Is P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) still regarded as true?

Post by Wolfgang Schmidle (20 October 2022)

Quick question: According to Christian-Emil's homework for issue 606, the reason to avoid the statement P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) was that it might create problems in hypothetical information systems that are clever enough to traverse the graph created by all P89 statements but not clever enough to not fill themselves up with large amounts of deduced P7 statements. 

If we accept this argument, do we still assume that P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) is true based on the semantics of P7 and P89? Or do we now say that we need to have an explicit statement that x was within a place y and regard only the statements P7(x,z) to be inferrable for all z the spatial projection and y? 

If the latter: If I have a statement in my information system that, lacking more precise information, an object is located (or the move of an object took place) somewhere in Europe, is P7 then automatically true for all places between the spatial projection and Europe but my information system couldn't actually infer any additional P7 statement because it doesn't know where the declarative place of the spatial projection is?

Best,
Wolfgang

Post by Wolfgang Schmidle (20 October 2022)

Sorry, second attempt: 

According to Christian-Emil's homework for issue 606, the reason to avoid the statement P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) was that it might create problems in hypothetical information systems that are clever enough to traverse the graph created by all P89 statements but not clever enough to not fill themselves up with large amounts of deduced P7 statements. 

If we accept this argument, do we still regard P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) as true based on the semantics of P7 and P89? Or do we now say that we need to have an explicit statement that x was within a place y and regard only the statements P7(x,z) to be true or inferrable for all z between the spatial projection and y? 

If the latter: If I have a statement in my information system that, lacking more precise information, a period such as the move of an object took place somewhere in Europe, is P7 then automatically true for all places between the spatial projection of the move and Europe but my information system couldn't actually infer any additional P7 statement because it doesn't know where the declarative place of the spatial projection is?

Post by Martin Doerr (20 October 2022)

Dear Wolfgang,

I regard that the statement P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) was never true, and following the decision of the last SIG it does no more appear.

The oral explanation in the SIG that is causes a useless recursion through the world was just an indication that it was nonsensical from the beginning.  In my understanding, it was a confusion taking an inverse shortcut for a shortcut.

In my understanding, and actual scholarly practice, P7 expresses a reasonable, NOT arbitrarily large, outer /approximation/ of the place where something happened. The narrower the better.

Indeed, "we now say that we need to have an explicit statement that x was within a place y and regard only the statements P7(x,z) to be true  or inferrable for all z between the spatial projection and y". 

That is in the new FOL, isn't it?

Indeed, "If I have a statement in my information system that, lacking more precise information, a period such as the move of an object took place somewhere in Europe, is P7 then automatically true for all places between the spatial projection of the move and Europe but my information system couldn't actually infer any additional P7 statement because it doesn't know where the declarative place of the spatial projection is"

We should be aware that "approximation" has no equivalent in FOL. It has a quality, which can be formalized by /metrics/. If you have some background knowledge in topology, you may be familiar with the respective concepts.

Automatically, the intersection of all yi, i=1...n of P7(x,yi) constitutes the best approximation.

Best,

Martin
 

Post by Christian-Emil Ore (21 October 2022)

Since my HW is mentioned. I tried to explain the change, P7(x,y) ∧ P89(y,z) ⇒ P7(x,z), seen form the point of view of practical applications. Martin argue correctly  from a principle point of view.

Time reasoning is similar, on  the the two dimensional time line. A historian or an archaeologist will try to date an event A from the intersection of the timespan of other events during which A must have happened, see https://proceedings.caaconference.org/paper/17_holmen_ore_caa2009/ for a pedagogical, fictitious example.   That the black plague in Norway happened in the 14th c.  can of course  be deduced form the usual estimate 1348-1350, but is usually not used in historical reasoning.

Best,

Christian-Emil

Post by Wolfgang Schmidle (21 October 2022)

Dear Martin, 

Thank you for your explanation! I am beginning to see clearer. 

