From: Adrian Giurca <giurca@tu-cottbus.de>

Date: Sat, 05 Jan 2008 22:01:54 +0100

Message-ID: <477FF042.4070700@tu-cottbus.de>

To: Michael Kifer <kifer@cs.sunysb.edu>

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

Date: Sat, 05 Jan 2008 22:01:54 +0100

Message-ID: <477FF042.4070700@tu-cottbus.de>

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. > This assumes all builtin functions to be total. Is that true? It might be a need to allow functions to throw errors even their arguments are appropriate i.e. to assume partial functions. > 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. > This is the case when a predicate has an argument interpreted as error. This makes no distinction between false atoms with wrong arguments and false atoms with proper arguments. For example, I(succ(2)>26)=false as well as I(pred(0)>2)=false while in the second case pred(0) is interpreted as error. This is an example of a partial function which might be interpreted as _|_ even its arguments are not interpreted as errors. I try one more example: I("rif" > 23.3) should be false even if I('"rif")="Rule Interchange Format" and I(23.3)=23.3 i.e. the arguments are not interpreted to _|_ > 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. > I suppose that E/\E=E and E\/E=E. If ~E=E then both the law of excluded middle and law of noncontradiction does not work. In this case consider again, I('"rif")="Rule Interchange Format" and I(23.3)=23.3 i.e. they are not interpreted in error, but I guess I("rif" > 23.3) should be E > > Comments? (esp. if anyone can see whether option (a) breaks somewhere) > > > --michael > > -Adrian GiurcaReceived on Saturday, 5 January 2008 21:02:25 UTC

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