.

• >> "my bent sine instantiates now both the universal spine and the universal disorder."
  

• I disagree. 'Bent Spine' is a defined class and not a legitimate universal, because it is formed on a logical operation that combines the Object 'Spine' with the Quality 'Bent.' One can certainly create an 'OWL ontology model' filled with defined classes, but I would use that for information modeling purposes only to represent subjectively contextualized business information needs. I would not use this within an 'OWL ontology model' which purpose is to represent objective reality in a set theoretic, machine-consumable form.
• >> "The formal definition of BFO's Generically Dependent Continuant includes the phrase 'c instantiates B at t1'..."
  Now, we are at my original point and purpose for this post. Here is where I need clarification. By the way, I located an updated version of the BFO 2 document, and I will rely on that version for the following.
  • Section 2.12 ("Related defined for any entity") has very specific definitions for 'instance_of' in terms of both Continuant and Occurrent.
    • c instance_of C at t  means: that the particular continuant entity c instantiates the universal C at t
    •   p instance_of P means: that the particular occurrent entity p instantiates the universal P
    • Notice the definitions do not state "instantiates some universal"; rather it says "instantiates the universal." This suggests a functional mapping, where the co-domain (or range) must be semantically unique. On your recommendation, I sought out BFO FOL axioms and came across this one. (I took liberties with the symbology because the character set here does not support universal & existential quantification and equivalence symbols).
      
      Va,t (Eu(universal(u)^instanceOf(a,u,t)^instanceOf(t,temporalRegion,t))
      <->particular(a)^instanceOf(t,temporalRegion,t)^existsAt(a,t)
      
      So, for all particulars a, there exists some universal u and a is an instance of u at time t and t is an instance of temporal region at time t is equivalent to particular a and t is an instance of temporal region at time t and particular a exists at time t.
      
      Unless I am reading this wrong, it seems that a specific particular, a1, satisfies this axiom if it is an instance of one or more universals, { u1, u2,...u(n) }. In other words, the existential quantifier refers to a specific type but not a cardinality value. As you stated, we should look at the FOL axioms and not only the definitions & elucidations. The use of 'the universal' in the human-readable definitions for instance_of should be taken with a grain of salt.
      
      I located several PDFs with BFO FOL axioms, but I do not know if this is a complete set covering the entirety of BFO 2020.
• Does BFO make a distinction between 'instance of' and 'instantiates'?
  • The revised BFO 2 documentation says the are equivalent terms...well, almost. It states that the 'instance of at' relation is synonymous with 'instantiates at.' (See: Section 3.1 ("Relations of parthood")) "Elucidation: relation that holds between a particular and a universal at a time" The domain value is particular; the range value is universal. The time-indexed part of this relation only applies to Continuants; drop the time part for Occurrents. So, my_water_bottle instance_of Bottle at 2025-07-09T15:00:00Z; 2025-07-09T15:00:00Z instance_of Temporal Instant. 

• >> "If by 'The Gettysburg Address' you mean that what was once spoken and now is concretized in different places then it is not a universal but a particular !!!"
  

• That's not what I mean; this is what ChatGPT returned. Frankly, I would say that 'The Gettysburg Address' is an instance of Generically Dependent Continuant (or Document if you want to drill down to the Information Artifact Ontology) and, for example, that some neural pattern in one's brain (Specifically Dependent Continuant and Independent Continuant within which it inheres) and as realized via a memorization process concretizes 'The Gettysburg Address.'
  • I am hung up on the "(c instantiates B at t1)" part of the g-depends on elucidation.
    

• • b exists at t₁ and c exists at t₁
    & for some type B it holds that (c instantiates B at t₁)
    & necessarily, for all t (if b exists at t then some instance_of C exists at t)
    

• • & not (b s-depends_on c at t1)
    
    Domain: GDC; Range: IC
    
    Considering B represents GDC and C represents IC, how is it that an instance if C, c, instantiates B at t1? How can an instance typed as IC instantiate GDC if, as shown earlier, instance_of and instantiates are synonymous? What am I missing?