Let us look more closely at the FOL statement. If we assume an established common reference space, then the FOL block of P7 after the usual
P7(x,y) ⇒ E4(x)
P7(x,y) ⇒ E53(y)
can be succinctly written as

P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y)
P7(x,y) ∧ E53(z) ∧ P161(x,z) ∧ E53(v) ∧ P89(z,v) ∧ P89(v,y) ⇒ P7(x,v)
 
Applied to the example "Ceasar's murder took place in Rome, but also on the Forum Romanum, and more precisely in the Curia" from the scope note: The first statement formalises that the phenomenal place falls within Rome, the Forum Romanum and the Curia. However, I am genuinely not sure what the second statement adds to that. 

The attestation "Ceasar's murder took place in Rome" establishes the reasonable upper bound y = Rome. Within this bound, i.e. for all places v within Rome, it becomes
E53(z) ∧ P161(x,z) ∧ E53(v) ∧ P89(z,v) ⇒ P7(x,v)

In other words: P89(spatial projection z, v) ⇒ P7(x,v)
Together with the first statement: 
for all v in Rome:  P7(x,v) ⇔ P89(spatial projection z, v)
P7(x,y) ∧ E53(z) ∧ P161(x,z) ∧ E53(v) ∧ P89(v,y) ⇒ [ P7(x,v) ⇔ P89(z,v) ]

And what do we learn from this? In order to determine whether a given place z is worthy of an inferred "Caesaer's murder took place at z" without ever explicitly being called this in the literature, one must not only verify the fact that it includes the established best approximation of the actual place (the intersection of all attested places), but also the fact that it lies within the "sphere of established reasonability" for Caesar's death (probably the union of all attested places). The sphere may become (even drastically) bigger by a single additional good-faith statement but probably never gets smaller, and each period/event/activity may have a different sphere of established reasonability. Both the intersection and the union are ideally but not necessarily entries in a gazetteer hierarchy. If an author writes "it happened in Rome, which was the capital of the Roman Empire", does it establish Rome or the Roman Empire? And probably implicitly with the extent at the time of Caesar's death? What about "it happened in Mölln, a town in Schleswig-Holstein, Germany"? Is this a matter of interpretation?

I find it hard to wrap my head around this. 

As an exercise, let us also try to formalise the intersection approach for all attested places. Define a function symbol F121 "overlap of":

z = F121(x,y) ⇒ E53(z) ∧ E53(x) ∧ E53(y) ∧ E121(x,y)
z = F121(x,y) ⇔ P89(z,x) ∧ P89(z,y) ∧ (∀w) [E53(w) ∧ P89(w,x) ∧ P89(w,y) ⇒ P89(w,z)]

I am not even sure if one needs a formal definition like this. Defining the intersection z is comparable to defining the place y in P161(x,y) as the result of a spatial projection, as it is done in the scope note of P161.

And there you have it: 

P7(x,y) ∧ P7(x,z) ⇒ P7(x, F121(y,z))

Best,
Wolfgang
 

Post by Wolfgang Schmidle (21 October 2022)

Re-reading my email, I would like to add:

My first main point is this: The second statement (S2) declares some non-attested places to be P7 places, but by definition no one knows this or can point to a single declarative place where it would apply. I can only establish such a fact via other means, never with the help of S2. Can you describe a scenario where S2 is actually useful?

And the set of places that S2 gives P7 status is strangely formed. Let us for a moment replace the spatial projection with the best known approximation z. If I have two attested places x and y, then I can infer P7 for any place between z and x and any place between z and y, but not for a place that is in the union of x and y but neither fully in x nor fully in y. So the sphere of established reasonability is not even the union of attested places.

About my "Mölln" example: Of course the place attestation is Mölln. My argument is that if someone deemed it necessary to add "a town in Schleswig-Holstein, Germany", then it makes it reasonable to say "it happened in Germany". 

My second main point is: Let us introduce function symbols, which are perfectly fine in FOL. With the help of F121 "overlap of" one can infer P7 statements that are actually useful, as the newly attested places provide better approximations of the phenomenal place.

