Draft Read Ahead For The May 7th Structural Modeling Project Video Conference

[joseph simpson]

Team:

We had an excellent video conference on April 2nd.

The current (new) version of the structural modeling software was presented and demonstrated.  This version allows more than one city to be located at the same latitude.

During the software demonstration, a number of questions arose.  The information in the attached 'Read Ahead' attempts to address the background necessary to answer these questions.

The primary questions, raised by Kevin Dye, related to the matrix operations associated with processing the empirical data about the relative position of the cities.

In particular, when discussing the matrix size reduction, Kevin noted that he had observed other structural modeling approaches that placed a one (1) in both matrix cells that represent the current relationship. He asked how this system handled the matrix size reduction.

The answer to this question traces back to the logical property of symmetry that is associated with the current natural language system structuring relationship.  In the case of 'north-of', the logical property is asymmetric.  For a valid system configuration where a one (1) is placed in both matrix cells, the natural language structuring relationship would have to be symmetric.

These ideas and issues are addressed further in the attached document.

Please let us know if you have any comments, questions, and/or concerns,

Joe

--

Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

[Kevin Dye]

On Apr 6, 2016, at 7:28 AM, syss...@googlegroups.com wrote:

In the case of 'north-of', the logical property is
asymmetric. For a valid system configuration where a one (1) is placed in
both matrix cells, the natural language structuring relationship would have
to be symmetric.

Can combinations of answers to asymmetric inquiries change the relationship to symmetric? The relation being inquired  about "North of” is asymmetric. I think for this relation answering yes both ways A>B and B>A would never make sense. But strangely, answering no in both directions would make the relation between the two symmetric.

Kevin Dye

[joseph simpson]

Kevin:

Great question and sharp insight...

The answer to this question in not as simple as it could be but it is not that involved either.  I will not attempt to answer this question in a general sense, but only as it applies to the current 'north-of' natural language relationship specific case.

First lets establish a context in which we may answer the question.  Two basic structuring situations will be addressed in this context:

  Case 1) North-of relationship: only one city at each latitude

  Case 2) North-of relationship: more than one city at each latitude

In Case 1, the asymmetric logical property is used to order the cities.  The cities are not ordered directly, however.  The equivalence classes are ordered and each equivalence class has only one city.  In this case we do not have to evaluate each city to see if it belongs in an equivalence with another city, it does not, by definition.

Therefore, in Case 1, the only operational function is ordering of the cities.

In Case 2, the asymmetric logical property is used to order the equivalence classes.  However, there are two functions in play in Case 2.  The first function is the  ordering of the equivalence classes.  The second function is the determination of class membership or equivalence. The ordering function requires an asymmetric logical property.  The equivalence function requires a symmetric logical property.

When answering 'no' in both directions, the natural language relationship is 'equal', which has a symmetric logical property.

After the equivalence function is completed, then more empirical data is collected and the Case 2 process is continued.

These uses are standardized and documented in the associated ART form.  If there are cases where the standard form needs to be adjusted, then the adjustment procedure is recorded in the standard ART form.

Please let me know if you have any further questions, comments and/or concerns,

Joe

[Kevin Dye]

On Apr 7, 2016, at 6:10 PM, joseph simpson <jjs...@gmail.com> wrote:

When answering 'no' in both directions, the natural language relationship is 'equal', which has a symmetric logical property.

It is symmetric as an inference of two assertions after the inquiry. In the typical ISM pairwise approach to inquiry we are not asking about an assertion of a symmetric relationship.

[joseph simpson]

Kevin:

Thanks for the additional information and insight.

At this time, using the ART form and the AMEI as they are developed to this point, there appears to be three alternatives:

  1) asymmetric

  2) symmetric

  3) non-symmetric

Many natural language system structuring relationships are not as logically constrained as the 'north-of' natural language relationship.

The AMEI outlines 27 groups of logical properties that may be used in combination with a natural language relationship to more precisely define the relationship.  The 'connected-to' natural language system structuring relationship was used in the development of the AMEI.  Connected-to is a valid natural language relationship for all 27 logical property groups.  Picking just one of the logical property groups greatly increases the definition of the relationship as well as reducing uncertainty and complexity.

The ART form was designed to provide a standard form and format for this system structuring information.  

At this time we are exploring the 'north-of' natural language structuring relationship which has the following properties:

  - irreflexive

  - asymmetric

  - transitive

The next area to explore is either a symmetric or non-symmetric natural language system structuring relationship. Influence is a natural language system structuring relationship that is not as logically constrained as the 'north-of' natural language relationship.  Influence can take a asymmetric, symmetric or non-symmetric logical form.

Many of the influence natural language structuring relationships that I have reviewed seem to allow a non-symmetric logical property.

The ART form and the AMEI provide the foundational structure and concepts necessary to discuss these relationships in a more precise manner.  

The plan is to continue the development and analysis of these various approaches.

Take care, be good to yourself and have fun,

Joe