On Tuesday, July 8, 2025 at 4:09:37 PM UTC-4 Anthony Petosa wrote:

[seanno...@gmail.com]

SB

 

From: Anthony Petosa

Sent: Wednesday, July 9, 2025 3:57 PM

To: BFO Discuss

Subject: [bfo-discuss] Re: Understanding ‘Instantiation’ within a Generically Dependent Continuant

 

WC: "Furthermore, if what you printed above is output from ChatGPT, toss it, because it misses the mark.   "
AP: Werner, how specifically does it miss the mark?

WC: you give already an example below: ChatGPT takes the GA to be a universal.

 

 

WC: "The triad object, fiat object part and object aggregate has nothing to do with zooming, but with changes that can occur so that my left pinky which instantiates fiat object part now, will instantiate object at a time that it is chopped off."
AP: Of the three I was talking about Object & Object Aggregate with respect to ontological zooming. For example, in one model, H2O (unable to subscript the '2'), is treated as an instance of Molecule, which in turn specializes Object. Within the same model, '1 pint of pure water' is treated as an instance of Object Aggregate and has one or more H2O Molecule instances as members. In another equally valid view of the world, H2O is treated as an Object Aggregate, and Hydrogen & Oxygen, specializations of Atom, are treated as Objects. At the instance level, 'this H2O molecule' has as members exactly two Hydrogen atom instances and one Oxygen atom instance.

WC: then I take it that these two models use different causal unity criteria for H2O and cannot be merged. But of course, at a meta level, you can describe the differences in the representation. But then you are describing instances of information content entities, not instances of H2O.

AP: The reason BFO does not assert Object & Object Aggregate to be disjoint is to account for the possibility that two or more models that are true about the part of reality they each represent but at different levels of granularity will not result in a logical fallacy. If this scenario occurred and Object & Object Aggregate were asserted to be disjoint, then an OWL 2 DL reasoner would complain that an H2O instance cannot be a member both of a type and its complement.

WC: levels of granularity have not been worked out in BFO.

 

WC>> "my bent sine instantiates now both the universal spine and the universal disorder."
AP: I disagree. 'Bent Spine' is a defined class and not a legitimate universal, because it is formed on a logical operation that combines the Object 'Spine' with the Quality 'Bent.' One can certainly create an 'OWL ontology model' filled with defined classes, but I would use that for information modeling purposes only to represent subjectively contextualized business information needs. I would not use this within an 'OWL ontology model' which purpose is to represent objective reality in a set theoretic, machine-consumable form.

WC: I was not talking about ‘bent spine’ but about my bent spine. And my bent spine in my back is certainly not a defined class.

 

AP:>> "The formal definition of BFO's Generically Dependent Continuant includes the phrase 'c instantiates B at t1'..."

Now, we are at my original point and purpose for this post. Here is where I need clarification. By the way, I located an updated version of the BFO 2 document, and I will rely on that version for the following.

• Section 2.12 ("Related defined for any entity") has very specific definitions for 'instance_of' in terms of both Continuant and Occurrent.
  • c instance_of C at t  means: that the particular continuant entity c instantiates the universal C at t
  •   p instance_of P means: that the particular occurrent entity p instantiates the universal P
  • Notice the definitions do not state "instantiates some universal"; rather it says "instantiates the universal." This suggests a functional mapping, where the co-domain (or range) must be semantically unique. On your recommendation, I sought out BFO FOL axioms and came across this one. (I took liberties with the symbology because the character set here does not support universal & existential quantification and equivalence symbols).
    
    Va,t (Eu(universal(u)^instanceOf(a,u,t)^instanceOf(t,temporalRegion,t))
    <->particular(a)^instanceOf(t,temporalRegion,t)^existsAt(a,t)
    
    So, for all particulars a, there exists some universal u and a is an instance of u at time t and t is an instance of temporal region at time t is equivalent to particular a and t is an instance of temporal region at time t and particular a exists at time t.
    
    Unless I am reading this wrong, it seems that a specific particular, a1, satisfies this axiom if it is an instance of one or more universals, { u1, u2,...u(n) }. In other words, the existential quantifier refers to a specific type but not a cardinality value. As you stated, we should look at the FOL axioms and not only the definitions & elucidations. The use of 'the universal' in the human-readable definitions for instance_of should be taken with a grain of salt.
    
    I located several PDFs with BFO FOL axioms, but I do not know if this is a complete set covering the entirety of BFO 2020.