We can define F121 in FOL or we can treat its definition as a black box, just like we don't explain in the scope note of P161 how the process of creating a spatial projection actually works, let alone attempt a definition in FOL. Instead, in the scope note of P121 we can say something like this:
The actual overlap defines another instance of P53 Place that is taken as the value of a function F121 "overlap of".

Post by Wolfgang Schmidle (22 October 2022)
 

Second addendum:

Strictly speaking, you *can* infer information from S2: First infer from S1 that the phenomenal place is in the Curia, and from the transitivity of P89 that any v that contains the Curia also contains the phenomenal place. Then apply S2 to any v between the Curia and Rome. But of course you can do the same if you reformulate S2 to apply directly to all places between two attested places, i.e. where P161(x,z) is replaced by P7(x,z):

P7(x,y) ∧ E53(z) ∧ P7(x,z) ∧ E53(v) ∧ P89(z,v) ∧ P89(v,y) 
∧ E18(u) ∧ P157(y,u) ∧ P157(z,u) ∧ P157(v,u) ⇒ P7(x,v)

Let's inspect Caesar's murder scene one more time. From the P7 scope note:

> Something that has happened at a given place can also be considered to have happened at a smaller place within it: for example, it is reasonable to say Ceasar's murder took place in Rome, but also on the Forum Romanum, and more precisely in the Curia. It is characteristic for different historical sources to use varying precision in such statements, without being in contradiction with each other. 

First of all, the example is not correct. Caesar wasn't murdered in the Curia Iulia on the Forum Romanum but in the Curia Pompeia, part of the Theatrum Pompeii.

With the corrected example and z = Curia Pompeia and y = Rome, we can infer P7 for v = Theatrum Pompeii. But the Theatrum Pompeii is of course attested in itself and doesn't need S2. In other words, while the quoted passage makes sense (although the first sentence makes it sound as if any smaller place qualifies, especially together with the example in its present form), it cannot be the rationale for introducing S2. The passage simply states that multiple P7 statements for attested places occur and do not automatically contradict each other. Instead, S2 can be applied to all the previously unattested places between attested places, for example the Campus Martius where the Theatrum Pompeii was located (assuming for the sake of argument that it hasn't been attested yet and that we are nonetheless interested in this fact, for example to avoid holes in our gazetteer hierarchy).

Post by Martin Doerr (22 October 2022)

Dear Wolfgang,

A lot of questions and text! I am not sure how to interpret a "sphere of 
reasonability". We can see two epistemological reasons why the area of a 
P7 is taken relatively wide:

A) no better knowledge. In that case, in information integration, one 
would regard the intersections of all given P7s as the best location. I 
do not see a utility in the union of P7s.

B) different interpretations of scholars of the area of immediate impact 
of the event. Caesar's murder has a context extending into Rome. 
Logically, this is more about what is thought that the event includes, 
i.e., differently defined instances of E5. Would need renegotiation of 
the identity of the event.

One utility of S2 is not to infer a new P7, but to decide that two 
different P7 are compatible, and the intersection is better.

Another utility is knowledge about the Presence of participants: If you 
know that Kant wrote his Kritik der Reinen Vernunft in Germany, and 
learn that he never left Königsberg, necessarily the Event took place in 
Königsberg at most.

There may be other such constraints. Need to think about!

"A town in Schleswig" is a finite set, and not Germany. Reasoning with 
alternatives and disambiguating is a different issue, not anything 
specific to P7, isn't it?

The "creation" of a spatial projection is probably a misunderstanding. 
It is not created, it is the phenomenon itself, and depends solely on 
the spatiotemporal unity criteria applying to the Event. These are 
normally fuzzy. CRMgeo describes in much detail the differentiation 
between declarative approximation and phenomenal places.

Would that make sense?

Cheers,

Martin

Post by Martin Doerr (23 October 2022)

Dear Wolfgang,

I would like to add that your argument that the respective FOL would 
"only" help to detect inconsistencies, in my opinion, is a 
misunderstanding of the importance of detecting inconsistencies.

