I will not continue the discussion of identifying an instance of E18 Physical Thing with its spacetimevolume.
The intention with my “explanations” was to see whether the current model support an equality of P4 and P160 from E4 and downwards. In a FOL description of CRM the cardinality constraints are not just guidelines, they have strong implications on the model. For example:
1) P160 (E92 <-> E52) has the cardinality constraint (1,1:1,1) and is a 1-1 mapping (isomorphism) between E92 and E52
2) P4 (E2 <-> E52) has the cardinality constraint (1,1:1,1) and is a mapping between E2 and E52 where all instances of E52 is related to one or more instances of E2.
1 & 2 say that all time-spans are a time-span both for an instance of E92 and at least one instance of E2. There are no instance of E2, which does not share a time-span with a STV. This, I believe, is not the intention.
If we change the cardinality of P4 (E2 <-> E52) from (1,1:1,n) to (1,1:1,1) which is required if P2 and P160 should be equal when lowered to E4 <-> E52, the result is even worse. Then E2 and P52 is in a 1-1 correspondence.
Therefore the cardinality of P4 and P160 should be (1,1: 0,1) allowing instances of E52 to be a time-span for an instance of E2 without being a time-span for an instance of E52 and vice versa.
Still there is nothing in the formal FOL definition stating that P4 and P160 seen as properties between E4 and E52 are equal here Martin’s additional FOL expression comes in:
(P4(x,y) ∧E4(x)) ⊃ P160(x,y) ∧ (P160(x,y) ∧E4(x)) ⊃ P4(x,y)
This expression states that P4 and P160 is equivalent when the domain is restricted to P4.
Would that mean that each instance of E4 must have two
time-spans, one for the P4 and one for the P160?
Another solution could be the infamous "punning": Declare P4 to
have two domains, E2 and E92. Makes life easy, until we know the
"true" superclass of both. Isn't it? That is actually what we mean
but do not dare to say;-).
This is the only such restriction in CRM. The question is where to put this FOL expression. One could perhaps introduce multiple inheritance for properties and then introduce a subproperty of P4 and P160?
In any case, the 326 issue requires that the cardinalities are changed and that the scopenote of P4 is changed to
“This property describes the temporal confinement of an instance of an E2 Temporal Entity. The related E52 Time-Span is understood as the real Time-Span during which the phenomena were active, which make up the temporal entity instance. It does not convey any other meaning than a positioning on the “time-line” of chronology. The Time-Span in turn is approximated by a set of dates (E61 Time Primitive). Time-Spans may have completely unknown dates but other descriptions by which we can infer knowledge.”
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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: email@example.com Web-site: http://www.ics.forth.gr/isl