Previously Copyright David Dodds 2008
There are ontologies in the NASA JPL SWEET set and in (the huge
ontology) openCYC which provide semantic information about Space and
Time amongst other domains. There is a namespace, '
xmlns:dl="http://ontology.dumontierlab.com/ ', its description
statement says , ' An ontology of statistical graphs and their
components.' The ontology also contains info that this is version 2,
on the subject of graphs; and has the title 'Statistical Graph
Ontology'. Ok so now we know what this ontology is said to be (about)
and that it is depicted in the rdf/xml format.

(( Copyright Michel Dumontier, (regarding specifically the
dumontierlab ontology excerpts in this article, treated as quotes from
' xmlns:dl="http://ontology.dumontierlab.com/ '))

<!-- http://ontology.dumontierlab.com/isAfter -->

<owl:ObjectProperty rdf:about="&dl;isAfter">
<rdf:type rdf:resource="&owl;TransitiveProperty"/>
<owl:inverseOf rdf:resource="&dl;isBefore"/>
</owl:ObjectProperty>



<!-- http://ontology.dumontierlab.com/isBefore -->

<owl:ObjectProperty rdf:about="&dl;isBefore">
<rdf:type rdf:resource="&owl;TransitiveProperty"/>
</owl:ObjectProperty>


Compare the (human) intent or purpose of the use of the terms (in
ontology.dumontierlab) "isAfter" and "isBefore"; with the intent or
purpose of the use of the terms "AtRight" and "AtLeft" (in my ontology=)

<svg xmlns = 'http://www.w3.org/2000/svg'>
<desc xmlns:myfoo="http://example.org/myfoo">
<myfoo:title>This is a financial report</myfoo:title>
<myfoo:descr>The global description uses markup from the
<myfoo:emph>myfoo</myfoo:emph> namespace.</myfoo:descr>
<myfoo:scene><myfoo:what>widget growth</myfoo:what>
<myfoo:contains>thirteen graph-bar</myfoo:contains>
<myfoo:when>1987 through 1999</myfoo:when> </myfoo:scene>
</desc>
<metadata xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:rdfs="http://www.w3.org/TR/. ..-schema#"
xmlns:omcsvg="http://www.open-meta.com/omcschema/" >

which was presented as David's SVG barchart a few episodes back, and
wherein we saw the following passage:

<rdf:Description about="#endlineleft">
<omcsvg:AtRight resource="#bar1"/>
</rdf:Description>
<rdf:Description about="#endlineleft">
<omcsvg:IsNear resource="#bar1" />
</rdf:Description>
<rdf:Description about="#endlineright">
<omcsvg:AtLeft resource="#bar13"/>
</rdf:Description>
<rdf:Description about="#endlineright">
<omcsvg:IsNear resource="#bar13" />
</rdf:Description>

The meaning of "isAfter", "isBefore", "AtRight" and "AtLeft" is
defined by the location in an ontology where these XML strings appear
as stringnames in XML IDs appearing in such ontology, and by the
relationships and values depicted by the ontological items in such
ontology which are associated with these IDs by virtue of the (XML)
"structure" . Notice that in "numerics.owl" (one of ontologies in the
NASA JPL SWEET set) there appears the passage:

<owl:ObjectProperty rdf:ID="lessThan">
<rdf:type
rdf:resource="http://www.w3.org/2002/07/owl#TransitiveProperty" />
<owl:inverseOf rdf:resource="#greaterThanOrEqual"/>
<rdfs:domain rdf:resource="#NumericalEntity"/>
<rdfs:range rdf:resource="#NumericalEntity"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="greaterThan">
<rdf:type
rdf:resource="http://www.w3.org/2002/07/owl#TransitiveProperty" />
<owl:inverseOf rdf:resource="#lessThanOrEqual"/>
<rdfs:domain rdf:resource="#NumericalEntity"/>
<rdfs:range rdf:resource="#NumericalEntity"/>
</owl:ObjectProperty>

