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Re: [ontolog-forum] Visual Notation for OWL Ontologies (VOWL)

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Tue, 13 May 2014 01:47:47 -0400
Message-id: <5371B203.4070200@xxxxxxxxxxx>
On 5/12/2014 9:13 PM, Simon Spero wrote:
> In Cyc you can say:
> (implies  (isa ?S Squid)
>     (thereExistExactly 10 ?T
>     (and (isa ?T Tentacle) (anatomicalParts ?S ?T))))
> In OWL you can write:
>   SubClassOf(:Squid
>    ObjectExactCardinality(10
>                       :anatomicalParts :Tentacle))
> Could you show what this looks like in graphical form?    (01)

A very simple logic such as EGs would need to supplemented with
an ontology for sets, elements, cardinality, etc.  But I have always
tried to design the notation to simplify the mapping to and from NLs.    (02)

In my 1984 book, I specified conceptual graphs as an extension of EGs
with syntactic sugar for such things.  That syntax is *not* in the CL
standard, because CL does not include all that ontology.    (03)

Let's assume that we would like to express the above Cyc or OWL
in English as "There is a squid that has exactly 10 tentacles."
In the CG notation of the 1980s, that would be represented as    (04)

    [Squid]->(HasPart)->[Tentacle: {*}@10].    (05)

In English, this can be read "There is a squid that has as parts
exactly 10 tentacles."  The notation {*}@10 is defined by an expansion
to a node of type Set, every element of which is of type Tentacle.
The node [Squid] is linked by HasPart to each node of type Tentacle.
But you would not normally do that expansion, except as a step
during some reasoning process.    (06)

One person who did some work on the definitions and expansions
of the set notation for CGs is Jim Slagle, who was a professor
at the University of Minnesota.    (07)

Jim is blind, but he really liked CGs.  The university bought
one of the first Kurzweil reading machines for him, but he also
needed human readers who would explain the diagrams (and record
the explanations).  Although he was blind (or perhaps because he
was blind), he had a good ability to "visualize" structures.    (08)

As another example, assume "Mary has less than 5 children, including
a girl named Sue, and a pair of twins, one of whom is named Bill."
In CGs, that would be    (09)

   [Person: Mary]->(HasChild)->[Person: {Sue, Bill, *x, *}@<5]
   [Girl: Sue]  [Person: Bill]->(HasTwin)->[Person: ?x]    (010)

In the pure graphic notation, coreference links could be drawn
as dotted lines.  Or they could be left as labels like *x,
if the diagram is complex and crowded.    (011)

How would you express that in OWL?    (012)

John    (013)

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