[Crm-sig] Issue 571, cardinality of properties of properties

Martin Doerr martin at ics.forth.gr
Mon Jan 24 19:58:07 EET 2022


Dear All:

Under “About the logical expressions used in the CIDOC CRM”, we find 
these paragraphs:


The present CIDOC CRM specifications are annotated with logical axioms, 
providing an additional formal expression of the CIDOC CRM ontology. 
This section briefly introduces the assumptions that are at the basis of 
the logical expression of the CIDOC CRM (for a fully detailed account of 
the logical expression of semantic data modelling, see (Reiter,1984)).

The CIDOC CRM is expressed in terms of the primitives of semantic data 
modelling. As such, it consists of:

· classes,which represent general notions in the domain of discourse, 
such as the CIDOC CRM class E21 Person which represents the notion of 
person;

· properties,which represent the binary relations that link the 
individuals in the domain of discourse, such as the CIDOC CRM property 
P152 has parent linking a person to one of the person’s parent.

Classes and properties are used to express ontological knowledge by 
means of various kinds of constraints, such as sub-class/sub-property 
links, e.g., E21 Personis a sub-class ofE20 Biological Object, or 
domain/range constraints, e.g., the domain of P152 has parentis class 
E21 Person.

In contrast, first-order logic-based knowledge representation relies on 
a language for formally encoding an ontology. This language can be 
directly put in correspondence with semantic data modelling in a 
straightforward way:

·    classes are named by unary predicate symbols; conventionally, we 
use E21 as the unary predicate symbol corresponding to class E21 Person;

·    properties are named by binary predicate symbols; conventionally, 
we use P152 as the binary predicate symbol corresponding to property 
P152 has parent.

·    properties of properties, “.1 properties” are named by ternary 
predicate symbols; conventionally, we use P14.1 as the ternary predicate 
symbol corresponding to property P14.1 in the role of.

—---------------------------------------------------------


Under “About Types”, we find this paragraph:


Analogous to the function of the P2 has type (is type of)property, some 
properties in the CIDOC CRM are associated with an additional property. 
These are numbered in the CIDOC CRM documentation with a ‘.1’ extension. 
The range of these properties of properties always falls under E55 Type. 
The purpose of a property of a property is to provide an alternative 
mechanism to specialize its domain property through the use of property 
subtypes declared as instances of E55 Type. They do not appear in the 
property hierarchy list but are included as part of the property 
declarations and referred to in the class declarations. For example, 
P62.1 mode of depiction: E55 Type is associated with E24 Physical 
Man-made Thing. P62 depicts (is depicted by): E1 CRM Entity.

--------------------------------------------------------------------------------------------------------------------- 


However, we completely missa statement about the actual form of the CRM 
under “Applied Form” in thefirst place!.


Instead, it is implicit in “About the logical expressions used in the 
CIDOC CRM”, as shown above, and *misses properties of properties.*


I therefore propose (changes in yellow):


    Applied Form

The CIDOC CRM is an ontology in the sense used in computer science. It 
has been expressed as an object-oriented semantic model, in the hope 
that this formulation will be comprehensible to both documentation 
experts and information scientists alike, while at the same time being 
readily converted to machine-readable formats such as RDF Schema or OWL. 
A CRM conformant documentation system can be implemented using RDF 
Schema or OWL, but also in Relational or Object-Oriented schema. CIDOC 
CRM instances can be encoded in RDF, JSON LD, XML, OWL and others.

More specifically, the CIDOC CRM is expressed in terms of the primitives 
of semantic data modelling. As such, it consists of:

· classes,which represent general notions in the domain of discourse, 
such as the CIDOC CRM class E21 Person which represents the notion of 
person;

· properties,which represent the binary relations that link the 
individuals in the domain of discourse, such as the CIDOC CRM property 
P152 has parent linking a person to one of the person’s parent.

  *

    properties of properties, such as the property P14.1 in the role of
      of the CIDOC CRMproperty P14 carried out by (see also section
    “About Types”). (They do not appear in the property hierarchy list,
    but are included as part of their base property declaration and are
    referred to in the class declarations. They all have the implicit
    quantification “many to many” (see also section “Property Quantifiers”))

Although the definition of the CIDOC CRM provided here is complete, it 
is an intentionally compact and concise presentation of the CIDOC CRM’s  
81 classes and 160 unique properties. It does not attempt to articulate 
the inheritance of properties by subclasses throughout the class 
hierarchy (this would require the declaration of several thousand 
properties, as opposed to 160). However, this definition does contain 
all of the information necessary to infer and automatically generate a 
full declaration of all properties, including inherited properties.

—-------------------------------------------------------------------------------------

Add to Naming Conventions:a *last bullet item*:

·    Properties of properties are identified by “P”, followed by the 
number of the base property extended with “.1”  and are named in one 
direction using a verbal phrase in lower case in the present tense. For 
example: the property P62.1 mode of depiction of the property P62 
depicts (is depicted by).


—--------------------------------------------------------------------------------------

About the logical expressions used in the CIDOC CRM”


The present CIDOC CRM specifications are annotated with logical axioms, 
providing an additional formal expression of the CIDOC CRM ontology. 
This section briefly introduces the assumptions that are at the basis of 
the logical expression of the CIDOC CRM (for a fully detailed account of 
the logical expression of semantic data modelling, see (Reiter,1984)).

(delete the text copied into "Applied Form").

In terms of semantic data modelling, classes and properties are used to 
express ontological knowledge by means of various kinds of constraints, 
such as sub-class/sub-property links, e.g., E21 Personis a sub-class 
ofE20 Biological Object, or domain/range constraints, e.g., the domain 
of P152 has parentis class E21 Person.

In contrast, first-order logic-based knowledge representation relies on 
a language for formally encoding an ontology. This language can be 
directly put in correspondence with semantic data modelling in a 
straightforward way:

·    classes are named by unary predicate symbols; conventionally, we 
use E21 as the unary predicate symbol corresponding to class E21 Person;

·    properties are named by binary predicate symbols; conventionally, 
we use P152 as the binary predicate symbol corresponding to property 
P152 has parent.

·    properties of properties, “.1 properties”, are named by ternary 
predicate symbols; conventionally, we use P14.1 as the ternary predicate 
symbol corresponding to property P14.1 in the role of.

………

—----------------------------------------------------------------------------------------------------------------

Add at the end of “Property Quantifiers” :

Note that the quantification of all properties of properties, “.1 
properties”, is “many to many”, and therefore does not appear explicitly 
in their definitions.

—--------------------------------------------------------------------------------------------------------------------------

-- 
------------------------------------
  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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