The fact that P7s are not trivially contradictory, if they are different 
for the same event, is really not marginal.
By chance, your remark about Caesar's death, which will duly be 
processed, shows:

Ceasar dying in Rome : Identical, correct.
Ceasar dying on the Forum Romanum has an empty intersection with the 
Theatrum Pompeii, on the Mars Field. Obviously inconconsistent.
Consequently, Curia Iulia must be wrong.

Also, note that approximations need a target of comparison. This target 
is the "real" spatial projection, which is not an approximation. This is 
not accessible to FOL, but to observation only. I think the reasoning 
you present does not give an adequate account of this. Unions of 
approximations do not make sense. Intersections of approximations, which 
are outer bounds, do make sense. The intersection of all outer bound 
approximations is the target (except for infinitesimal wholes and other 
weird math forms). Therefore, we need an FOL that identifies all P7s as 
outer bound approximations of one, unique, real extent.
Fuzziness introduces another complication. It means that outer bound 
approximations coming "too near" to the real one, may become questionable.

Inner bound approximations would require unions for improvement.

Other approximations may minimize deviations from borders by various 
metrics.

The outer bound approximations are the ones which are processed most 
economically with FOL, except for the observational facts, which cannot 
be inferred.

would you agree on that?

Cheers,

Martin
 

Post by Wolfgang Schmidle (24 October 2022)

Dear Martin, 

Thank you for your insightful comments! Yes, I agree on your points about fuzziness and about FOL for outer bound approximations.

> The "creation" of a spatial projection is probably a misunderstanding. 

Fair enough, my words were not chosen well. My point was that the intersection belongs to a group of phenomenal or unique declarative thingies that behave like functions. I was trying to elaborate that we can introduce a function symbol representing the intersection even if FOL doesn't "know" about intersections. 

And let's forget about the union of attested places. My point was simply that we shouldn't argue with wobbly terms like "reasonable" or "context". For example, especially in the case of Caesar's murder one could argue that the context is in fact the whole Roman Empire. I am fine with S2 on that end of the scale if we don't burden it with semantic ballast. 

On the other end we have, assuming a shared reference system:
S1: P7 => P161
S2: P7 => all places between phenomenal place and P7 are also P7
S2a: S2 but with P7 instead of P161
F: the (explicitly named) intersection of two P7 is also P7

We know S2 => S2a and F

With the help of your comments I can now sharpen my point to this: S1 plus S2a plus F are enough to describe the known knowledge. Everything else that could theoretically be inferred by S2 is not known knowledge.

Take your example about detecting inconsistencies:

> Ceasar dying on the Forum Romanum has an empty intersection with the Theatrum Pompeii, on the Mars Field. Obviously inconconsistent.
> Consequently, Curia Iulia must be wrong.

This can be done with F. 

Best,
Wolfgang
 

Post by Martin Doerr (26 October 2022)

Dear Wolfgang,

I must admit that I cannot easily answer large e-mails that mix up 
several issues.

Firstly, a philosophical question for the below: Why do make the 
distinction of known knowledge? The CRM FOL are explicitly about being, 
not (only) about knowing.  If you implicitly argue that the CRM should 
describe only known knowlegde, I'd recommend you to read the paper by 
Carlo Meghini (and me) formalizing the CRM, and we discuss details!

Secondly,

I am a bit at loss what you mean by S1,S2,S2a.

I regard that P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y) is wrong. It is 
definitely that P7 implies that there exists a spatial projection inside 
the y in the same reference space. NOT, that if a spatial projection 
exists, it is inside the Y.

Please clarify!

Best,

Martin

Post by Wolfgang Schmidle (27 October 2022)

Dear Martin,

> I must admit that I cannot easily answer large e-mails that mix up several issues.

Yes, sorry for the mess.

> Firstly, a philosophical question for the below: Why do make the distinction of known knowledge? The CRM FOL are explicitly about being, not (only) about knowing.  If you implicitly argue that the CRM should describe only known knowlegde, I'd recommend you to read the paper by Carlo Meghini (and me) formalizing the CRM, and we discuss details!

