Re: Semantics of rule implication in RIF-FLD

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. 
> 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. 
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Regards 
RIF WG 

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