Re: model theory of error [Yes, proposing one!]

From: Christian de Sainte Marie <csma@ilog.fr>
Date: Tue, 15 Jan 2008 16:45:36 +0100
Message-ID: <478CD520.2080309@ilog.fr>
To: Michael Kifer <kifer@cs.sunysb.edu>
CC: RIF WG <public-rif-wg@w3.org>
```
Michael Kifer wrote:
>>
>>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 (so,
>>the intuitive semantics of E is more like "undefined" than "error")?
>
> This is not a truth table for undefined (U). With the U value, U/\F=F and
> U\/T=T.  In any case, it is not very clear what the truth table should
> really be. In my proposal the only diff with yours was E\/T=T, but I think
> I made a typo there (do not remember what I was thinking).

No, apparently, what you were thinking is to use a thruth table for
undefined:
>    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 _|_.

So, we might call option (b) the "undefined" option, and the one
corresponding to the truth table where everything that touches E becomes
E: the "error" option.

> So, I consider this a risky path given our time constraints.

But we must consider it to make an informed decision, right?

>>>Comments? (esp. if anyone can see whether option (a) breaks somewhere)
>
> It is not easy to "see" something like that. One needs to check, which is
> very time consuming.  My crystal ball says that the chances of breakage are
> over 50%.