From: Jos de Bruijn <debruijn@inf.unibz.it>

Date: Sun, 06 Jan 2008 17:48:51 +0100

Message-ID: <47810673.8020109@inf.unibz.it>

To: RIF WG <public-rif-wg@w3.org>

Date: Sun, 06 Jan 2008 17:48:51 +0100

Message-ID: <47810673.8020109@inf.unibz.it>

To: RIF WG <public-rif-wg@w3.org>

<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/ ---------------------------------------------- Doubt is not a pleasant condition, but certainty is absurd. - VoltaireReceived on Sunday, 6 January 2008 16:49:03 UTC

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