Hi,
May I make a separate proposal on this issue? It's sort of like Anne's
alternative #2 below with a couple of differences.
First, NOT-APPLICABLE (or Inapplicable?) and Error, are values that do not
have an XML representation and are merely a artifact of evaluating policy
expressions.
I propose the following consistent semantic model.
T = true, F = false, N = NOT-APPLICABLE, E = Error
The basic crux is that getting a NOT-APPLICABLE in the equation is as if
its the NOT-APPLICABLE value isn't even there. For instance,
(and x N y) = (and x y)
(or
x N y) = (or x y)
I think that is the semantics we want. That is to say, if the policy
doesn't apply, it doesn't enter into the equation.
I also surmise to keep things easily consistent in inductive arguments
about ANDs and ORs of sequences. The AND or OR of a zero length sequence
of values can be anything constant we want, but the minimum element
NOT-APPLICABLE would make the most sense, since
(and x N) = (and x), from our assumption above, and,
(and x) = x, which is still another wily assumption, but makes sense,
So therefore (and N) = N,
but from above,
(and N) = (and),
Therefore,
(and) = N
So we would have,
<and></and> = NOT-APPLICABLE
<or></or>
= NOT-APPLICABLE
Also, to satisfy Hals "the customer's want it", I am almost on the side of
allowing NOT in the language with the following semantics:
p
NOT p
---------
T
F
F
T
N
N
E
E
That is to say NOT of NOT-APPLICABLE is still NOT-APPLICABLE. Then NOT
distributes through the AND and ORs (i.e. DeMorgan's Law) quite nicely.
(NOT (AND N x)) = (OR (NOT N) (NOT x))
(NOT x)
= (OR N (NOT x))
(NOT x)
= (NOT x)
(NOT (OR N x)) = (AND (NOT N) (NOT x))
(NOT x)
= (AND N (NOT x))
(NOT x)
= (NOT x)
However, differing from alternative #2 in the proposal below, I believe
<NOT></NOT> shouldn't exist, and it should have one and only one
constituent. And empty NOT is a syntax error, as well as having more than
one, i.e. <NOT> x y </NOT> shouldn't type check either. (how do you say
that in XML? minoccurs=1, maxoccurs=1?).
For completeness the truth tables in the 4-valued logic are below for
"and", "or" and "not",
p
q
p and q
-------------
T
T
T
T
F
F
T
N
T
T
E
E
F
T
F
F
F
F
F
N
F
F
E
E
N
T
T
N
F
F
N
N
N
N
E
E
E
T
E
E
F
E
E
N
E
E
E
E
p
q
p or q
-------------
T
T
T
T
F
T
T
N
T
T
E
E
F
T
T
F
F
F
F
N
F
F
E
E
N
T
T
N
F
F
N
N
N
N
E
E
E
T
E
E
F
E
E
N
E
E
E
E
p
NOT p
---------
T
F
F
T
N
N
E
E
Cheers
-Polar
On Thu, 7 Feb 2002, Anne Anderson wrote:
> PM-1-?: how NOT-APPLICABLE impacts a combinator expression
>
> A "combinator expression" is a combination of predicates, where
> possible combinators are <AND>, <OR>, <NOT>, <N-OF>,
> <ORDERED-[AND|OR|N-OF]>. This list of Combinators can be
> extended.
>
> Example:
>
> <AND>
>
predicate1,
>
predicate2,
>
predicate3
> </AND>
>
> The issue occurs when one or more of the predicates in the list
> returns a result of NOT-APPLICABLE (this can occur if the
> predicate is a <referencedPolicy>). What should the result of
> the combinator expression be? What if ALL predicates in the
> bominator expression return NOT-APPLICABLE?
>
> Potential Resolution:
>
> a) Any predicate evaluating to NOT-APPLICABLE is logically
>
removed from the combinator expression.
>
>
Example: if predicate3 in the example above returned a result of
>
NOT-APPLICABLE, then the combinator expression is the result of
>
>
<AND>
>
predicate1,
>
predicate2
>
<AND>
>
> b) An empty combinator expression has the following results:
>
>
<AND></AND>
-> TRUE
>
<OR></OR>
-> FALSE
>
<NOT></NOT>
-> TRUE
>
<N-OF></N-OF> -> FALSE
>
>
<ORDERED-[whatever]> has same result as [whatever] above.
>
Extended combinators must define the result of an empty
>
expression.
>
>
Example: If predicates 1, 2, and 3 in the example above all
>
evaluate to NOT-APPLICABLE, then the combinator expression is
>
<AND></AND>, and the result is TRUE.
>
> b)-alternative: An empty combinator expression has a result of
>
NOT-APPLICABLE.
>
> Champion: Anne
> --
> Anne H. Anderson
Email:
> Sun Microsystems Laboratories
> 1 Network Drive,UBUR02-311
Tel: 781/442-0928
>
Burlington, MA 01803-0902 USA
Fax: 781/442-1692
>
>
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