- From: Michael Kifer <kifer@cs.sunysb.edu>
- Date: Tue, 05 Feb 2008 01:04:15 -0500
- To: Chris Welty <cawelty@gmail.com>
- Cc: Jos de Bruijn <debruijn@inf.unibz.it>, RIF WG <public-rif-wg@w3.org>

> OK, I see. I read this thread in reverse order. This proposal does boil > down to adding a third truth value as Michael pointed out. > > I think the problem is caused by trying to propagate the error through > the truth valuation. Let's talk about it tomorrow. Please do it the last thing in the telecon so that I could disconnect and go off to do something useful. --michael > -Chris > > Jos de Bruijn wrote: > > Dear all, > > > > In the telephone conference last Tuesday I mentioned that I had an idea > > for dealing with errors in built-in predicates and functions by not > > defining the semantics in case errors occur. > > > > My proposed solution is the following: > > > > For the purpose of this definition I assume that built-in predicates and > > functions are written as ' Builtin ( ' Uniterm ' ) ', following the > > proposal "syntactic representation of built-ins in RIF" at [1]. > > > > The definition of basic semantic structures is extended as follows: > > I(Builtin(f(t1 ... tn))=IFb(f)(I(t1),...,I(tn)) > > ITruth(Builtin(r ( t1 ... tn ))) = IRb(r)(I(t1),...,I(tn)) > > > > This is merely a routine extension of the interpretation of terms and > > atomic formulas to that of built-in terms and atomic formulas. Note that > > we use the mappings IFb and IRb for the interpretation of built-in > > functions and predicates; it would have also been possible to extend the > > current interpretation functions, but in this case are both that > > introducing new mappings which make things clearer. > > > > Now for the interpretation of built-in functions and predicates: > > > > IFb is a mapping from Const to partial functions from D* into D > > > > IRb is a mapping from Const to partial truth-valued mappings D* TV > > > > Note that the difference with the definitions of IF and IR is that the > > functions and truth value mappings are *partial*. > > > > A consequence of the fact that these mappings are partial is that the > > truth valuation function ITruth may become undefined in case any errors > > in built-in functions or predicates occur. > > > > > > Let's now consider satisfaction of rules, which is defined as follows > > (from the document): > > > > I |= then :- if > > > > iff ITruth(then) =t ITruth(if). > > > > If ITruth(then) or ITruth(if) is undefined, ITruth(then) =t ITruth(if) > > will also be undefined. Therefore, I |= then :- if is undefined. This > > extends to satisfaction of rule sets I |= R. > > > > Now consider an entailment, which is defined as follows: > > > > S |= f > > > > iff for every semantic structure I, such that I |= S, it is the case > > that Itruth(f)=t. > > > > If there is an error in the rule set S, then I |= S is undefined, so > > clearly S |= f is undefined. If there is an error in f, then clearly > > ITruth(f) is undefined, so S |= f is undefined. > > > > So, the model theory simply does not interpret rule sets or conditions > > with errors in built-ins. > > > > We should probably include a remark saying that implementations should > > return an error whenever they encounter a rule set which is not > > interpreted. > > > > Best, Jos > > > > [1] http://www.w3.org/2005/rules/wg/wiki/List_of_BLD_built-ins > > -- > Dr. Christopher A. Welty IBM Watson Research Center > +1.914.784.7055 19 Skyline Dr. > cawelty@gmail.com Hawthorne, NY 10532 > http://www.research.ibm.com/people/w/welty > >

Received on Tuesday, 5 February 2008 06:05:23 UTC