[Top] [All Lists]

[ontolog-forum] Defining everything in terms of relations (was Charles F

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 24 Feb 2014 08:05:44 -0500
Message-id: <530B43A8.2050209@xxxxxxxxxxx>
On 2/23/2014 11:18 PM, William Frank wrote:
> I have found that n-ary relations with n = 0 to *, together with roles
> (my 'computer science' meta-ontology or upper ontology) is a more
> expressive,  more flexible,  simpler, way to represent knowledge for
> computing purposes than 'entities', 'attributes, and 'relationships' (an
> can easily be done with UML diagrams).    (01)

I strongly agree.    (02)

I have no objection to using terms like 'entity', 'attribute',
'property', 'class', etc.  But each of them should be defined
in terms of relations.    (03)

For example, my preferred axiom for entity:    (04)

    (Ax)Entity(x).    (05)

In other words, everything in the ontology is an entity.  If your
logic lets you quantify over relations, then relations are also
entities.  That lets You dispense with the endless wrangling about
reifying stuff.  If you want to refer to something, then refer to it.    (06)

A class is defined as a pair (t,s), where t is a monadic relation
called the type, and s is the set of everything for which t is true.    (07)

If you want properties, define them:    (08)

   (Ax)(Ay)(Entity(x) & HasProp(x,y) => Property(y))    (09)

This says that a property is anything that an entity has.    (010)

Q:  What do you mean by HasProp?
A:  HasProp is a relation between entities and properties.    (011)

Q:  Isn't that a circular definition?
A:  Of course it is.  All your basic terms can only be defined
     by their relations to one another.  For examples, see Euclid.    (012)

Q:  How would anyone know what kinds of things are properties?
A:  Formally, state more axioms.  Informally, show some examples
     and discuss the pros and cons of various options.    (013)

This gives you clear, precise definitions of all the metalevel
terminology for talking about ontologies and relating them to
any system(s) that happen to use different terminology.    (014)

John    (015)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (016)

<Prev in Thread] Current Thread [Next in Thread>