On production rules and phase I&II

Part of the proposed plan is to partition the handling of production  
rules across the phases, with phase I being the 'pure' subset of  
production rules.

The pure subset corresponding to an extremely small subset of horn  
clause logic (no recursion!) and an extremely small subset of PR (no  
modify or remove in the action part of the rule)

Quite apart from the fact that that to isolate this small subset of  
PRs is to completely miss the point & approach of PRs, there is a  
further technical issue.

It is possible to map a rule of the form

when A & B then assert C

into a 'horn clause' of the form

isTrue(C) <- A ^ B

A point to bear in mind: to support chaining, it will be nec. to  
conclude from

isTrue(C)

to

C

This appears to imply a Kripke-style possible world semantics.

A much more serious point is this: in order to support modify and  
remove (phase II aspects) it will be necessary to undo this reading  
of PRs. I.e., to model PRs in terms of predicate logic, it will be  
necessary to get into modeling causal relationships/actions etc. A  
simple straw man approach being to use the situation calculus:

isTrue([C|W]) :- show(W,A), show(W,B)

(using Prolog here...:-)

where show is analogous to

show(W,C) :- C in W.
show(W,C) :- originallyTrue(C).

Actually it would have to be considerably more complex than this and  
one would not use situation calculus anyway because it cannot model  
serendipitous reasoning.

The point I am trying to make is that the characterization of PRs  
including modify and remove has to undo the prior characterization  
*even of the 'pure subset' of PRs*.

In effect, the bottom line is:

if there is a Phase I spec published as planned, any Phase II spec  
will not be monotonic wrt Phase I. In addition to the usual health  
warning attached to preliminary specs being incomplete we would have  
to declare that we already know that its wrong.

In any case, I think that the modeling of PRs (if we bother to do it)  
will not be based on a simplistic mapping of PR rules onto a horn  
rule: we must take the state into account. And, of course, that  
raises the nasty frame axiom.

Frank

Received on Tuesday, 7 March 2006 22:56:44 UTC