WC: They are here: https://github.com/BFO-ontology/BFO-2020/tree/master/src/common-logic 

And I believe you are reading the elucidations about instantiation wrongly. What they say is that for ‘c instance-of C at t’’ to be true, it has to be the case that c instantiates C at t. It doesn’t say that C is the only universal that c at that time instantiates. The existential quantifier should not be read as ‘there exists precisely one’, or ‘there exists that one’. Here is the relevant axiom:

 

(cl:comment "If you exist you instatiate a universal and vice-versa [bee-1]"

  (forall (a t)

   (iff

    (exists (u)

     (and (universal u) (instance-of a u t)

      (instance-of t temporal-region t)))

    (and (particular a) (instance-of t temporal-region t)

     (exists-at a t)))))

 

WC: "If by 'The Gettysburg Address' you mean that what was once spoken and now is concretized in different places then it is not a universal but a particular !!!"
AP: That's not what I mean; this is what ChatGPT returned.

WC: So ChatGPT misses the mark.

 

AP: Frankly, I would say that 'The Gettysburg Address' is an instance of Generically Dependent Continuant (or Document if you want to drill down to the Information Artifact Ontology)

WC: I agree

AP: and, for example, that some neural pattern in one's brain (Specifically Dependent Continuant and Independent Continuant within which it inheres) and as realized via a memorization process concretizes 'The Gettysburg Address.'

WC: except for ‘and as realized via a memorization process ‘ I agree to.

 

 

AP:I am hung up on the "(c instantiates B at t1)" part of the g-depends on elucidation.

b exists at t₁ and c exists at t₁
& for some type B it holds that (c instantiates B at t₁)
& necessarily, for all t (if b exists at t then some instance_of C exists at t)
& not (b s-depends_on c at t1)

Domain: GDC; Range: IC

Considering B represents GDC and C represents IC, how is it that an instance if C, c, instantiates B at t1? How can an instance typed as IC instantiate GDC if, as shown earlier, instance_of and instantiates are synonymous? What am I missing?

 

WC: I think it is just the use of ‘B’ that confuses you. Although b is an instance of GDC, ‘B” in the elucidation is a variable that does not denote a subtype of GDC, but of IC. And so does C.

[Pierre Grenon]

Hi Anthony, 

thanks for following up. I was not very clear, let me try again.

BFO 2020 doc, as you quoted it:

b g-depends on c at t₁ means:
              b exists at t₁ and c exists at t₁
              & for some type B it holds that (c instantiates B at t₁)
              & necessarily, for all t (if b exists at t then some instance_of C exists at t)
              & not (b s-depends on c at t₁)

should read 

b g-depends on c at t₁ means:
              b exists at t₁ and c exists at t₁

              & for some type B it holds that (c instance_Of B at t₁)

              & necessarily, for all t (if b exists at t then some instance_of C exists at t)
              & not (b s-depends on c at t₁)

Explanation:

'instantiation' is the name of the relation (I am mindful that the document occasionally refers to 'the instanceOf relation' to mean the same, this is a mere abuse of language). In English phrases, you find 'instantiation relation', instantiates', (perhaps 'instantiated', I didn't check).

'instance_Of' is the symbol used for the relation in formalisation.

In other words, it is not the case that there are two distinct relations involved here.

Further comment: 

The elucidation seems garbled and at any rate is hard to follow. The second conjunctive clause for example is vacuous (every individual instantiates a universal and that's not a contribution here). It would make more sense to have it as:

              & for some type C it holds that (c instance_Of C at t₁)

and then the next clause could be made less dodgy if it read:

              & necessarily, for all t (if b exists at t then there is an x such that x instance_of C and x exists at t)

It seems to me it also should be the same 'type' else, I don't see what this is trying to say.

Perhaps it's still a little bit dodgy -- but that is a mere 'elucidation', and we say we're OK with that.

So, Bingus is generically dependent on Chungus at some time when 

a) both Bingus and Chungus exist at that time

b) Bingus is not specifically dependent on Chungus at that time

c) Chungus is (of a type that is) such that Bingus requires there being an individual (of that type) to co-exist with it.

c) really can't be made much more stronger than 'there has to be something that exists, just not one particular thing' -- the use of 'necessarily' in the elucidation shows how hard it is to formulate and while generic dependence is useful to define certain types, at the instance level, it's debatable whether picking a type is so useful. In the elucidation and the two clauses above, it seems important these clauses go together and that's not well reflected by the formatting (it seems to me it has to be the same C, if we involve types); at the same time, it's not clear why there is even a mention of types. So the elucidation could be trying to do too many things and types may only be required for a type-type level relation.

g-depends is intended as a weak form to say that something needs something else to exist but not necessarily one particular such something else. 

