Re: Semantics of rule implication in RIF-FLD

Dear Christian,

On Dec 9, 2009, at 11:40 PM, Christian De Sainte Marie wrote:

>
> Dear Carlos,
>
> Carlos Damasio wrote on 9 September 2009:
> >
> > The semantics of the several connectives in FLD-RIF is many-valued,
> > with the single exception of the rule implication symbol.
> > The rule implication symbol has only two possible values, t and f,  
> the
> > top and bottom of the lattice of truth-values.
> > For instance, this prevents the definition of fuzzy logic dialects  
> of
> > RIF without introducing new implication connectives.
> >
> > I suggest that that the rule implication symbol semantics to be
> > generalized in the following way:
> >
> > Rule implication:
> > TValI(head :- body) = t, IFF TValI(head) ≥t TValI(body).
> > TValI(head :- body) < t   otherwise.
> >
> > This has nice theoretical properties, namely the existence of  
> minimal
> > model for every definite Horn program.
> > This will not affect the notion of model, and would be much more
> > general.
> Thank you for the suggestion. It has been adopted and the semantics  
> of :- has been generalized per your suggestion.
>

For helping interested readers, the motivation for the definition as  
well as the mentioned results can be found in

C. V. Damásio and L. M. Pereira. Monotonic and Residuated Logic  
Programs.
In, Salem Benferhat, Philippe Besnard (Eds.): Symbolic and  
Quantitative Approaches to Reasoning with Uncertainty, 6th European  
Conference, ECSQARU-2001,
Toulouse, France, September 19-21, 2001, Proceedings Lecture Notes in  
Artificial Intelligence 2143, Springer 2001, ISBN 3-540-42464-4, pp.  
748-759.
© Springer-Verlag.
> > Disclaimer:
> > I've tried to browse the mail archives to see if there was any
> > discussion about this, and could not find it.
>
> No, there was no prior attempt to generalize :- in the direction  
> that you suggested.
>
> > I don't discuss here the issue of equality, since I am not an expert
> > on the subject.
>
> The semantics of = is two valued. It is possible to generalize it  
> and make equality multi-valued, but perhaps this is better done as a  
> separate predicate (which FLD allows dialects to have). Your and  
> others comments regarding this issue are welcome.
>
> Please acknowledge receipt of this email to <mailto:public-rif-comments@w3.org 
> > (replying to this email should suffice). In your acknowledgment  
> please let us know whether or not you are satisfied with the working  
> group's response to your comment.
>
>
I am satisfied with the answer.

Best,

Carlos
> Regards
>
> RIF WG
>
> --------------------------------------------------
> Christian de Sainte Marie
>
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Carlos Viegas Damásio                   | Tel: +351 21 294 8536 (ext.  
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