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
On 10/22/2022 11:23 PM, Martin Doerr via Crm-sig wrote:
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
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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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