I did read it. I skipped the skolemisation part and only read the Wikipedia article, though  :-)

The term "known knowledge" was not good. Let's go with "current knowledge" instead.

I don't say that the CRM should describe only current knowledge. I do say specifically about P7 that it should make up its mind whether it is about being or about knowing. Concretely, I suggest that P7 statements should only describe what is currently known, especially since it is so important to you to model finding the best known approximation of the phenomenal place. In other words, I see P7 as a "declarative property" that encodes explicit attestations and inferred knowledge. P161, on the other hand, is a "phenomenal property" and about being rather than knowing. Both are fundamentally different. I think it is pointless to soften this up by saying that all places between the phenomenal place and an attested P7 are also P7. Then one has to distinguish between known and as-yet-unknown P7. Take this scale of P7 statements from small to big:

phenomenal place 
… P7 places that are as-yet-unknown 
… the smallest inferrable P7 
… some inferred P7 
… an explicit attestation 
… more inferred P7 
… the largest explicit attestation that we know of and still regard as P7 
… places that are regarded as too big to be P7 
… planet Earth

So, my point is that the "P7 places that are as-yet-unknown" part at the beginning of the scale obscures the semantics of P7 and is neither useful nor necessary. It is enough to be able to find the smallest inferrable P7. 

In particular, I used to think that the relationship between P161 and P7 is vaguely similar to "has current X" and "has former or current X",  but I now think it is pointless to say P161(x,y) ∧ E4(x) ⇒ P7(x,y) because it says that the phenomenal place is automatically the best P7 approximation of itself, only that it can never actually be known. 

Even if you see it differently, would you agree that my interpretation of P7 is consistent and "does the job"?

> Secondly,
> I am a bit at loss what you mean by S1,S2,S2a.

Perhaps my description was too terse.

S1: P7 contains P161 (not "P7 => P161" as I wrote earlier)
* this is the first statement in the FOL block of P7 (after the domain and range statements)
* S1 states that each P7 provides an approximation of P161
* the exact form of S1 is discussed at length below

S2: P7 => all places between phenomenal place and P7 are also P7
* this is the second statement in the FOL block of P7
* S2 covers the scale above from "phenomenal place" to "the largest explicit attestation that we know of and still regard as P7"
* i.e. mixing up being and knowing

S2a: S2 but with P7 instead of P161
* this is the version of the second statement where the term P161(x,z) is replaced by P7(x,z)
* S2a covers everything between pairs of known P7
* if we can reach "the smallest inferrable P7", it covers the scale above from "the smallest inferrable P7" to "the largest explicit attestation that we know of and still regard as P7"
* i.e. purely about knowing

F: the (explicitly named) intersection of two P7 is also P7
* F makes sure that we can indeed reach "the smallest inferrable P7"
* i.e. purely about knowing

> I regard that P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y) is wrong. It is definitely that P7 implies that there exists a spatial projection inside the y in the same reference space. NOT, that if a spatial projection exists, it is inside the Y.

It doesn't mean that. The convention in the CIDOC CRM document is that implicit quantifiers are always "for all", not "exists". So it's more like "if z is the spatial projection".

P161 is one of the thingies that behave like a function. It depends on x and a reference system, and it exists independently of any P7. Let's call this function F161. It is defined as 
z = F161(x) ⇔ P161(x,z)

The reference system is conveniently left out here but could easily be added as a second variable u, as in F161(x,u). With the usual implicit (∀x,y), all the following statements are equivalent:

P7(x,y) ⇒ (∃z) [E53(z) ∧ P161(x,z) ∧ P89(z,y)]
P7(x,y) ⇒ (∀z) [E53(z) ∧ P161(x,z) ⇒ P89(z,y)]
P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y)  with an implicit (∀z)

P7(x,y) ⇒ (∃z) [z = F161(x) ∧ P89(z,y)]
P7(x,y) ⇒ (∀z) [z = F161(x) ⇒ P89(z,y)]
P7(x,y) ∧ z = F161(x) ⇒ P89(z,y)  with implicit (∀z)

P7(x,y) ⇒ P89(F161(x), y)

We haven't introduced function symbols yet. From the remaining versions I chose the one with P161 on the left-hand side because then I don't need to write down the implicit "for all" and can pretend there is no quantifier for z at all.