Dunno if that helps, 

Pierre 

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[Bill Hogan]

If it's helpful:

Let #iui-1 denote the particular "Language and Reality", 2nd edition, a book by Michael Devitt and Kim Sterelny

Let #iui-2 denote my print copy of "Language and Reality" on my bookshelf

Let #uui-1 denote the universal "Book"

Let #uui-2 denote the universal "Print copy of book"

#iui-1 instance_of #uui-1 since 1999

#iui-2 instance_of #uui-2 at t1

t1 after 1999 (it's not clear when my specific copy was actually printed--if anyone knows how to figure that out let me know, I looked and couldn't see any markings--but it was circa 2010)

#iui-1 g-depends-on #iui-2 since t1

You could go on to say:

Let #iui-3 denote the sum total of ink patterns on the cover and pages of the particular denoted by #iui-2, when it was printed (i.e., we won't count any notes written in pen in the margin later)

Let #uui-3 denote the universal "Quality"

#iui-3 instance_of #uui-3 at t1

#iui-2 bearer_of #iui-3 at t1

#iui-3 concretizes #iui-1 at t1

To view this discussion visit https://groups.google.com/d/msgid/bfo-discuss/CD3581A267CA42809ACBFD7093C095FC%40LAPTOP2R6SIR1R.

[Anthony Petosa]

>> [Pierre] "...should read...& for some type B it holds that (c instance_Of B at t₁)"

If this is simply a question terminology, then Section 3.1.A.1.2.3 in the Sep 9, 2020 revision of the Jun 26, 2015 BFO 2 specifications and user's guide document is in error. It reads as follows for the 'instance of at' relation (which you name here as 'instance_Of'):

Synonym: instantiates at
Elucidation: relation that holds between a particular and a universal at a time [200-BFO]

Domain: particular

Range: universal

EXAMPLES: John instance of human; this laptop instance of laptop; the year 2012 instance of temporal region; Johns' birth instance of process, all at time: now.

NOTE: Instantiation relations for occurrents hold trivially at every time at which the occurrent exists.

Your claim is the proper relation name is 'instance_Of' and neither 'instance_of,' 'instance of at' nor 'instantiates.' Is this true? If so, then the BFO 2 documentation requires an update.

[Anthony Petosa]

Thank you for the feedback.

Let me reframe this exclusively in terms of BFO. I will avoid IAO constructs (e.g., denotes, document). In place of ‘denotes’ or its top object property, ‘is about,’ I will use BFO’s ‘g-depends on,’ and in place of IAO’s ‘document’ I will used BFO’s Generically Dependent Continuant.

When you refer to the universals ‘Book’ and ‘Print copy of book,’ I interpret this as follows:

- ‘Book’ is an information artifact and not the physical object upon which it g-depends. For readability, I rename ‘Book’ to ‘Book Content’ and extend it from Generically Dependent Continuant.

·       - ‘Print copy of book’ is tangible thing. For readability, I rename it to ‘Book’ and extend it from Object.

:language_reality_content instanceOf Book-Content at some instance of Temporal Region

:language_reality_book instance_Of Book at some instance of Temporal Region

:language_reality_content g-depends on :language_reality_book at some instance of Temporal Region

For this example, :language_reality_ink_pattern instance_Of Specifically-Dependent-Continuant at some instance of Temporal Region. I opt to instantiate SDC directly rather than instantiate a subtype of SDC.

:language_reality_ink_pattern concretizes :language_reality_content at some instance of Temporal Region

:language_reality_ink_pattern inheres_in :language_reality_book at some instance of Temporal Region

(Temporal Region is specialized by Temporal Instant and Temporal Interval.)

