Simple schema metamodel

Simple schema for metamodels. 

2008-04-12 

snsama@gmail.com 
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INTRODUCTION: 

Begin considering the simplest elements a language, or something similar,
might have. We can have a look at thing that are something, "Values", in our
term-set, which, in turn, have "Name"s, and then, from they nature, we can
infer or know its "Type". 

So, Values, Types and Names will be our simplest, or atomic, elements in our
namespace. 

For simplicity, and inheritance, reason, we could speak of Names being
either Types or Values, so our "class" hierarchy would have "Name" as its
superclass, being "Type" and "Value" subclasses of "Name". 

Considering them as sets, we can have the following diagram: 

http://www.nabble.com/file/p16646391/sets.gif 
 
In which the sets have been asigned binary values, being the position of any
of the three digits representing that something belongs to each set. (Type's
set is the first digit, a 1 in the representing number means that we are
threating with a Type, and so on...) 

In the preceding diagram, we have that the intersection of two sets, given
the binary OR operation on the digits representing them, gaves rise to a
third set, being the binary digits representation of it, the binary NOT
operation of the third set, which it's not in the intersection. 

We could state, for future mathematic foundations of this theory, that this
third intersection set is the set of the, for example, instances of types
(110), being the other (001) the set of classes of types. 

Given this distinction, we could thing, looking at the following image, that
an instance of some of the three elements given in this documents, is formed
upon two of the other elements: 
 


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RECURSIVE PYRAMID VIEW: 

http://www.nabble.com/file/p16646391/piramide.gif  

Let's go to something more concrete: 


Given this space of three classes of elements who should describe, at least,
kind of ontologies, we should have that: 

1. Given a Name, for example, of a relationship, like "Fatherhood" we should
state that: 

a. A fatherhood relationships occurs between a father and a son, which, in
turn, are both of type Person. 

    - Fatherhood := ( Father, Person ) 

In the preceding statement, Fatherhood is a Name, Father is another Name,
which have as Type 'Person' and 'Father' as value. 

2. Given a Fatherhood relationship, we should be able to assign to any both
persons the value of the two roles in the relationship: 

     - aFatherhood ( "Peter", Father) 

In the preceding statement, aFatherhood is the name of an instance of the
relationship, "Peter" is an instance of Person (a value) and Father is the
Type of the role in the relationship. 

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http://www.nabble.com/file/p16646391/classInstance.gif 


The preceding diagram shows how the different elements in the metamodel can
compose each other, being the rightmost (Name, instance) whose who reifies
those at the left, which are in turn classes for them. 

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SERIALIZATION: 


The proposal for this is to be able to serialize to, for example, XML, all
of an ontology, using only the the three elements discused above. 


PROTOTYPE CLASS DIAGRAM: 

Next is a sample class diagram that could be useful as a starting point to
further development. 

http://www.nabble.com/file/p16646391/classes.gif 

It's worth nothing that Names and so on are context(s), which are themselves
statements like RDF triples. 
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References: 

W3C Semantic Web: www.w3.org/2001/sw/ 

Ontopia (ISO TopicMaps consulting): http://www.ontopia.net 

2008-04-12 
snsama@gmail.com
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Received on Saturday, 12 April 2008 07:51:37 UTC