Re: [Crm-sig] Is P7(x,y) ∧ P89(y,z) ⇒ P7(x,z) still regarded as true?

[Martin Doerr via Crm-sig]

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

On 10/22/2022 12:39 PM, Wolfgang Schmidle via Crm-sig wrote:
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".


Am 21.10.2022 um 10:51 schrieb Wolfgang Schmidle via Crm-sig 
<crm-sig@ics.forth.gr>:

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


Am 20.10.2022 um 20:56 schrieb Martin Doerr via Crm-sig <crm-sig@ics.forth.gr>:

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


On 10/20/2022 3:12 PM, Wolfgang Schmidle via Crm-sig wrote:
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?



Am 20.10.2022 um 13:56 schrieb Wolfgang Schmidle via Crm-sig 
<crm-sig@ics.forth.gr>
:

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


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--
------------------------------------
Dr. Martin Doerr

Honorary Head of the
Center for Cultural Informatics

Information Systems Laboratory
Institute of Computer Science
Foundation for Research and Technology - Hellas (FORTH)

N.Plastira 100, Vassilika Vouton,
GR70013 Heraklion,Crete,Greece

Vox:+30(2810)391625
Email:
mar...@ics.forth.gr

Web-site:
http://www.ics.forth.gr/isl
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--
------------------------------------
 Dr. Martin Doerr
              
 Honorary Head of the
 Center for Cultural Informatics
 
 Information Systems Laboratory
 Institute of Computer Science
 Foundation for Research and Technology - Hellas (FORTH)
                  
 N.Plastira 100, Vassilika Vouton,
 GR70013 Heraklion,Crete,Greece
 
 Vox:+30(2810)391625
 Email: mar...@ics.forth.gr
 Web-site: http://www.ics.forth.gr/isl


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