Re: [ontolog-forum] Defining everything in terms of relations (was Charl

[William Frank <williamf.frank@xxxxxxxxx>]

On Mon, Feb 24, 2014 at 8:05 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:

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).

I strongly agree.

Horray! 

(by the way, I wrote this before receiving Ed's remarks on the subject.  I have to agree with him that 0-ary 'relations' are problematic, and worthy of more consideration.  As an overview, I think the computer science side of the problem can be approached with the iota operator and the lamda operator, while I would fully expect that my philosophical ontology is naive, and fraught with potential contradictions.  
 

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

Exactly.   In other words, they are DERIVED terms.
 

For example, my preferred axiom for entity:

    (Ax)Entity(x).

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.

Exactly. That reification hagling was the very most convoluted part of the dasterdly official UML semantics.  They actually believed that each 'level' of abstraction was a model of **a different world**, hence metametameta models.  I thought this went out in logic with Carnap, almost 75 years ago.  Now, logicians use 'meta' the way you do below. As a way to discourse about the language of some other discourse, E.g. a meta model for ontologies) not as of 1930's-old and of the (bad) 'fathers of UML"  where they seem to use it as a way to separate sets from individuals, sets of sets from sets, etc, and treat them all as somehow incompatable.

Your set of axioms here is exactly what I have been using implicitly.    The roles in a relation are yet more entities, of course.

I only just now rediscovered, following along the Fillmore path, that the idea of 'case grammars', which after all, are syntactic features of individual langauges, has been largely replaced in generative linguistics by the concept of a 'theta role', an underlying set of trans-language roles that enable inter-language mappings. 

As far as I know, this began with Ed Keenan's discovery of what he at-the-time called 'voices' in Malagasy, where the subject of a sentence is preceded by a separate particle that describes in role in the verb.  A more formal and modern presentation of this is in his "Morphology is Structure - A Malagasy Test Case"

 

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.

If you want properties, define them:

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

This says that a property is anything that an entity has.

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

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.

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.

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.

John

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