Re: model theory of error

<snip/>

> I thought a bit about a direct model-theoretic semantics, and there is at
> least one solution that does not seem too complicated. Comments are welcome.
> 
> 1. We need a special constant (not sure if it should be in rif:IRI or
>    in its own symbol space) of the form rif:error.
> 
> 2. The domain of interpretation of any semantic structure will also have a
>    special distinguished element called _|_.
> 
> 3. All semantic structures will be required to interpret rif:error as _|_
>    (i.e., I_const(rif:error) = _|_)
> 
> 4. The builtin functions will be defined so that they will return rif:error
>    whenever their arguments are of the wrong type.

This semantics makes sense to me, but I was wondering why we need
rif:error.  It seems to me that we only need to worry about the truth
value of predicates which have _|_ as one of its arguments.

> 
> 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 _|_.
> 
>   The advantage of option (b) over option (a) is that we have an explicit
>   representation for errors. 
>   The disadvantage is that it is much more complicated. Many results need
>   to be ported to account for this new truth value, and I did not check
>   this carefully. Quite possible that this idea breaks somewhere.
> 
>   I think option (b) is too much work for very little gain.
> 
> 
> Comments? (esp. if anyone can see whether option (a) breaks somewhere)

I agree that we should probably go for (a).  Adding an additional truth
value would (in my view) unnecessarily complicate the semantics.

Best, Jos

> 
> 
> 	--michael  
> 

-- 
Jos de Bruijn            debruijn@inf.unibz.it
+390471016224         http://www.debruijn.net/
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