[Crm-sig] Homework Issue 517

Martin Doerr martin at ics.forth.gr
Sun Oct 3 22:12:30 EEST 2021


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: martin at ics.forth.gr
  Web-site: http://www.ics.forth.gr/isl

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