RE: Datalog With Only Binary Relations Is Too Weak

> > [Pat]
> > You talk above about a  PROOF of C from A->B and B->C, which I guess
> > I don't understand since C doesnt follow from those two premises. Do
> > you mean a proof of C from those two implications plus the assumption
> > A?
>
>definitely (I should also sleep more instead of giving half-baken replies;-)
>
> > That would go
> > A + A->B ==> B + B->C ==> C
> > using forward reasoning. Written as resolution and using backward
> > inference, it would be
> >
> > C->    B->C
> > ------------
> >     B->          A->B
> >      ---------------
> >           A->          ->A
> >          ---------------
>
>Are you suggesting a notation for the ------------ or the above ==> ?
>Is it something like *log:entails* or what could it be (and fitting
>with http://www.w3.org/DesignIssues/Notation3.html )?

I was just (informally) trying to indicate the sequence of applying 
rules of inference. They are often written with premises above the 
line, conclusions below. The -> notation for clauses follows Prolog 
usage, where one 'negates' an atom (or queries it) by saying that it 
implies nothing (=false in a disjunction, ie a clause), so ' C->' 
means 'not C', and the backward search terminates with a null clause 
(which I should really have written as the conclusion '->')

Its not really log:... anything, since its not an expression but more 
like a step in a process. One can think of inference rules as things 
that add sentences to proofs, and then the proof can itself be seen 
as a kind of execution trace of the process by which it was built, 
structured so as to demonstrate the validity of the sentence. This is 
quite a neat way to think about proofs in general, actually.

Pat Hayes

Pat Hayes

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Received on Tuesday, 20 March 2001 17:56:03 UTC