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Re: model theory of error

From: Axel Polleres <axel.polleres@deri.org>
Date: Sat, 05 Jan 2008 13:34:41 +0100
Message-ID: <477F7961.1030806@deri.org>
To: Michael Kifer <kifer@cs.sunysb.edu>
CC: RIF WG <public-rif-wg@w3.org>

Michael Kifer wrote:
> Last Tuesday we were unable to resolve the issue of builtin functions
> because we could not decide on their semantics. The problem is that builtin
> functions are partial and are supposed to return an error if given wrong
> arguments.
> 
> One approach we considered was to simulate them using predicates by
> translating functional expressions into formulas that involve builtin
> predicates. Unfortunately, this has a problem that occurrences of such
> functions in the conclusions of rules must have a different translation
> than the occurrences in rule premises. This was perceived as a problem if
> we were to consider BLD as a subset of the (future) first-order dialect,
> since the first-order dialect will not have such a distinction.
> 
> 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.
> 
> 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 handing of truth value E in option b) seems to be very exactly the 
way SPARQL handles errors in built-ins in FILTER expressions.


>   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)

Does that mean you suggest only builtin-functions and no bult-in predicates?




-- 
Dr. Axel Polleres
email: axel@polleres.net  url: http://www.polleres.net/

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Received on Saturday, 5 January 2008 12:34:59 GMT

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