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Re: [ontolog-forum] language vs logic - ambiguity and starting with defi

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 21 Sep 2010 20:34:39 -0500
Message-id: <1EFD427B-E38E-4105-9185-F135471E2A61@xxxxxxxx>
On 9/21/2010 6:08 PM, Jerry Hobbs wrote:
> Chris,
> I was rather surprised to see you criticizing Ernie Davis, since he is
> probably the best there is in formalizing commonsense knowledge.  His
> 1990 book "Representations of Commonsense Knowledge" is still probably
> the best introduction to the field.
> So I checked out the 6-page note cited.  It is limited in ambition --
> it is only a list of common student errors, presumably for use by his
> students.  But I didn't see where it is wrong.  I'm curious about what
> mistakes you found.    (01)

Hi Jerry,    (02)

No doubt I'm overly snooty about such things (and I'm certainly glad to hear 
someone of your stature vouching for the quality of his work), but several 
features put me off right away:    (03)

1. The use of upper case letters for first-order variables.  The usual 
convention among logicians is to reserve upper case letters for second-order 
variables.    (04)

2. Constructing the quantifiers by tacking the bound variable on as a 
*subscript* to the quantifier.  Why?  I know of no commonly used text that 
adopts this convention.    (05)

3. The more serious issue: unconventional quantifier scoping.  On the first 
page, Davis translates "Same has a male child" as:    (06)

  (1.3) ∃X child(X,sam) ∧ male(X)    (07)

So the scope of the quantifier here is obviously supposed to be the entire 
formula "child(X,sam) ∧ male(X)" to its right.  But according to the grammar 
found in most any modern text, (1.3) is a conjunction formed from "∃X 
child(X,sam)" and "male(X)"; the occurrence of X in the latter formula is 
simply free -- a perfectly acceptable formula in a basic, context-free 
first-order language.  To get the intended scope, you need appropriate 
delimiters:    (08)

  (1.3a)  ∃X [child(X,sam) ∧ male(X)]    (09)

I guess Davis's convention is to give quantifiers the widest possible scope 
unless delimiters indicate otherwise, as in his example:    (010)

  (7.3)  ∀X [∃Y meat(Y) ∧ eats(X,Y)] ⟺ ¬vegetarian(X).    (011)

And perhaps that is the way it's done by a lot of folks in the commonsense 
realm. But it certainly seems to me to be out of step with standard practice 
amongst most logicians and philosophers.  I'm sure Davis's syntax can be made 
rigorous but, even aside from its unconventional qualities, it seems to me it 
would be awkward to state the truth definition for the language.  (Perhaps the 
best way to do it would be to have a more standard formal syntax where (1.3a) 
would be strictly correct and (1.3) would be acceptable via certain parenthesis 
dropping conventions.)    (012)

Regards,    (013)

-chris    (014)

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