>> t1 after 1999 (it's not clear when my specific copy was actually printed--if anyone knows

>> how to figure that out let me know, I looked and couldn't see any markings--but it was

>> circa 2010)
To the best of my knowledge, the latest BFO model implementation has the following temporally based relations: first instant of / has first instant; last instant of / has last instant; precedes / preceded by. Since all Continuants are time-indexed and require a specific temporal reference (a snapshot in time), then I assume the ‘precedes’ relation is the best option in BFO for determine relative temporal positions.

[Bill Hogan]

On Thu, Jul 10, 2025 at 10:15 AM Anthony Petosa <petosa...@gmail.com> wrote:

Thank you for the feedback.

Let me reframe this exclusively in terms of BFO. I will avoid IAO constructs (e.g., denotes, document). In place of ‘denotes’ or its top object property, ‘is about,’ I will use BFO’s ‘g-depends on,’ and in place of IAO’s ‘document’ I will used BFO’s Generically Dependent Continuant.

When you refer to the universals ‘Book’ and ‘Print copy of book,’ I interpret this as follows:

- ‘Book’ is an information artifact and not the physical object upon which it g-depends. For readability, I rename ‘Book’ to ‘Book Content’ and extend it from Generically Dependent Continuant.

Correct. I meant to mention that Book (which you call 'Book Content') is a subtype of GDC 

·       - ‘Print copy of book’ is tangible thing. For readability, I rename it to ‘Book’ and extend it from Object.

Correct.  

:language_reality_content instanceOf Book-Content at some instance of Temporal Region 

:language_reality_book instance_Of Book at some instance of Temporal Region

Yes, specifically :language_reality_book is my copy of the book. If some other person has a print copy, we would have to designate theirs as something like :language_reality_book_2 

 

:language_reality_content g-depends on :language_reality_book at some instance of Temporal Region

Yes.

For this example, :language_reality_ink_pattern instance_Of Specifically-Dependent-Continuant at some instance of Temporal Region. I opt to instantiate SDC directly rather than instantiate a subtype of SDC.

Fair enough.  

:language_reality_ink_pattern concretizes :language_reality_content at some instance of Temporal Region

Yes, I called the specific instance of Temporal Region 't1' 

:language_reality_ink_pattern inheres_in :language_reality_book at some instance of Temporal Region

(Temporal Region is specialized by Temporal Instant and Temporal Interval.)

>> t1 after 1999 (it's not clear when my specific copy was actually printed--if anyone knows

>> how to figure that out let me know, I looked and couldn't see any markings--but it was

>> circa 2010)
To the best of my knowledge, the latest BFO model implementation has the following temporally based relations: first instant of / has first instant; last instant of / has last instant; precedes / preceded by. Since all Continuants are time-indexed and require a specific temporal reference (a snapshot in time), then I assume the ‘precedes’ relation is the best option in BFO for determine relative temporal positions.

I defer to others. 

To view this discussion visit https://groups.google.com/d/msgid/bfo-discuss/fb0824ae-30f8-467f-8466-e34f98cefbc8n%40googlegroups.com.

[Anthony Petosa]

>>  WC: They are here: https://github.com/BFO-ontology/BFO-2020/tree/master/src/common-logic

Thank you. Yes, this is the same collection of formalized axioms, expressed in Common Logic, as I have seen in the PDFs I mentioned, which capture the axioms in FOL syntax. I do not know if the formalized axioms in the various syntaxes covers all of BFO.

>>  WC: levels of granularity have not been worked out in BFO.

Apologies for any redundancy; I don't know if I commented on this already. Yes, BFO has not yet worked out granularity, but I think it allows for this by not asserting disjointedness in the triad of Object / Fiat Object Part / Object Aggregate for the reasons I mentioned. Another example is 'Tree.' At one level of granularity (a.k.a., ontological zoom) 'Tree' is a member part of 'Forest' at some point in time. At a different granularity level, 'Tree' is an Object Aggregate having a countable number of 'Leaf,' 'Trunk,' 'Branch,' 'Twig,' 'Root,' etc., as its member parts at some point in time.

>> WC: you give already an example below: ChatGPT takes the GA to be a universal.

Yes, but that was a trivial observation on my part. In what substantive ways does ChatGPT miss the mark?

>> The existential quantifier should not be read as ‘there exists precisely one’, or ‘there exists that one’.

