Formal Concept Analysis ...

[joseph simpson]

Formal Concept Analysis (FCA)  is an interesting component of information science that produces a concept hierarchy as well as a formal ontology.

See:

   http://en.wikipedia.org/wiki/Formal_concept_analysis

A formal context consists of a set of objects O, a set of unary attributes A, and an indication of which objects have which attributes.

One can create a concept lattice of a context.

There are some very interesting aspects of FCA that support the design and discovery of systems, objects, attributes and the implied relationships between and among the objects and their attributes.

A formal concept is determined by the identifying the a set of objects and attributes that are related by the FCA incidence relation.

This creates a situation where a formal context could have no formal concepts. (absence of the incidence relation)

Anyway, FCA is very similar to my definition of a system.

I define a system as a relationship mapped over a set of objects. (The type of relationship in not restricted)

In FCA only one relationship is allowed, incidence of.

Have fun,

Joe


Joe Simpson

Sent From My DROID!!

[Jack Ring]

Seems to me you are inserting the "Codd Error" here. Peirce just rolled over in his grave.

If objects can participate in relationships then why do you need 'attributes'? Is not an attribute an object? Aren't you using the term attribute to refer to some kind of object instead of simply noting that attribute is a relationship between two or more objects?

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[joseph simpson]

Formal Concept Analysis is well defined.

It has many similar traits and aspects that appear to be congruent with a large portion of systems science practice and understanding.

FCA only allows one very basic binary relation, "incidence of."

This arrangement of components provides a connection pattern that then becomes the primary indicator of value. (like a signature)

Each formal concept has an extent and an intent which again provides a very interesting configuration signature.

These simple arrangements form a Galois connection that specify that each operator of the connection uniquely determines the other.  Which is very similar to some of the work done by Kent Palmer.  The Galois connection is very important for the analysis of objects under incomplete information. 

Anyway fun stuff... so what error did Codd make?

Have fun,

Joe

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[Jack Ring]

1. ERA, not noting that a supposed A was really another E.

2. Not acknowledge Usage, U, which constrains the kinds of relationships that are viable (OK to subtract 10/18/2012 from11/1/2013 but not to multiply the two). The root of failure to discern configuration vs. behavior.

[joseph simpson]

Interesting set of statements but the connection to Formal Concept Analysis (FCA) seems to be quite obscure.

FCA allows only one type of relation (incidence of) .

FCA allows a mark  or no mark (or value (0 or 1) ) to indicate the existence of the "incidence-of " relation.

The bulk of FCA operations evaluate the entire FCA structure of interest.

Take care and have fun,

Joe

[Jack Ring]

The connection to FCA is quite clear for those who want to see it. The use of 'attributes' as entities instead of kind of relationships (beyond incidence of) locks you into a reductionist view. 

[joseph simpson]

It appears to me that two models of information, each of which contain the idea of an attribute are being addressed in a manner that is not clear to me ....

Can you provide an example of a domain space that is modeled in FCA and the other information model..

A simple model in both forms may help me see clearly...

Have fun,

Joe

[Jack Ring]

Simply restrict yourself to entities and relations. If some facet or aspect of an entity is relevant then that is another entity and the relation to the first is "attribute"

[joseph simpson]

I simply do not understand.

Which model of information are you addressing?

One or both?

If one which one, if both it makes no sense.

Have fun,

[Jack Ring]

I am responding to your May 18 post:

A formal context consists of a set of objects O, a set of unary attributes A, and an indication of which objects have which attributes.

One can create a concept lattice of a context.

There are some very interesting aspects of FCA that support the design and discovery of systems, objects, attributes and the implied relationships between and among the objects and their attributes.

I am telling you that attribute, the way you use the term, is semantically equivalent to object whereas attribute should signify a kind of relation ship between two (or more) objects.

(O) man

(O) eyes

(O) color

(O) blue

(O) sky

c.f., Rosen's relational theory

[joseph simpson]

A working paper that addresses some of these issues in more detail is in the development process.

It is clear that there are information models that are different from Formal Concept Analysis (FCA).

These different information models use the term "attribute."

The FCA information model is not impacted because other models use the term attribute.

It is difficult or impossible to discuss FCA using definitions from other information models.

It is difficult to discuss other information models if there are not named and referenced.

I use the term attribute in a manner that aligns with the information model I am discussing, in this specific case FCA.

I agree that the word attribute is used in many different ways...

Have fun,

Joe

[Jack Ring]

My error, I thought you were engaged in system models.

[Georg...@aol.com]

 

 

In a message dated 20/05/2012 07:13:01 GMT Daylight Time, jri...@gmail.com writes:

agree that the word attribute is used in many different ways...

Have fun,

Joe

Usually  disambiguated  by  an  adjective  or  even  a  phrase,  but  where  is  the  INCOSE  fun  in  that  ?

 

George

 

[joseph simpson]

Have fun,

Joe

[joseph simpson]

Terms can also be disambiguated by understanding the specific context of use...

That is why the dual pattern of concept and context is very interesting... in the application of Formal Concept Analysis

These two patterns indicate if there is an association between an object and an attribute.

These patterns are artifacts of the complete arrangement (total system) ....

The well defined terms FCA concept and FCA context provide two total system metrics similar to the idea of entropy as a total system metric.

An interesting FCA context is an empty FCA context that has no marks of association (the empty FCA context)

The empty FCA context has very interesting properties.

Another interesting FCA context is an full context where every possible association is marked (the full FCA context)

Even more interesting patterns evolve when these two boundary FCA patterns are evaluated against each other.

There are other very interesting patterns associated which the evaluation of other combinations of FCA artifacts....

Have fun,

Joe

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