Dear All,
I have extended the description of reflexivity with a motivation for
normal users, and created a clone description of non-reflexivity, in
yellow below. "Asymmetry" should disappear in the CRM following past
decisions.
reflexivity
Reflexivity is defined in the standard way found in mathematics or
logic: A property P is reflexive if the domain and range are the same
class and for all instances x, of this class the following is the case:
x is related by P to itself. The intention of a property as described in
the scope note will decide whether a property is reflexive or not. An
example of a reflexive property is E53 Place/. P89 falls within
(contains): /E53 Place. Since geometric areas can be arbitrarily close
to each other, the distinction, if two places with unprecisely known
extent are identical or are contained one in the other, can be difficult
or unknown. Defining this property as reflexive allows for describing in
one statement the topological constraint that a place x is either
contained in a place y or identical to y. However, it is not meant to
instantiate this property in a knowledge base for all instances of the
domain class. In First Order Logic, we denote reflexivity by:
“Pnn(x,x)”
Non-reflexivity
Non-reflexivity is defined in the standard way found in mathematics or
logic: A property P is non-reflexive if the domain and range are the
same class but for all instances x, of this class the following is the
case: x cannot be related by P to itself. The intention of a property as
described in the scope note will decide whether a property is
non-reflexive or not. An example of a non-reflexive property is E18
Physical Thing. /P46 is composed of/ (forms part of): E18 Physical
Thing. Since instances of E18 Physical Thing are required to be
distinct, it is reasonable to use the property /P46 is composed of/ only
for associating an instances of E18 Physical Thing with a part being
different from the whole. In logic, this is expressed by
non-reflexivity. In First Order Logic, we denote non-reflexivity by:
“ ¬Pnn(x,x)”
--
------------------------------------
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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