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 >>>> >>>> >>>> _______________________________________________ >>>> Crm-sig mailing list >>>> >>>> Crm-sig@ics.forth.gr >>>> http://lists.ics.forth.gr/mailman/listinfo/crm-sig >>> >>> _______________________________________________ >>> Crm-sig mailing list >>> >>> Crm-sig@ics.forth.gr >>> http://lists.ics.forth.gr/mailman/listinfo/crm-sig >> >> >> -- >> ------------------------------------ >> 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 >> _______________________________________________ >> Crm-sig mailing list >> Crm-sig@ics.forth.gr >> http://lists.ics.forth.gr/mailman/listinfo/crm-sig > > > _______________________________________________ > Crm-sig mailing list > Crm-sig@ics.forth.gr > http://lists.ics.forth.gr/mailman/listinfo/crm-sig _______________________________________________ Crm-sig mailing list Crm-sig@ics.forth.gr http://lists.ics.forth.gr/mailman/listinfo/crm-sig
