Re: RIF vs Rule Language

A similar issue to the one described below surfaced early on in 
MathML.  The detailed evaluation semantics (in general, and as 
implemented by various computer algebra systems) differed 
greatly.  Default domains and domain extensions differed for 
various "standard" mathematical functions and even  basics like 
numerical arithmetic differed between systems.

For some consumers, the differences mattered - for others (like 
editors) they did not. Only the author could say for sure which 
definitions they were using if the details of those definitions 
became important.

The common thread, however was that nearly all mistakes in the 
mathematical information exchange between systems had the 
following  in common.  The consumer made invalid assumptions 
about the mathematical semantics of an object.  Yet, only the 
producer (author) could know for sure what definition they were 
using and when the details were important.

So, we identified three key goals. 

        1.  Provide a limite standard vocabulary (including 
        definitions) to facilitate and encourage simple exchange.

        2.  Provide a mechanism for the author to explicitly 
        identify what definition they were using (to be used as 
        necessary) vocabulary in a significant way.  This could 
        be used by authors to "warn" consumers.

        3.  Provide an extension mechanism for both vocabulary 
        and definitions - primarily so that we could actually 
        agree on the contents of the list in 1.

Ultimately we settled on the following approach. 

1.  There is a set of standard functions,  e.g.  <sin/>, <cos/> 
that one might expect in a basic mathematical system.  (for 
convenience and for usability so that the common mathematical 
expressions were easily recognizable) and which have default 
definitions.  The only way we could finalize this list was by 
providing an extension mechanism (see 4 below).  In future, 
heavily used extensions might migrate to this list.

2.  Each function has an optional  "definitionURL", which is 
really a URI used to identify a specific variant.   If the 
definitionURL is absent then the definition is the default 
definition (as outlined in the recommendation). However, the 
author can always flag their definition as different. by 
assigning a value to this attribute.

3.  We made a formal distinction between a function, and the 
result of applying it to a set of arguments -- that is, between f 
and f(x).  For example, the "function" sin  lies in a domain of 
functions, while  sin(x) represents (say) a real number.  To 
facilitate this distinction, we provided an "apply" operator that 
could be used to apply any function to its arguments.

4.  We provided a generic function element which used its 
definitionURL attribute to "name" its definition.

This scheme has worked very well.  We have had some feedback that 
a formal system needs to go beyond just naming definitions (all 
that is really possible with an attribute) to inclusion of a 
definition object, but at the time (and even now, we are a long 
way from a conscensus of what that definition language aught to 
look like). 

---

All the above is somewhat historical. The really big issues to get 
us to something useful were: 

        1.  a basic vocabulary.
 
        2.  a definition "naming mechanism".
 
        3.  an extension mechanism.


Stan Devitt


4.  We provided a generic function element which used its
required definitionURL attribute to name its definition.

public-rif-wg-request@w3.org wrote on 12/08/2005 06:38:13 PM:

> 
> On Dec 8, 2005, at 3:27 PM, Uli Sattler wrote:
> 
> > On 8 Dec 2005, at 14:49, Enrico Franconi wrote:
> >>
> >
> > [snipp]
> >
> >> While I believe, like you, that tehre may be the necessity of 
> >> different behaviours of reasoners, this can only be justified by the 
> >> existence of different semantics for the same rule constructs.
> >>
> >
> > Do you mean that, for such a case, we should provide 2 different 
> > syntactic constructs to make this difference explicit? For example 
> > "implies1" for horn rules without contraposition and "implies2" for 
> > horn rules with contraposition?
> 
> Or you could have a flag for the whole document which one could 
> override at one's own risk.
> 
> Cheers,
> Bijan.
> 
>

Received on Friday, 9 December 2005 10:14:09 UTC