Re: How to capture modeling information in WOL

On December 27, Dieter Fensel writes:
> "The differences in RDF and WOL entailment is a brilliant feature"
> 
> I recall many discussions on how to deal with modeling information in
> a logical framework. Lets take a simple example. A statement like
> 
> 	(1) a & b
> 
> should be treaded completely equal to a statement
> 
> 	(2) b & a
> 
> at a logical level. However, at a modeling level you may want to know
> whether a person wrote (1) or (2) because it may reflect the fact that
> b is more "important" to him.

On the web we often wont know who (or what) said what, or in what
order. Machine processing may mangle syntax. Users may have widely
divergent backgrounds and cultures. All these considerations (and
probably others) suggest that it would be dangerous to make
assumptions based purely on one interpretation of the meaning of a
given ordering.

> A more real-life example is whether a
> person define
> 
> 	- a relation "r" as an attribute of a class "c" or
> 	- as a global property "r" with "c" as its domain.
> 
> Logically they are the same but from a modeling point of view
> they are quite different.


It is rather a sweeping statement to say that "Logically they are the
same". It depends on what you take each of them to mean, which is
difficult to say without a precise specification. In particular, if we
consider the two axioms:

Forall x,y . r(x,y) -> c(x)                                       (1)
Forall x . c(x) -> (Exists y . r(x,y))                            (2)

stating that "r" is a global property with "c" as its domain would
probably be taken to be equivalent to (1) - I believe this is the line
taken by both RDF and DAML+OIL - while stating that "r" as an
attribute of a class "c" might be taken to be equivalent to both (1)
and (2), or possibly to (2) only.


These sorts of problem illustrates just why we need a precisely
defined semantics for our languages. If we allow for two possible
interpretations we may get into all sorts of difficulties:

- it may be impossible to say something in DAML+OIL without stating
  something unintended in RDF (and vice versa)

- it may be impossible to know which of two (possibly conflicting)
  meanings is the intended one

Ian

> 
> By having two types of entailments we can capture this without
> running into any problems. With syntactical RDF reasoning we
> can ask for different syntactical styles of an Ontology and with
> semantic WOL reasoning we infer logical consequences of an
> Ontology. This view point would also allow us to deal with
> different modeling paradigms people are asking for. Many
> emails and papers were asking for the frame-based syntax of
> OIL that disappeared in DAML+OIL (i.e., OIL was a web-based
> modeling language whereas DAML+OIL is "just" a web-based
> logic). We could just define a frame syntax for WOL in RDF
> making sure that it behaves the same as the non-frame version
> at the logical level but behaves different at the syntactical level,
> i.e., in the frame version you could ask whether something is
> explicitly defined as an attribute or as a property.
> 
> In a nutshell, I think it is a brilliant feature having a reasoning
> level that reasons "non"-logically but syntactically over an WOL
> Ontology. It is the layer that allows us to capture, infer, and
> query modeling information. Therefore, this type of information
> no longer needs to be messed up with the logical layer,
> where indeed you do not want to care about the different syntax of
> logically equivalent statements.
> 
> So I would strongly vote for encoding WOL as closely as possible
> in RDF and taking the differences in entailment as a beautiful gift.
> 
> 
> Dieter
> 
> ----------------------------------------------------------------
> Dieter Fensel
> Division of Mathematics & Computer Science,
> Vrije Universiteit Amsterdam,
> De Boelelaan 1081a, 1081 HV Amsterdam, NL
> The Netherlands
> Tel. (mobil): +31-(0)6-51850619,
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> Email: dieter@cs.vu.nl
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> Tel.: +31-(0)20-365 52 60.
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Received on Thursday, 27 December 2001 17:37:48 UTC