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Re: Web Rule Language - WRL vs SWRL

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Thu, 7 Jul 2005 20:53:39 -0400
Message-ID: <17101.52883.401574.826635@DVM-Powerbook.local>
To: www-rdf-rules@w3.org


> [Ian Horrocks]
> 
> I hope we are not talking about "meaning" in any higher sense - I am 
> but a humble computer scientist, and know little of this meaning of 
> which you speak! ...

I've encountered this attitude before, about how "mere mortals" are
incapable of talking about any semantics except "hard nosed" semantics
of data structures.  It's an odd attitude to take for people working
on the semantic web.

> All I am talking about is a formal "language" that, 
> given a theory (set of statements), specifies the set of models that 
> are admitted by the theory. The specification typically also defines 
> entailment in terms of models, i.e., a statement is entailed by a 
> theory iff it is true in every model admitted by the theory.

It's the meaning of the word "admit" here that is the crux of the
issue.  Let's look at a concrete example.  Suppose one has a temporal
logic, whose semantics are spelled out by specifying (e.g.) what
relationships among situations and timelines make (eventually P)
true.  Even the most humble computer scientist can understand such
specifications (for which I'll use the letter M.)

Now let's suppose that a nonmonotonic reasoning scheme is superimposed
on the temporal-logic system (or included from the beginning).  The
consequence relation for this system takes the form we're discussing,
namely, "Q follows from S if and only if Q is true in all P-models of
S," where a P-model of S is a model satisfying some extra
requirement.  My claim is that this inference framework doesn't change
the meanings of (eventually P) in any way.

Look at it from a complementary viewpoint:  Suppose, as often happens,
that the P-models are exactly that subset in which a certain extra set
of statements S' are true.  So an equivalent way of specifying the
nonmonotonic inference scheme is: "Q follows from S if and only if Q
is true in all models of S U S'(S)."  (It's necessary in general that
S' depends on S.)  Is it somehow supposed to be the case that adding a
few extra statements changes the meaning of S?  Isn't the meaning
determined by M in spite of the way the nonmonotonic inference scheme
is set up?

Here's simpler case.  Consider a simple first-order theory with
equality, and focus on the definition of 'forall'.  Now suppose
someone wants to add the Unique Names Assumption.  You can do it by
restricting attention to models in which the function that maps
constants to objects is injective.  Or you can do it by adding a bunch
of inequalities.  Neither one changes the meaning of 'forall' in the
slightest. 

> [...]
> Two languages can interoperate if, given the same theory, they admit 
> the same models (and perhaps under other circumstances, e.g. if, as has 
> been suggested w.r.t. DLP, we restrict our means of examining models so 
> that we are unable to distinguish some differences in models).

Think of it this way: "admit" is ambiguous.  

A theory T admits_1 model D if D is the in the set of models allowed
  by the intended meaning of T

T admits_2 model D if T admits_1 D and no conclusion ruled out by the
  intended inference machinery is true in D

(If the inference machinery is deductive, then admits_1 and admits_2
are the same; otherwise, they aren't.)

I simply disagree with your statement "Two languages can interoperate
if...they admit the same models..." if you insist on admits_2.  It
seems like an extremely strong requirement on interoperation that two
modules must agree on inference mechanisms in order to interoperate.

> [...]
> According to my simple view of formal languages, if the semantic 
> specification of the formal language restricts all models to have 
> property P, ...

The word "restricts" is ambiguous the same way "admits" is.

                                             -- Drew
Received on Friday, 8 July 2005 00:52:36 GMT

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