Re: lack of model theory for errors in built-ins

> OK, I see.  I read this thread in reverse order.  This proposal does boil
> down to adding a third truth value as Michael pointed out.
> 
> I think the problem is caused by trying to propagate the error through
> the truth valuation.  Let's talk about it tomorrow.

Please do it the last thing in the telecon so that I could disconnect and
go off to do something useful.


	--michael  


> -Chris
> 
> Jos de Bruijn wrote:
> > Dear all,
> > 
> > In the telephone conference last Tuesday I mentioned that I had an idea 
> > for dealing with errors in built-in predicates and functions by not 
> > defining the semantics in case errors occur.
> > 
> > My proposed solution is the following:
> > 
> > For the purpose of this definition I assume that built-in predicates and 
> > functions are written as ' Builtin ( ' Uniterm ' ) ', following the 
> > proposal "syntactic representation of built-ins in RIF" at [1].
> > 
> > The definition of basic semantic structures is extended as follows:
> > I(Builtin(f(t1 ... tn))=IFb(f)(I(t1),...,I(tn))
> > ITruth(Builtin(r ( t1 ... tn ))) = IRb(r)(I(t1),...,I(tn))
> > 
> > This is merely a routine extension of the interpretation of terms and 
> > atomic formulas to that of built-in terms and atomic formulas. Note that 
> > we use the mappings IFb and IRb for the interpretation of built-in 
> > functions and predicates; it would have also been possible to extend the 
> > current interpretation functions, but in this case are both that 
> > introducing new mappings which make things clearer.
> > 
> > Now for the interpretation of built-in functions and predicates:
> > 
> > IFb is a mapping from Const to partial functions from D* into D
> > 
> > IRb is a mapping from Const to partial truth-valued mappings D*   TV
> > 
> > Note that the difference with the definitions of IF and IR is that the 
> > functions and truth value mappings are *partial*.
> > 
> > A consequence of the fact that these mappings are partial is that the 
> > truth valuation function ITruth may become undefined in case any errors 
> > in built-in functions or predicates occur.
> > 
> > 
> > Let's now consider satisfaction of rules, which is defined as follows 
> > (from the document):
> > 
> >  I |= then :- if
> > 
> > iff ITruth(then) =t ITruth(if).
> > 
> > If ITruth(then) or ITruth(if) is undefined, ITruth(then) =t ITruth(if) 
> > will also be undefined.  Therefore, I |= then :- if is undefined.  This 
> > extends to satisfaction of rule sets I |= R.
> > 
> > Now consider an entailment, which is defined as follows:
> > 
> >  S |= f
> > 
> > iff for every semantic structure I, such that I |= S, it is the case 
> > that Itruth(f)=t.
> > 
> > If there is an error in the rule set S, then I |= S is undefined, so 
> > clearly S |= f is undefined.  If there is an error in f, then clearly 
> > ITruth(f) is undefined, so S |= f is undefined.
> > 
> > So, the model theory simply does not interpret rule sets or conditions 
> > with errors in built-ins.
> > 
> > We should probably include a remark saying that implementations should 
> > return an error whenever they encounter a rule set which is not 
> > interpreted.
> > 
> > Best, Jos
> > 
> > [1] http://www.w3.org/2005/rules/wg/wiki/List_of_BLD_built-ins
> 
> -- 
> Dr. Christopher A. Welty                    IBM Watson Research Center
> +1.914.784.7055                             19 Skyline Dr.
> cawelty@gmail.com                           Hawthorne, NY 10532
> http://www.research.ibm.com/people/w/welty
> 
>

Received on Tuesday, 5 February 2008 06:05:23 UTC