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Re: [PRD] review of the frozen draft of Nov 25

From: Christian de Sainte Marie <csma@ilog.fr>
Date: Fri, 05 Dec 2008 17:44:07 +0100
Message-ID: <49395A57.8000001@ilog.fr>
To: kifer@cs.sunysb.edu
CC: RIF WG Public list <public-rif-wg@w3.org>

Michael,

As I said, I have some questions about your comments re the semantics of conditions in PRD. Maybe they are very naive and/or completely silly, but here they are, anyway...

(That email is independent of Adrian working on answering your comments for WD2).

Michael Kifer wrote:
> 
>   10. Section 2.1.2.1, Semantic structures.
> 
>       For production rules you need to use Herbrand domains. Otherwise,
>       the definition of the models would be broken (as it is right now).
>       PRD uses inflationary semantics for negation, and using general
>       domains is problematic in this context.

But we are talking about the interpretation of condition only, not rules formulas. In that case, the semantics of negation cannot be inflationary: it is more like negation as failure under CWA, isn't?

>   12. Sec 2.1.2.3, definition of condition satisfaction.
> 
>       This definition is incorrect, if you have PRD negation. If Ψ has
>       negation, for instance, And(p not q) then this definition is not
>       strong enough to ensure that, say, p |= And(p not q).

You are right. But what if we add the following sentence to the definition of logical entailment: "or there is a formula theta such that psy = Not theta and for some semantic structures I+, I+ |= phi and I+ |= psy and for some semantic structures I-, I- |= phi and I- |=/= psy"?

Ok, that may not be logical entailment anymore, but wouldn't that make the usual PR semantics of conditions with a general notion of semantic structures, and allow us to sepcify condition satisfaction wrt to that kind of entailment?

>       What production systems do is different from logical entailment.
>       You are constructing semantic Herbrand structures instead. [...]

Right. But, again, we are talking about the semantics of conditions only, not rules. The knowledge base is static, as far as the semantics of conditions is concerned.
For that purpose, we do not need consider whether the knowledge base might change or not.

Or do we? If we have to take that into account when specifying the semantics of condition, there is really something that I do not understand. Oh, ok! There are lot of things that I do not understand, there :-) But that one I really need to understand! Can someone explain that to me, please?

> In fact, I do not think that
>       you need the motion of logical entailment in the first place. You
>       do need the notion of condition satisfaction, but it should be
>       satisfaction in particular Herbrand structures, *not* the notion
>       that you are defining. (The current document defines entailment of
>       conditions by ground facts, not the notion of satisfaction in
>       semantic structures.)

Well, the real reason to specify the satisfaction of condition, and pattern matching, on a more general basis than against a base of ground facts only is that, ultimately, we (may) want to be able to import external knowledge such as, e.g., data models, and that external knowledge may not be ground facts only, e.g., data models include axioms that are not ground facts (e.g. forall x, if x#C1 and C1##C2, then x#C2).

Actually, considering only a base of ground facts requires that everything that is imported one way or another (including externally defined functions and predicates) be considered in extension for the purpose of the semantics of condition.

That is probably possible, but I thought that it would be more convenient to just be able to say that, if a RIF document imports a theory T, then that means that weherever the semantics required entailment by the fact base: w |= p, you simply need to consider entailment by the conjunction of w and T, instead: w, T |= p.

I am perfectly ready to accept that it does not make sense, if it does not. But somebody will have to explain to me why :-)

>   13. Definition of matching substitution.
> 
>       This definition seems broken, and is an overkill in any case. Why
>       not simply define it as σ(Ψ) ⊆ Φ?

Same reason as above: what if Phi is not only a base of ground facts?

Sorry if the questions are silly, but I really want to understand that.

Cheers,

Christian
Received on Friday, 5 December 2008 16:45:01 GMT

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