Response to CD2
Thank you for the suggestion. It has been adopted and the semantics of :- has been modified per your suggestion.
> Dear all, > > 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.