(PRD) Safeness and the semantics of conditions (Was: Re: [PRD] proof that model theory of conditions != matching substitution semantics)

Gary, all,

(This is only about the safety/safeness part of your email. I reply to the 
part about the semantics of conditions in another message.)

Gary Hallmark <gary.hallmark@gmail.com> wrote on 27/05/2009 21:26:51:
> 
> I think it would be more useful to specify an alternative semantics
> for conditions that is operational. It would be equivalent to the
> model theory combined with the Core safety restriction (extended to
> PRD).

I do not understand why safeness is part of the semantics of conditions?

What we want to guarantee, is that all the variables that are used in the 
actions part are bound in the condition part (except for the action 
variables, of course). We need that because is is an assumption that is 
made in the semantics of rules and rule sets.

If so, it is a condition on the well-formedness of a rule that Var(A) is a 
subset of VarB(C), where Var(A) are the free variables in the the action 
block and VarB(C) are the variables that must be bound to establish the 
truth value of the conjunction of all the binding patterns and the 
condition of the rule (something like the "restricted variables" in [1]).

Did I miss something?

Then, there is the (different) constraint, that we want the evaluation of 
conditions to be implementable with pattern matching; that is, we want to 
guarantee that it does not require constraint solving.

This implies restrictions on the condition formulas, of course, like 
P(f(?x)), where P is a predicate symbol and f is the symbol of an external 
function, is allowed only if ?x can be bound otherwise, e.g. if P(f(?x)) 
is in a conjunction with Q(?x), where Q is a predicate symbol, and, thus, 
?x can be bound by matching Q(?x) to a fact (if we have only P(f(?x)) and 
a fact P(a), we need to solve the constraint f(?x) = a, to bind ?x).

But, again, these are not related to the semantics of condition, but to 
implementations: we do not want that RIF-PRD conformance requires 
producers and consumers to support constraint solving (in the above 
sense).

If so, these restrictions belong to the conformance clause, not the 
semantics of conditions, or even of rules (in principle, at least: it may 
be easier to specify them along with the well-formedness condition on 
variables in the action part being bound in the condition).

Again, did I miss something?

Could somebody clarify this issues for me, please?

Cheers,

Christian

[1} Joohyung Lee, Vladimir Lifschitz, and Ravi Palla. A reductive 
semantics for counting and choice in answer set programming. In 
Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 
2008.

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