RE: Datalog With Only Binary Relations Is Too Weak

> > >     {{:gregorian :grandparent :bret} log:implies
> > >      {{:gregorian :skolemfun :bret} :parent :bret}} log:implies
> > >    {{:gregorian :skolemfun :bret} a :isLoved}.
> >
> > This is intriguing stuff...
> >
> > (...meaning I'm not sure that I understand the details ;^)
>
>Well, I was hoping this was kind of selfexplanatory ...

It is not self-explanatory. In fact it is completely opaque; I don't 
even know how to parse it. Does this notation have any syntactic 
rules, or any semantics?

The above appears to have the overall structure
(A implies B) implies C
which is rather unlikely, if 'log:implies' means logical implication, 
because that is equivalent to the conjunction
(A or C) and (B implies C)

>I agree that more is needed for a proof language, this is
>just something to start with ... any suggestions?

Well, there are rather a lot of proof languages out there, and many 
of them have powerful provers implemented already, so I wonder why 
you are going to all this trouble to re-invent an old wheel (?) For 
deductive efficiency, stick to the Horn clause subset of first-order 
logic. You could probably use some recent implementation of Prolog if 
you want to really burn rubber, for example.

> > > I try to find evidence that having (nested) dyadic formulae
> > > is a good thing to limit to ...
> >
> > Are you referring here to the idea that the form "{:gregorian :skolemfun
> > :bret}" for Skolem functions limits us to Dyadic Skolem functions?
>
>Actually *nested* ones, such as {{{a b {c d e}} f g} h i}

Could you (or someone) explain what this means? Which of the symbols 
here are functions, and what are they being applied to? It could be 
read any number of ways as it stands.

Pat Hayes

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Received on Monday, 19 March 2001 10:51:56 UTC