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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: William Frank <williamf.frank@xxxxxxxxx>
Date: Wed, 14 May 2014 10:09:30 -0400
Message-id: <CALuUwtADx4y2EGOEgwA5ZAUU8Y50zFrAs8i9jusz2uqis-FO2w@xxxxxxxxxxxxxx>

On Tue, May 13, 2014 at 11:51 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
Kingsley, William, and Ed,

> "For every Squid s, there exist exactly 10 Tentacles t,
> such that s has-part t."
> It may be only me, but I don't think you have to become familiar
> with anything new to understand this formulation.

Before you can translate that sentence to FOL (or any other logic),

I 'translated' this sentence DIRECTLY FROM a definitionally  extended  FOL with lambda word for word.  I did not use alot of symbols, because the sybmos are irrelevant.  No backward E 10! to mean exists exactly 10, while backward E 10 means at least 10.  Changing the symbols chosen does not constitute a translation.

you need some way to represent plurals, such as "10 tentacles".

of course.  this is done ***very simply*** in extensions of FOL. 

but not by representing 'plurals'.  Again, the problem is you all want to apply the quantifier to the class tentacles, instead of applying the quantifier to the variable, which can occur at multiple places, creating a formal language that is HARDER to read than the formal language that has been around, and been extended, for 100 years. Much much harder to read than English. 

here is how it is done:

there exists at least one x such that Fx


there exists exactly one x such that Fx:


there exists at least one x such that Fx and for all y, if Fy, then y = x


there exists at least n  x such that Fx


there exists at least one x1, ...., and at least one xn, such that Fxi,

then say that all these xi are all pairwise unequal

there exists exactly n  x such that Fx


the above, plus the fact that any y such that Fy is equal to one of the xi.

I thought defining there exists exactly n was a common excersize for students. Certainly was when I was a student in the late 60s.   

And more questions arise with sentences like "Five cats ate six fish."
A lot has been published on those issues, and I'd rather ignore them
at the moment.

Sorry, but this is an entirely different matter that you bring up. I can't imagine why you have .  

Five cats ate six fish may have an ***ambiguity*** problem, but once it has been resoled, it is easy.  If people are today publishing how to represent it??? 

\> It looks to me, though, that CG and OWL *both* want to attach quantifiers
> directly to classes, instead of to free variables...

The basic EGs and CGs have a simple mapping to predicate calculus.

Yes, but EG and CG and OWL and OCR are all ***awkward**, and not easy for the uninitiated to read, because they HIDE the free variables.  People easily come to understand variables. These new attempts to replace something excellent happened because of a desire to make the formal language look more like English, the most complex part, which mathematicians reformed long ago, by using variables.   Variables are not hard.    


But even the simplest plurals raise thorny questions, which get
even thornier when you try to answer them in a general way:

    Bob and Sue ate an apple.  (Same apple?  One apple each?)
    Bob and Sue danced all night.  (One long dance?  Many dances?

    Together?  Separately?  With different partners?  Who cares?)

Again, these are issues of ambiguity, not representation, once the ambiguity is resolved.  I do also wonder that you would honestly think I did not know how to represent numerically exact existential quantifiers in logic and have proposed this in the Forum.   Or that I would confuse representation issues and ambiguity issues. 

NIST Recon, Common Logic.   YES!  We know so much about this family of languages.


My question remains ignored and unanswered, but now I know it will not be by you and Kingsley: Why in the world invent these new awkward formal languages when an easier to read by people family of formal languages for which there is a huge existing body of knowledge about how to reason with them already exists?  

I have two answers: 1. every since Peter Chen, the Boolean Fallacy of attaching quantifiers to classes instead of to variables has gotten a death grip on system modelling; 2. the world's growing unmoring from the accumulated knowledge of the centuries: just as programmers would rather reinvent the wheel than reuse software, so too the leaders of the world of system modelling would rather reinvent science than use it. 

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