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
