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Re: [ontolog-forum] mKR (was Thing and Class)

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sat, 13 Sep 2008 13:28:59 -0500
Message-id: <B918F2FC-D43D-4CF7-9D35-F59031237C56@xxxxxxxx>
On Sep 12, 2008, at 8:43 PM, Richard H. McCullough wrote:
> Chris
> I don't have all the answers at this point, but I want to discuss
> a few things, to try and establish some understanding between
> us.
> Starting with (b), just because it's easier.  mKR has
>    if-then-else-fi  iff  implies
>    and or not
>    quantifiers: no a any the some all every
>    for quantifier loops similar to many logic languages
> I don't know why you say mKR is completely lacking
> the apparatus of propositional and first-order logic.    (01)

My apologies, I missed those, but a worry right off here is that you  
are giving what appears to be a computational, or procedural,  
semantics to the quantifiers.  Is that your intention?  That is a very  
different kind of semantics than the usual Tarski-style, declarative  
semantics typically given to KR languages.  This is *just* the sort of  
thing that an explicit formal semantics is meant to clear up.    (02)

> In regard to (a), primitives such as "action", "context", "part",
> "attribute", "relation", "time" are axiomatic concepts upon
> which all other concepts depend.    (03)

I think you are mixing up "axiomatic" and "primitive".  The expression  
above are *primitives* of your system, in that they are not defined in  
terms of any other expressions.  However, in addition to a rigorous  
semantics, axioms are exactly what are missing from mKR -- you don't  
provide any account of the logical properties of, and the logical  
connections among, the expressions above that reflects their intended  
meanings.  They are just meaningless marks.  And this is exactly where  
an appeal to English will not do -- the terms above are *notoriously*  
ambiguous and controversial.  Any use of them has to be tied down by  
axioms in a language with a clear semantics.  (To get just a taste of  
the complexities here, have a look at Pat Hayes' Catalog of Temporal  
Theories -- http://www.ihmc.us/users/phayes/timecatalog.pdf .  And  
that is just one of your primitives.)    (04)

> They are dependent upon
> each other.  I have given terse genus-differentia definitions of
> each.  For example
>    attribute is characteristic with single entity, non-separable;
>    action is characteristic with single entity, non-separable,  
> space, time.
>    part is characteristic with single entity, separable;
>    relation is characteristic with multiple entity;
> My model of an action is something that takes place in an interval of
> (real number) space, time, but I allow space, time measurements
> to be real or discrete.    (05)

That is not a model.  It is not a semantics.  It is a terse, informal  
gloss whose component notions are as complex and problematic as the  
term you are attempting to clarify.    (06)

> mKR is English-like, but it is formal, precise and unambiguous.    (07)

It might be adequately formal (I see you do appear to provide a BNF  
for it) but it is most assuredly neither precise nor unambiguous, as  
you provide no more than informal English glosses at most, and English  
itself is imprecise and ambiguous.    (08)

> The simplest mKR proposition has the form
>    at space=s, time=t, view=v { sentence };
> v names a list of propositions    (09)

What's a proposition?    (010)

> (the context) which disambiguates the sentence.    (011)

What's a context?    (012)

> s,t name the sub-context associated with the changes of an action.    (013)

What's an action?  What's a change?    (014)

> Genus-differentia definitions are used to make terms precise.    (015)

They do no such thing.  They merely compound the problem by  
introducing yet more undefined, unaxiomatized terminology.    (016)

> Sentence structure is governed by a formal grammar.    (017)

As far as I can see, that is the only part of your language that  
appears to be adequate -- assuming the BNF is legit.  But that's only  
the starting point for a robust, usable KR language.    (018)

> In effect, mKR starts with a "Simple English" language -- no word
> variations for number, tense, etc. -- and prefixes every sentence with
> the context which disambiguates it.    (019)

Perhaps you have in mind something like the simplified English that  
John Sowa often touts here.  Have you looked at that?  It might  
already do what you want mKR to do.    (020)

-chris    (021)

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