Re: [xdi] $or and $and may not be necessary

I agree the $any$1+age doesn't feel right.

How about this?

=giovanni
    +friend
        $any$1
        $any$2
($any$1/+age)
    $greater
        "40"
($any$2/+age)

    $lesser

        "27"

Markus

On Thu, Apr 17, 2008 at 7:08 AM, Drummond Reed <> wrote:

I like the variable approach very much, but in the example 
in Markus' messageI don't understand how the reference to "$any$1" resolves to 
"$any$1+age".

 

Would it be better to keep a clear mapping between the 
variable XRIs and the XDI statements they represent? For 
example:

 

=giovanni
    
+friend
        $any$1
    
    $any$2
$any$1

    
$context

        
/

            
+age

                
$greater
                    
"40"
$any$2

    
$context

        
/

            
+age
                
$lesser
                     
"27"

 

 

=Drummond

  

  
  From:  
  [mailto:] On Behalf Of Markus 
  Sabadello
Sent: Wednesday, April 16, 2008 9:21 AM
To: 
  Giovanni Bartolomeo
Cc: 
Subject: 
  Re: [xdi] $or and $and may not be necessary

  

Yes.. I think everyone who has some experience in logic will find 
  this pattern familiar.

In some cases this disjunctive normal form will 
  appear to be more complicated than your original form with brackets, for 
  example:

"Give me all of Giovanni's friends who are younger than 27 OR 
  older than 40". In order to implement the OR, you have to introduce two 
  variables, i.e. you have to do it this 
  way:

=giovanni
    +friend
    
      $any$1
        
  $any$2
$any$1+age
    $greater
    
      "40"
$any$2+age
    
  $lesser
        "27"

Whereas in your 
  original bracket form you would probably be able to somehow do this with just 
  one variable.

BTW you don't need $not either, because you can convert 
  your $not queries like this:
"Give me all of Giovanni's friends who are NOT 
  (younger than 27 OR older than 40)".

Well that's just the same 
  as
"Give me all of Giovanni's friends who are >= 27 AND <= 
  40.

It really seems to be just a simple matter of boolean algebra to 
  convert just about any arbitrarily complex query to what you call "normal 
  form".

Markus

P.S. You can try the query above at http://graceland.parityinc.net/xdi-querier/XDIQuerier

  
On Wed, Apr 16, 2008 at 1:47 PM, Giovanni Bartolomeo 
  <> 
  wrote:

  Coming 
    back a bit to this thread... I've made some thoughts.

The solution 
    proposed by Markus works because he has been able to express this complex 
    query into a "normal form" compliant with the one used for "traditional" 
    $get. He correctly identified that this format allows to disjoin the graph 
    into multiple graphs (he called them "clusters"). Adding different $any 
    variables, we can implicitly create AND and OR statements, in a simple way: 
    AND statements are created when the same $any variable appears into two or 
    more clusters, OR statements are the default.
So this solution will work 
    in general for any AND/OR expression. The only concern is that we've to 
    arrange the query into this "normal form". Interestingly, the existence of a 
    "normal form" for XDI has reminded me some expressions in logic which are 
    known as disjunctive normal forms: http://en.wikipedia.org/wiki/Disjunctive_normal_form... 
    not sure, but maybe it worths to be further investigated in the 
    future.

Bests,
Giovanni
    

    

    

At 15.40 01/04/2008, Giovanni Bartolomeo 
    wrote:

    
      

      

      
Hello Markus,

at a first glance it seems that 
      this solution works fine, however I'm
not sure whether this could 
      replace $and, $or etc. in any possible use
case (we need to elaborate 
      some more examples).
But I agree that for now this is a good solution 
      and we can reccomend
to use it :-)

Giovanni

At 20.46 
      30/03/2008, you wrote:
Maybe $or and $and are not necessary at all, 
      because I think that
1) There's an implicit AND relation between query 
      statements that
share variables.
2) There's an implicit OR relation 
      between query statements that do
not share variables.

For 
      example, take this query:

=giovanni
  
       +friend
       $any$1
  
       +brother
      
       $any$2
$any$1+age
   $lesser
      
       "40"

It means give me all statements that are matched by the 
      following:
( [=giovanni[+friend[$any$1]]] AND 
      [$any$1+age[$lesser["40"]]] ) OR (
[=giovanni[+brother[$any$2]]] 
      )

In other words, you can divide the query graph into multiple 
      disjunct
graphs (let's call them clusters). Every variable you use 
      appears in
only one cluster. The query above consists of two 
      clusters:

Cluster 1:

=giovanni
  
       +friend
       $any$1
$any$1+age
  
       $lesser
       "40"

Cluster 
      2:

=giovanni
   +brother
      
       $any$2

Now the rule is that when executing the query you 
      select everything
from your input graph that matches ALL statements in 
      AT LEAST ONE of
the clusters. This results in the implicit AND and OR 
      relations.

I'm not 100% sure, but I think that with Giovanni's $any 
      and $all
words you can automatically model any query you want, without 
      the need
for $or and $and.

Markus

P.S. I'm sure that in 
      graph theory there's a better word for those
"clusters", but I don't 
      know the correct expression in either English
or German. The point is 
      that variables that are not "connected" end up
in different 
      clusters.

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