which states that (the rdf:ID=) "lessThan" and (the rdf:ID=)
"greaterThan" are both
"NumericalEntity"s in addition to being "owl#TransitiveProperty". Both
ontology.dumontierlab and sweet.jpl.nasa.gov/ontology/numerics.owl
state that the concepts behind (the rdf:ID=) "lessThan" and (the
rdf:ID=) "greaterThan", and (the rdf:ID=) "isBefore" and (the
rdf:ID=) "isAfter" are "owl#TransitiveProperty". The difference is
that sweet.jpl.nasa.gov/ontology/numerics.owl states that (the
rdf:ID=) "lessThan" and (the rdf:ID=) "greaterThan" are both
"NumericalEntity"s (ie 'numerical things'). This is important for it
allows the computer to "realize" (as in detect) that number values and
numeric tests (like a.eq.b, or d.gt.e (stated as a = b, d > e, t < l
in some programming languages)) can be pursued vis-a-vis semantic
items like (the rdf:ID=) "lessThan" and (the rdf:ID=) "greaterThan".
(Nobody's home in a computer.) It is possible to make the terms
equivalent via the OWL term: '<owl:equivalentClass
rdf:resource="#placestringnamehere"/>'. David Dodds has done just that
by using the 'ontology merge' technique described by Stanford Protege OWL.

In the merged ontology (the rdf:ID=) "isBefore" and (the rdf:ID=)
"lessThan" are 'owl:equivalentClass' ("equivalent) and similarly for
(the rdf:ID=) "isAfter" and (the rdf:ID=) "greaterThan"; and this
allows the computer to relate numeric values and relationships with
these terms. In the same way, in the bargraph file the concept 'below'
can be equivalenced with (the rdf:ID=) "greaterThan".

<rdf:Description about="#text1">
<omcsvg:Below resource="#xbaseline"/>
</rdf:Description>

<rdf:Description about="#text2">
<omcsvg:Below resource="#text1"/>
</rdf:Description>

'Greater than' is correct instead of 'less than' in this particular
case because of the context wherein the numerical relation
'omcsvg:Below' is used. The context is that of an SVG 'program' which
has an x,y origin of upper left corner. This means that an increasing
Y-axis value tends towards the bottom of the screen or page, and not
towards the top which is ordinarily where we orient "up" or "above" in
our daily thinking. SVG provides the option to in effect put y=0 at
the bottom left of the screen or page but that was not done in the
bargraph SVG 'program', the default x=0, y=0 occurs at the upper left.
'omcsvg:Below' is intended to reflect values of Y (axis). If one looks
at openCYC one sees that it also uses the same conceptual intent for
(the rdf:ID=) 'above' and (the rdf:ID=) 'below', and it make
distinctions between aspects such as directly above and so on, in
addition.

Through the use of ontologies like "ontology.dumontierlab" I can also
talk about specifically
'statistical graphs and their components', as these depicted semantics
relate contents of the SVG bargraph 'program'. In a future posting I
continue this use of ontolgies to 'clue in' the computer (however
slightly) as to the meaning / use of bargraph. In a next post we see that
elements in "ontology.dumontierlab" combined with David Dodds Topic
Map representation can 'explain' that the bargraph's 'endbars', the
vertical black lines you see in the illustration of the bargraph in
the picture section of this Yahoo group, are "part of" a bargraph.
'Part of' or membership is a meaningful semantic construct, for it
allows the computer to use 'forward chaining logic' (explained next
post) to determine from its discovered parts what an object is. We see
how the computer can analyse the bargraph XML file and determine that
the stuff found there comprises a bar graph as defined by
"ontology.dumontierlab". Here's a tiny preview about (graph) "bar" :


<owl:ObjectProperty rdf:ID="hasWidth">
<rdfs:range
rdf:resource="http://sweet.jpl.nasa.gov/ontology/property.owl#Length"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="hasHeight">
<rdfs:range
rdf:resource="http://sweet.jpl.nasa.gov/ontology/property.owl#Length"/>
</owl:ObjectProperty>
</rdf:RDF>