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

Jos de Bruijn wrote:
> 
> You're right.  The definitions don't work.  If we would fix them, we end 
> up with your option (b).
> So we're back where we started, with the two choices you described in [1].

That is:
> 5. For predicates, we have two options.
>    a. The simplest option is to say that a predicate, p(a,b,c,...), is false if
>       any of its arguments evaluates to _|_ in the interpretation.
> 
>    b. This option introduces a new truth value, called E (error) such that 
>       ~E = E, E/\F=F, E/\T=E, E\/F=E, E\/T=T. Then we can say that
>       p(a,b,c,...) has truth value E if at least of of the args is _|_.

If it is the case that we are, indeed, back to that point, may I insist 
that we should also consider a third choice (or that someone provides me 
with an explanation why we should not consider it) [2]:
>> What if the new truth value E was such that:
>>   ~E = E/\F = E/\T = E\/F = E\/T
>>      = E :- T = E :- F = T :- E = F :- E
>>      = Forall E = Exists E
>>      = E
>> so that as soon as you have an E somewhere, everything becomes E?

"If", because it is still not clear to me why we cannot just say that 
RIF-BLD does not provide semantics for ExtTerms outside of their domains 
of definition...

Cheers,

Christian

[1] http://lists.w3.org/Archives/Public/public-rif-wg/2007Dec/0099.html
[2] http://lists.w3.org/Archives/Public/public-rif-wg/2008Jan/0061.html