Best,
Wolfgang

Post by Martin Doerr (2 November 2022)

Dear Wolfgang,

Well, I do not think that the phenomenal place can never be known. Naming another thing y as approximation for x does not mean that x is unknown. It can be observed. It has an identity that can be used in reasoning. Fuzziness is not ignorance. If you ask me, if the distinction does the job, I am not sure which one. We have similar approximation questions with time-spans.

"It doesn't mean that. The convention in the CIDOC CRM document is that implicit quantifiers are always "for all", not "exists". So it's more like "if z is the spatial projection". "

Yes, I understand that. But if there is no spatial projection in the same reference system, the formula you give still holds. But I wanted to say, that it must exist.

So, is that different or not?

Best,

Martin 

Post by Wolfgang Schmidle (3 November 2022)

Dear Martin,

This bit from your "E9 Move and its relationship with the origin/destination" email seems to be about P7 and spatial projections of periods rather than specifically about E9 Move, so I reply to it here:

> The FOL formalisation is NOT about publicly available place attestations. This has not be said anywhere. Generally, the FOL statements are not constraint by known knowledge. If you question this, or require in the FOL to distinguish known knowledge from ontologically necessary one, we need another issue
>
> The spatial projection of the move is a P7. It exists regardless knowledge. 

My starting point was the question whether P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) is still regarded as true, and you said you regard that it was never true. This implies the big end of the P7 scale from small to big:

phenomenal place 
… the largest explicit attestation that we know of and still regard as P7 
… places that are regarded as too big to be P7 
… planet Earth

So at this end of the scale, the P7 statements are not about being, but represent knowledge and possibly a decision by the knowledge base maintainers. 

How does that fit together?

> Well, I do not think that the phenomenal place can never be known. Naming another thing y as approximation for x does not mean that x is unknown. It can be observed. It has an identity that can be used in reasoning. Fuzziness is not ignorance. If you ask me, if the distinction does the job, I am not sure which one. We have similar approximation questions with time-spans.

Yes, "can never be known" was poor wording. I meant: For most periods the boundaries of the phenomenal place can not be exactly described in a knowledge base. Which is why you want find outer approximations. 

"does the job": my interpretation of the P7 statements as representing the current attested and inferrable knowledge about outer approximations of the spatial projection, and providing a set of axioms that does exactly that.

>> "It doesn't mean that. The convention in the CIDOC CRM document is that implicit quantifiers are always "for all", not "exists". So it's more like "if z is the spatial projection". "
>
> Yes, I understand that. But if there is no spatial projection in the same reference system, the formula you give still holds. But I wanted to say, that it must exist.
>
> So, is that different or not?

For me it's not. Let me explain.

First, just to be clear: you no longer regard the axiom as wrong, but only as insufficient because it doesn't include the fact that the spatial projection must exist?

If you really want to express that a P7 statement is proof that a spatial projection exists, fine. If not, I don't think this axiom is the right place for that. It simply says that every P7 statement provides an outer approximation of the spatial projection in the same reference space, which we already know to exist regardless of any P7 statements. The right place to express that the spatial projection exists is, in my view, the FOL of P161. 

I think each FOL block should attempt to formalise what has been (explicitly or implicitly) stated in the respective scope note, and only that. With the exception "About the logical expressions used in the CIDOC CRM", see below. 

The P7 scope note does not say that a P7 statement causes the spatial projection to exist. On the contrary: "By the definition of P161 has spatial projection, an instance of E4 Period takes place on all its spatial projections to respective reference systems, that is, instances of E53 Place." 

The P161 scope note says: "The spatial projection is unique with respect to the reference system. For instance, there is exactly one spatial projection of Lord Nelson's dying relative to the ship HMS Victory". The scope note also talks about useful reference spaces. But it still seems to assume that for each spacetime volume and each reference space (not only the useful ones), a place exists that is the spatial projection. If this is wrong then the scope note should clarify this, and what the conditions are for the spatial projection to exist.