Yes, and I apologize if I worded my comments in a manner that implies this. Existential quantification requires some instance of a type to exist, have existed or to imminently exist, and it does not specify cardinality. However, some infers >=1, but the cardinality should be explicitly asserted to avoid confusion. Still, this does not present the complete picture, because the empty set is a valid set member. From what I recall, an OWL 2 DL validator will not complain if an OWL class in the model includes a value property restriction on some property but no cardinality property restriction on that same property and one instantiates it without adding an instance-level property assertion on that property. Frankly, if this is true (I don't remember), then it's silly. An empty set member satisfies the math, but what value does it have ontologically? Why would we want an ontology to allow the empty set with existential quantification or universal quantification for that matter? When we ontologically claim some 'thing' exists we do not mean nothing exists. Yeah, yeah, the empty set is not 'nothing' mathematically, but we do not need an ontology to represent some 'thing' with some other 'thing' whose value is nothing. I think BFO should be more precise on this.

>> WC: I think it is just the use of ‘B’ that confuses you. Although b is an instance of GDC, ‘B” in the elucidation

>> is a variable that does not denote a subtype of GDC, but of IC. And so does C.

I thought BFO followed a naming convention where an italicized, lower-case letter represents a particular and an italicized, upper-case version of the same letter represents the universal it instantiates. For convenience, I repeat the g-depends on elucidation below.

b exists at t₁ and c exists at t₁
& for some type B it holds that (c instantiates B at t₁)
& necessarily, for all t (if b exists at t then some instance_of C exists at t)
& not (b s-depends_on c at t1)

Domain: GDC; Range: IC

(From Pierre) "The elucidation seems garbled and at any rate is hard to follow. The second conjunctive clause for example is vacuous (every individual instantiates a universal and that's not a contribution here). It would make more

sense to have it as:

              & for some type C it holds that (c instance_Of C at t₁)

and then the next clause could be made less dodgy if it read:

              & necessarily, for all t (if b exists at t then there is an x such

              that x instance_of C and x exists at t)

It seems to me it also should be the same 'type' else, I don't see what this is trying to say."

Pierre's recommendation is to reword

b g-depends on c at t₁ means:

              b exists at t₁ and c exists at t₁
              & for some type B it holds that (c instantiates B at t₁)
              & necessarily, for all t (if b exists at t then some instance_of C exists at t)

              & not (b s-depends on c at t₁)

...as...

b g-depends on c at t₁ means:

              (omit b exists at t₁ and c exists at t₁ because it is trivially true)

              for some type C it holds that (c instance_Of C at t₁)

              & necessarily, for all t (if b exists at t then there is an x such that x instance_of C and x exists at t)

I respectfully suggest the following revision.

b g-depends on c at t₁ means:

              b exists at t₁ and c exists at t₁

              & b not c

              & b instance_Of Generically Dependent Continuant at t₁)

              & c instance_Of (Independent Continuant and not(Spatial Region)) at t₁)

              & necessarily, for all t (if b exists at t then there is a c such that c carrier_of b)

The first condition states two particulars independently exist at the same point in time, although up to this part of the elucidation we do not know if they are semantically unique. The second condition explicitly asserts they are pairwise disjoint and, therefore, semantically unique. The third & fourth conditions assert which BFO types the particulars instantiate at the same point in time, and this aligns with the relation's domain & range values. Conditions three & four should be stated; we should not rely on a naming convention. After all, B can only be Generically Dependent Continuant for the g-depends on relation, and C can only be (Independent Continuant and not(Spatial Region)) for the g-depends on relation. The last condition states if b exists at all times, then there is some c, which we have already established to be of type (Independent Continuant and not(Spatial Region)), that is its 'carrier.' In other words, at least one (Independent Continuant and not(Spatial Region)) particular is the carrier_of b.

For me, this elucidation is more precise, but I welcome this community's constructive criticism.

[Anthony Petosa]

Quick follow-up on "& b not c" in the g-depends on elucidation. This condition is not needed BFO formalizes a disjointedness relation between IC, SDC & GDC, but I added it to the definition for completeness.

[Pierre Grenon]

Hi Anthony,

> Your claim is the proper relation name is 'instance_Of' and neither 'instance_of,' 'instance of at' nor 'instantiates.' Is this true? If so, then the BFO 2 documentation requires an update.

