Dear All,
The issue 294 ended with this open question:
"I suspect the cardinality is logically wrong again. If a type of thing
is restricted to a period, it is not excluded for all its
subperiods.Needs more thought."
http://cidoc-crm.org/Issue/ID-294-e55-type-relations
<http://cidoc-crm.org/Issue/ID-294-e55-type-relations>
The definitions are the following:
*restricted to*
Domain: E55 Type
Range: E4 Period
Subproperty: appears in
Quantification: many-to-one
*/Scope Note: /*
This property associates a kind of object (documented as an instance of
E55) to an instance of E4 Period for indicating that objects of this
kind have exclusively been generated in this period.
This property makes a strong statement concerning the distribution of
the kind of object in the observation record: If the genesis of an
object of this type can plausibly be assumed to fall within the genesis
of the context in which it was found, then the statement made with this
property would support reasoning, ceteris paribus, that the genesis
period of the find context actually forms part of the related instance
of E4 Period, or at least overlaps with it.
In contrast, objects from previous periods may appear in a context
because they are still in use, and objects from later periods may have
been pushed into an older context.
Weaker claims can be made using the properties ‘typical for’ and
‘appears in’.
*typical for*
Domain: E55 Type
Range: E4 Period
Subproperty: appears in
Quantification: many-to-one
*//**/Scope Note: /*
This property associates a kind of object (documented as an instance of
E55) to an instance of E4 Period for indicating that objects of this
kind have been generated in this period in significantly higher numbers
and wider distribution, than in other periods.
This property makes a moderate statement concerning the distribution of
the kind of object in the observation record: If a sufficient number of
objects of this type are found in some context, and their genesis can
plausibly be assumed to fall within the genesis of the find context,
then the statement made with this property would support reasoning,
ceteris paribus, that the genesis period of the find context is likely
to forms part of the related instance of E4 Period, or at least overlaps
with it. “Sufficient number” means that the density of objects of this
kind in the find context is compatible with the general density this
kind of object had in the respective period in comparable contexts and
deposition history.
A stronger claim can be made using ‘restricted to’ while a weaker claim
is made using ‘appears in'.
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My reasoning:
If a type Y is restricted to a Period A, it is also restricted to any
wider Period of A.
The current quantification disallows the type Y to be restricted to any
other period. This is equivalent to a minimality requirement for the
range of "restricted to".
If we would require minimality, i.e., that there is no smaller Period B,
such that B falls within A, and the type Y is actually restricted to B,
we require complete knowledge of the appearance of Y in A. Further, a
later definition of a smaller period B, with B falls within A, and the
type Y actually restricted to B, would invalidate the statement about A.
Both are against the Open World assumption.
The intrinsic violation of the Open World assumption by "restricted to"
is already enough: It requires complete knowledge of what happened
outside this period. In practice, this is not so dramatic, because
creating the same type of some item by chance in a distant context may
be very unlikely, if local characteristics of workmanship are included
in the type definition, and the expert would not apply the property to
trivial items. Also in biology, the same species will never emerge at
independent places, even though similar environments may bring about
similar species.
Concluding, we need a cardinality many to many (0,n:0,n), *BUT *we can
formulate a minimality axiom:
restricted_to(x,y) AND restricted_to(x,z) => ¬(∃u)[E4(u) ˄
restricted_to(x,u) ˄ ¬ (P132(u,z) ˄P132(u,y)) ]
In other words, if a type X is restricted to a Period y and a Period z,
any other period restricted X is restricted to must overlap with both y
and z. As a consequence, the minimal Spacetime Volume will be the
intersection of all periods known to restrict X.
Opinions?
Best,
Martin
--
------------------------------------
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 protected]
Web-site: http://www.ics.forth.gr/isl
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