Existence and uniqueness are the justification for introducing the function symbol F161, as in Place z = F161(Spacetime Volume x, Physical Thing u). So far I have taken the definition of F161 and all other function symbols as an implicit acknowledgement of the existence and uniqueness. This could be stated in the introduction section "About the logical expressions used in the CIDOC CRM". But I am also fine with making it explicit in each case.

We already have an axiom that expresses the uniqueness:
P161(x,y) ∧ E53(z) ∧ P161(x,z) ∧ (∃u) [E18(u) ∧ P157(y,u) ∧ P157(z,u)] ⇒ (z = y)

We can add an explicit axiom for the existence:
(∀x,u) [E92(x) ∧ E18(u) ⇒ (∃z) [E53(z) ∧ P157(z,u) ∧ P161(x,z)]]

Once we have established the formalisations of the existence and uniqueness of the spatial projection, the different formulations of the P7 axiom are, in fact, equivalent.

(There are now at least four different names for the FOL lines: expression, statement, axiom, formula. Here I have called them axioms, and any P7(x,y) for instances x and y of P53 Place a statement.)

Best,
Wolfgang

Post by Wolfgang Schmidle (5 November 2022)

Dear Martin,

Thinking about your last comment again, would it be acceptable to you to add notes to certain FOL axioms? For example, one note in the P89 FOL and two notes in the P7 FOL:

P89 FOL:
domain, range
P89(x,x)

P89(x,y) ∧ P89(y,z) ⇒ P89(x,z)
Note: Typically, a knowledge base will not infer all possible P89(x,z) statements but may create a directed graph that can be traversed for reasoning.

(P89(x,y) also implies that x and y share the reference space. How this is done is a separate issue.)

P121 FOL:
domain, range
P121(x,y) ⇒ P121(y,x)
P121(x,x)

P121(x,y,z) ⇒ P121(x,y) ∧ E53(z)
(in the scope note: This symmetric property associates an instance of E53 Place with another instance of E53 Place geometrically overlapping it. The overlap defines a third instance of P53 Place that is taken as the third value in a ternary relation.)

P121(x,y,z) ⇒ P89(z,x) ∧ P89(z,y)
P121(x,y,z) ∧ E53(v) ∧ P89(v,x) ∧ P89(v,y) ⇒ P89(v,z)
(the usual properties of an intersection, applied to instances of P53 Place)

P161 FOL:
domain, range

P161(x,y,u) ⇔ P161(x,y) ∧ E18(u) ∧ P157(y,u)
(∀x,u) [E92(x) ∧ E18(u) ⇒ (∃y) [E53(y) ∧ P161(x,y,u)]]
P161(x,y,u) ∧ P161(x,z,u) ⇒  y = z
(existence and uniqueness of the spatial projection)

(P161(x,y) ∧ E4(x) ⇒ P7(x,y) has moved to the P7 FOL because it isn't mentioned in the P161 scope note)

P7 FOL:
domain, range
P7(x,y) ∧ E18(u) ∧ P157(y,u) ∧ E53(z) ∧ P161(y,z,u) ⇒ P89(z,y)

P7(x,y) ∧ P7(x,z) ∧ E53(v) ∧ P89(y,v) ∧ P89(v,z) ⇒ P7(x,v)
(This is the version with P7(x,z) instead of P161(x,z). The version with P161(x,z) follows from P7(x,y) ⇐ E4(x) ∧ P161(x,y).)

P7(x,y) ∧ P7(x,z) ∧ (∃u) [E18(u) ∧ P157(y,u) ∧ P157(z,u)] ⇒ P121(y,z)
(This additional axiom is needed to rule out Caesar's murder on the Forum Romanum, unless we add "otherwise z is the empty place" in the definition of P121(x,y,z).)