Not really my claim as it's not charitable -- basically I accept the relation is referred to using different English phrases and don't really believe it matters in text. 

My claim is that the elucidation ought to use a single term for the avoidance of the ambiguity you raise, I see it as a mere typo and so, however, yes the elucidation (hence the document) ought to be corrected in that respect.

'instance_of' or 'instance_Of' - same difference... I intended 'instance_of' in the present context. Another typo :) nothing deep.

All the best,

Pierre

[seanno...@gmail.com]

WC: They are here: https://github.com/BFO-ontology/BFO-2020/tree/master/src/common-logic

AP:Thank you. Yes, this is the same collection of formalized axioms, expressed in Common Logic, as I have seen in the PDFs I mentioned, which capture the axioms in FOL syntax. I do not know if the formalized axioms in the various syntaxes covers all of BFO.

WC: They cover of the BFO theory what can be expressed in FOL with equality, and whatever number of predicate arguments required (thus not restricted to binary relations).
---

WC: The existential quantifier should not be read as ‘there exists precisely one’, or ‘there exists that one’.

AP: Yes, and I apologize if I worded my comments in a manner that implies this. Existential quantification requires some instance of a type to exist, have existed or to imminently exist, and it does not specify cardinality. However, some infers >=1, but the cardinality should be explicitly asserted to avoid confusion.

WC: Why would that be? And in this specific case for GDC? ‘exists’ in FOL means at least 1.

AP: Still, this does not present the complete picture, because the empty set is a valid set member. From what I recall, an OWL 2 DL validator will not complain if an OWL class in the model includes a value property restriction on some property but no cardinality property restriction on that same property and one instantiates it without adding an instance-level property assertion on that property. Frankly, if this is true (I don't remember), then it's silly. An empty set member satisfies the math, but what value does it have ontologically? Why would we want an ontology to allow the empty set with existential quantification or universal quantification for that matter? When we ontologically claim some 'thing' exists we do not mean nothing exists. Yeah, yeah, the empty set is not 'nothing' mathematically, but we do not need an ontology to represent some 'thing' with some other 'thing' whose value is nothing. I think BFO should be more precise on this.

WC: The BFO theory is not based on sets, but on mereology. The OWL rendering of BFO does not cover everything that is covered in the FOL axioms. I never work with the OWL rendering, so any questions about it, I let pass.

---

WC: I think it is just the use of ‘B’ that confuses you. Although b is an instance of GDC, ‘B” in the elucidation is a variable that does not denote a subtype of GDC, but of IC. And so does C.

AP: I thought BFO followed a naming convention where an italicized, lower-case letter represents a particular and an italicized, upper-case version of the same letter represents the universal it instantiates.

WP: you are right about the use of the principle re bold and italicized, except that if ‘b’ and ‘B’ are used, the former would be an instance of the latter. The definition below is in quasi-formal language.

AP: For convenience, I repeat the g-depends on elucidation below.

 

b exists at t₁ and c exists at t₁
& for some type B it holds that (c instantiates B at t₁)
& necessarily, for all t (if b exists at t then some instance_of C exists at t)
& not (b s-depends_on c at t1)

Domain: GDC; Range: IC

 

WC: indeed. The elucidation is about ‘b g-depends on c’. The domain and range statement clearly says that c is an IC, thus the ‘B’ in the second line must be IC or a subtype thereof.

 

[Anthony Petosa]

>> WC: The existential quantifier should not be read as ‘there exists precisely one’, or ‘there exists that one’...

>> WC: The BFO theory is not based on sets, but on mereology. The OWL rendering of BFO does not cover everything that is covered

>> in the FOL axioms. I never work with the OWL rendering, so any questions about it, I let pass.

Yes, existential quantification asserts that at least one 'thing' exists; that is why it is 'existential'...and, yes, BFO theory is based on Mereology (whole-part relations) and not class membership (sets). Unfortunately, we need somehow to resolve mereological ideas with a set-theoretic design, because most folks use some form of OWL to represent 'ontologies.' This is why I raise the point about the empty set being a legitimate set member mathematically. Of course, it makes no sense mereologically. Also, as has been pointed out many times, OWL is only capable of expressing binary relations, so the FOL axioms that use time, for example, as part of ternary relations will not translate to OWL unless we create additional RDF triples that address the temporal aspect of a relation. BFO has done this in its OWL implementation. Since,  'ontology development' generally uses OWL in practice (in the business world), we are confronted with this issue.

