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Re: [ontolog-forum] Interpreting OWL

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Mon, 18 Oct 2010 12:14:24 -0700
Message-id: <20101018191428.3F9FD138CCD@xxxxxxxxxxxxxxxxx>

Hi Doug, John, Pavithra in that order of your posts, et al,

 

I seem to have a talent for underspecifying my visual descriptions. Let me use a drawing to better, more precisely state the situation in words that map onto the figure.  Consider three symbol tables, each allocating an identifier in one dimension in the order of arrival of that UNIQUE integer arrival identifier, which can occur multiple times in a database.  Here is a figure which kinda illustrates what I am visualizing:

 

 

Sign IDs start begin allocated from the origin, starting at ID=1 for the first sign, and incrementing the symbol ID (2,3, .. Ns) for signs, one at a time upon encountering them.  Those signs, let me further constrain, are allocated IDs in one pass through a text file which has well formed statements of the vocabulary in which a sign, first encountered, gets assigned a new ID.  If that sign is encountered again later in the text file, the symbol table pairs it with its very first ID for the rest of the pass through the text.  

 

Similarly, the events are IDed in order of their being encountered in the same text file during one pass scan.  They use (conceptually) a distinct symbol table, and some of the events may be named identically with the signs, so that “write” can be a sign or an event since it is in reality naming two different kinds of things.  That set of events is on the Y axis above, and are recognized as events, not signs, based on the syntax of the text tokens to be an event, not a sign.  

 

On the third axis, Individuals - the constant <object/thing/designating phrase..> IDs allocated in arrival order by a third conceptual symbol table - which appears in the expressions for event statements (e.g. sentences) that identify slot fillers for specific events, some of which may be the same KIND of sentences (Michael rowed the boat ashore.  Michael threw a stone into the sea.  Janet hurled the sandwich onto the wall. …) based on a similarity measure of syntax TBD.  

 

I may STILL not be stating this in a recognizable way (your forebearance is appreciated), but what I am trying to say is that the two independent axes (Event IDs and sign IDs) which are arbitrarily defined as pattern types, one type for each position (ID) on these two axes.  

 

The third axis is dependent on the pattern fillers which (glossed over mostly, but please try to imagine what I am seeing) identify individual designations (Michael, rowed, boat, ashore, threw, stone, sea, Janet, hurled, sandwich, wall, …) each with a concept.  

 

Later in the text, there are phrases which refer to Michael (The man, he, the rower, the thrower, …) based on correlating event slot fillers to identify which phrases refer to which individual.  These phrases occupy the intersections of the three axes. 

 

===================  ====================

 

Now having constructed the cube above with that one pass scan of the text, the next task is to sort each of the three axes, maintaining the integrity of the cube elements so that they are maintained as the same statements, just reordered into the cube so that they form a positionally. 

 

Given two sortings, the one with the same event types occupying one block of entries on the event axis is preferred.  So perhaps the events of a given type appear contiguously on the event ID axis, even though the ID numbers are no longer in sequential order.  

 

The result is a sorted version of the three D cube with a slice of a specific event type (with many instances) are contiguous, the IDs appear almost randomly placed in their value sequence along the event axis.  Here is another view of that cube after sorting:

 

 

The gap at the highest gradient on all three axes indicates that there are no statements which intersect the highest sort order sign with the highest sort order event and the highest sort order individual.  

 

Now by partitioning the image along each of the three axes, I can organize the cube into six volumes, as shown below:

 

 

Note that the min and max points of the coordinate system on each axis are subscripted in a Gray code way: p000 is the origin, p001, po10, p100, p111, and so forth.  

 

The purple line is, by construction describing a monotonically increasing subscript for transitioning from the origin p000 to the highest enumerated ID at p111.  

 

I suggest that the ordering produced by this process can be searched by three binary search iterators, each visiting only one axis.  I also suggest that the purple line can be viewed as an ordering of the three axes, using gray code subscripts as above after the sort operation.  

 

Having done all this, you may ask why bother?  The construction I am trying to organize (underspecified so far) is that a single binary search can be used to find any statement(s) which unify with a query that may have designations (event, individual, sign specifiers) which are combinations of variables and constants.  

 

Having constructed such, the ways in which unification of the query _expression_ with the cube contents appears to me to have a geometrical interpretation which can be exploited to reduce the number of unifications which must be searched to enumerate the possible resolutions for each potential unification, not fully specified in some mappings, but fully specified to constants in others.  

 

The goal is to find a way to partition the number of cases that have to be fully evaluated to determine if there exists one or more unifications of the query with the content. 

 

Comments and questions, suggestions, appreciated. 

 

Quizzically,

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

 

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Sunday, October 17, 2010 9:20 PM
To: '[ontolog-forum] '
Subject: Re: [ontolog-forum] Interpreting OWL

 

John, Pavithra, Doug et al,

 

A DAG is the normal, prototypical situation of databases then. That

constraint means that there is an ordering of the <relation>s on one axis

and the <person/object/thing>s on another which would look like a

topographic map of a square of land.  Specifically, the ordering of

<relation>s by identifier associated with the temporal arrival sequence of

the relation references in a <text/ontology/dictionary/lexicon> in ascending

order by arrival, mapped against an ordering of <person/object/thing>s in

ascending order of their own arrival.  This is the structure of a single

pass analysis from beginning to end of the model. 

 

Is that intuition correct?  I.e., a topographically level or sloping model

of two <property/attribute/column>s in the value plane is ALWAYS REALIZABLE

given the axes are ordered by arrival sequence in ascending order from the

start (origin) of the <text/ontology/dictionary/lexicon> being scanned in

one pass?

 

Queriously,

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

 

-----Original Message-----

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx

[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa

Sent: Sunday, October 17, 2010 8:30 PM

To: ontolog-forum@xxxxxxxxxxxxxxxx

Subject: Re: [ontolog-forum] Interpreting OWL

 

On 10/17/2010 10:59 PM, doug foxvog wrote:

> It seems to me that the graph would have many disconnected subgraphs,

> and certainly not be a single tree.

 

Yes.  Technically, it would be a forest.

 

> The unusual case would be when there was a loop.  This could happen if

> a professor were to go for another PhD after a number of years, and

> have as a thesis advisor in the new field a former student or even

> student of a student.

 

Yes.

 

On 10/17/2010 11:20 PM, Rich Cooper wrote:

> Is there any looser constraint, or must the graph be a DAG at all to be

> fully distinguishable<persons/objects/things>  among the paths?

 

If all relations are symmetric, the graph would not be directed.

But most relations are not symmetric.

 

John

 

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