P7(x,y) ∧ P7(x,z) ∧ E53(v) ∧ P121(y,z,v) ⇒ P7(x,v)
(the intersection of two P7 places is also a P7 place)

P7(x,y) ⇐ E4(x) ∧ P161(x,y)
Note: A knowledge base may choose to leave out this axiom and reserve P7 statements for places whose known extent provides an outer approximation of the spatial projection.

P7(x,y) ⇒ (∃z) [E53(z) ∧ P89(y,z) ∧ ¬P7(x,z)]
(this is the negation of "for any given period x and place y, P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) is not true")
Note: A knowledge base may not contain any instance z of P53 Place with P89(y,z) ∧ ¬P7(x,z). In this case, the axiom should not be read as an instruction for adding one.

Best,
Wolfgang

Post by Martin Doerr (5 November 2022)

Dear Wolfgang,

Your proposal well-taken, but please!, it is the SIG that decides: "would it be acceptable to you to", not me. 
At best, I may support a particular proposal.

My opinion: of course, comments are most welcome!!!. We have to consider:

A) keep the Definition document as small as possible. Otherwise, people read only the RDFS or OWL.

B) Keep it digestable to a variety of audiences with different background

C) Consider ancillary documents.

D) We have a huge amount of work, volunteers welcome, concentration on the most important also welcome. A lot of expected, useful homework is not done. Anybody capable doing it?

E) Implementation of inferences in a KB is a very wide field. Approximations, alternative knowledge, contradictory knowledge, spatiotemporal and causal reasoning, negative knowledge, plausible deductions for increasing recall in incomplete knowledge (IBE="inference to the best explanation"), etc.  Are we on the relevant track?
Note also "minimal commitment" by Thomas Gruber. Logic can be a nice game, but often the necessary precision is not in the data, and the deduction not what is of cultural interest.

F) Someone capable to review the work. See, e.g., our principles guidelines

G) Will it be read, by whom?

Currently, I would like to finish first all basic background assumptions in FOL.

For instance, what utility should this have:

"P121(x,y,z) ⇒ P89(z,x) ∧ P89(z,y)
P121(x,y,z) ∧ E53(v) ∧ P89(v,x) ∧ P89(v,y) ⇒ P89(v,z)
(the usual properties of an intersection, applied to instances of P53 Place) "
Introducing a ternary relation is "not fun".

We can say that a place exist that falls within both. For me, that would be the basic thing to define.
Tricky question: What if a place does no more exist, because its reference frame is lost? What about frames that are at rest for some time (ship in harbour)?

In historical data, may be nothing more is known, neither where the one nor where the other place was. Needs also considering fuzzy zones. Well-defined borders as in modern states were rare from medieval times backwards. Typical question: What historical phenomena, I mean what people are doing, make us conclude that some places overlap?

For many of these advanced things, I'd prefer an implementation and use cases demonstrating the practical utility, so that we understand what is really needed and what is worth the effort.

Therefore, I think a first set of comments should stay strictly within things we are confident about. As few distinctions as possible.

Best,

Martin

Post by Christian-Emil Ore (28 November 2022)

Dear all,

The question is: If an instance x of E4 Period took place at an instance y of E53 place, can we conclude that x took place at all places containing  y? This was explicitly stated in CRMbase before the September meeting. The decission in Rome was to reformulate this as

Therefore, this property implies the more fully developed path from E4 Period through P161 has spatial projection, E53 Place, P89 falls within to E53 Place, where the intermediate place is also defined in the same geometric system. 

FOL:

P7(x,y) ⇒ (∃z,u) [E53(z) ˄ P157(x,u) ˄ E18(u) ˄ P157(y,u) ˄ P157(z,u) ˄ P161(x,z) ˄ P89(z,y) ]

or simplified

P7(x,y) ⇒ P161(x,z) ˄ P89(z,y) ]

The answer to the question is that P7(x,y) ∧ P89(y,z) ⇒ P7(x,z)  is in general is not considered true. This axiom has to be reintroduced if this is the general understanding. It is not needed in practical database/KB implementations.

Best,

Christian-Emil