Here is a very simple example.

Consider this OWL model:

• OWL Classes
  • Car
  • Engine
• OWL Properties
  • member-of (OWL Object Property: no rdfs:domain & rdfs:range values defined (implicitly, owl:Thing))
• OWL Property Restrictions
  • On Engine: subclassOf (member-of exactly 1 Car)
• OWL Individuals
  • Car01
  • Car02
  • Engine-A
• Axioms
  • Car01 disjointWith Car02

Suppose I assert the following:

• Test #01
  • Engine-A member-of Car01
    • Run Pellet, an OWL 2 DL reasoner: No issues
• Test #02
  • Engine-A member-of   Car 02
    • Run Pellet, an OWL 2 DL reasoner: No issues
• Test #03
  • Engine-A member-of   Car01
  • Engine-A member-of   Car02
    • Run Pellet, an OWL 2 DL reasoner: Pellet complains; the cardinality rule is violated
• Test #04 (the interesting one)
  • There are no Engine-A member-of assertions
    • Run Pellet, an OWL 2 DL reasoner: No issues
      • Why not? From a set-theoretic perspective (we are implementing in OWL) Pellet does not complain because the empty set (i.e., no Engine-A member-of assertions) is a legitimate set member
      • From a mereological perspective, this is flawed.
      • Conclusion: In the case of existential quantification, we cannot rely solely on OWL cardinality constraints for the reason mentioned. I guess this also requires a rules language to enforce the "at least 1" mereological requirement, or at the data level, we can validate "at least 1" as a SHACL PropertyShape.

One more point. Suppose the preceding exists but we remove the 'Car01 disjointWith Car02' assertion. If we run Test #03, Pellet will not complain. In an Open World Assumption, the reasoner assumes Car01 & Car02 are semantically equivalent, where as in the Closed World Assumption + Unique Name Assumption considers Car01 & Car02 to be pairwise disjoint. With OWA, we need to allow for the inferred possibility that Car01 owl:sameAs Car02 (and vice versa), which is why we should explicitly assert the Car01/Car02 disjointedness axiom.

[Anthony Petosa]

Any thoughts? The academic discussions on Ontological Realism and its BFO implementation are fascinating, but we also need to apply them to practical scenarios, especially if we expect people to examine BFO, let alone adopt it. With that in mind & considering most 'ontologies' in the business world are modeled in OWL, do members of this discussion group have any different ideas concerning the trivially true empty set element scenario I presented with respect to expressing a mereological whole-part relation in OWL?

[Chris Mungall]

This seems to have nothing to do with BFO or GDCs and is simply the open-world assumption? I don't think it has anything to do with assumptions about the empty set. The engine is a part of a car, you just haven't said which one. If you want to do closed-world constraint checking, then use a closed-world constraint framework like Prolog or SQL or SHACL or LinkML....

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[Alan Ruttenberg]

> member-of (OWL Object Property: no rdfs:domain & rdfs:range values defined (implicitly, owl:Thing))

Not sure which version of BFO you are looking at. BFO2020 is at http://purl.obolibrary.org/obo/bfo/2020/bfo.owl or bfo-core.owl

The relation is "member part of" and has domain and range material entity.

BFO core differs from bfo.owl in that the former does not include the "at all times" relations, and the "at some time" relations omit "at some time" in their labels.

There are other differences but these are not intended. See https://github.com/BFO-ontology/BFO-2020/issues/110

Regarding instance-of, in the BFO axiomatization only has a single instance-of relation that is time indexed, so the BFO documentation is not accurate about that point, at least wrt. axiomatization. I made that choice because a) I had a policy of not using the same predicate for name different arities - I consider a different arity predicate to be a distinct relation and b) not including t in instance-of for occurrents is a shortcut. Everything, including occurrents, instantiates a universal at a specific temporal region. The shortcut works because all occurrent classes are rigid.

I haven't caught up with the whole conversation, but I may have other comments when I do.

BTW, if you think there is a bug in BFO, please submit an issue at https://github.com/BFO-ontology/BFO-2020/issues. Discussing the issue here is fine, but bugs are tracked at the issue list, not here.

Alan