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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 12 Sep 2008 18:53:51 -0500
Message-id: <0BB67356-7304-4FC6-9BF1-FBE2564FEA90@xxxxxxxx>
On Sep 12, 2008, at 6:04 PM, Richard H. McCullough wrote:
> Chris
> I would appreciate some pointers on how to do that. The things that  
> I have read say that a formal semantics maps the "meaningless"  
> symbols of formal logic to the "meaningful" symbols of English.    (01)

No, that is nothing like a formal semantics; that is at best an  
informal semantics, which is generally pretty useless for the central  
purposes of KR.  The point of a formal semantics is (a) to provide  
interpretations of the non-logical primitives of a language and (b)  
to  provide a *systematic* account of how the meanings of complex  
expressions in a language are determined by the meanings assigned to  
their component parts.  This, in particular, is what is missing from  
mKR.    (02)

(b) has to do primarily with the interpreting the logical components  
of your language -- boolean operators, modal operators, quantifiers,  
etc.  You can learn about this in any good text on mathematical  
logic.  (And just note: It appears to me that your language is  
completely lacking the apparatus of propositional and first-order  
logic.  These are essential to any modern KR language.)    (03)

In regard to (a), many of your important non-logical primitives --  
e.g., "action", "context", "part", "attribute", "relation", "time",  
etc -- are left utterly uninterpreted.  Try replacing them with "foo,  
bar, baz, etc" and you get an idea of how useful your language is for  
KR.  The notions above are ambiguous and difficult.  They need to be  
nailed down by a semantics that fixes (as far as possible) their  
properties and the logical connections.  For instance, what is the  
relation between "action" and "time"?  Intuitively, the two are  
*intimately* connected.  A good formal semantics will do that: for  
example, it might represent time as the real line and will map each  
action to an interval.  Alternatively, if one has ≠ discrete  
processes in mind, a semantics might represent time by the integers  
and assign to each action a start point and a (later) endpoint.   
Again, what is an attribute?  Can you combine different attributes  
like "red" and "smooth" into a single attribute?  A good semantics  
will represent attributes as functions of some ilk, or as objects with  
extensions, or perhaps extensions at possible worlds, or whatever.   
But however, it is done, it will be perfectly clear what you do and do  
not mean by "attribute".  See the idea?  You might have a look at the  
NIST Process Specification Language for a good example of a language  
whose non-logical primitives are rigorously interpreted in a formal  
semantics, and how those interpretations are reflected in the PSL  
axioms.  Or, for that matter, have a look at the model theory for RDF  
and OWL on the W3C web site.    (04)

> But mKR propositions are paraphrases of English. mKR is composed of  
> English words and phrases, not "meaningless" symbols of formal logic.    (05)

But the symbols of formal logic are not meaningless *at all*.  They  
are given very rigorous interpretations in any standard semantics  
(a.k.a model theory) for a given formal language -- of which any  
useful KR language is a species.    (06)

> I haven't seen any formal semantics for English.    (07)

Sure thing, but neither is English anything like a KR language; indeed  
it is the very opposite of a KR language.  It is informal, imprecise,  
fraught with ambiguity, and impossible for computers to process  
(without severe restrictions).  It is WHY we have KR languages; it is  
WHY we build ontologies.  KR exists precisely because you can't rely  
on informal, intuitive understandings of English when you want to  
share and process information, and use computers to aid significantly  
in the process.    (08)

-chris    (09)

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