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

From: Adrian Paschke <adrian.paschke@gmx.de>
Date: Sat, 6 Dec 2008 10:24:42 +0100
To: <kifer@cs.sunysb.edu>
Cc: <public-rif-wg@w3.org>, "'Christian de Sainte Marie'" <csma@ilog.fr>, "'Gary Hallmark'" <gary.hallmark@oracle.com>
Message-ID: <039401c95784$795d7f80$6c187e80$@paschke@gmx.de>

>> As a result you would now get {p,q,s} (which is also the inflationary
>> of it) from a production rule program 
>>      p :- q
>>      q :- NOT r
>>      s :- NOT p
>> as opposed to default negated logical model where you only would get {p,
>> but not s.

>I think both {p,q} and {p,q,s} are possible in production systems, right?
>(That is, if q :- NOT r is selected first.)
>Is this what you meant?

Yes, both are possible intended models. However, the truth valuation using
states (snapshot of the world represented as Herbrand interpretation) is
depended on the operational semantics of the state transition system,
selection policy etc. For instance, an inflationary semantics would be:  

Round 0: None of p, q, r, and s are true. 
Round 1: The falsehood of r lets us infer q, and the falsehood of p lets us
infer s. The inflationary model so far is {q,s}. 
Round 2: The truth of q lets us infer p. The inflationary model is now
{p,q,s}. Even though p is now true, the use of NOT p to infer s stands. 
Round 3: No new inferences are possible; the inflationary model is {p,q,s}.

This lack in declarativity of the inflationary semantics with negation of
course brings problems. One of the problems with inflationary semantics is
that if the order of rules is not written carefully or the selection policy
is not right, it winds up inferring certain facts too early, that is, using
a negated subgoal that eventually turns out not to be true later. For
instance, in the example it is of the form NOT p, where p becomes true later
and hence is in the model. In a logical declarative semantics this would not
be possible. 

Unfortunately, there is no agree upon declarative semantics for production
rules and RIF as an interchange format between different production rules
systems implementing different operational semantics should be as general as

Received on Saturday, 6 December 2008 09:25:23 UTC

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