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Subject: Re: [xdi] Associativity of XDI $has statements
sorry but I believe instead that we should take care of the placement of the $has operation between multiple XRI subsegments that have been associated.
To see why, focus on the following English statement:
house door keyhole
1) house door has keyhole: you are asserting that a specialized DOOR (house door), has a KEYHOLE
2) house has door keyhole: you are asserting that HOUSE has a specialized KEYHOLE (door keyhole)
Which one does it make sense? To me only 1).
Consider now: contract markus' signature
1) contract Markus has signature: you are asserting that a "specific" MARKUS (contract Markus) has a signature
2) contract has Markus' signature: you are asserting that CONTRACT has a specific SIGNATURE (Markus' signature)
only 2) seems to make sense to me.
A formal proof follows below.
Formal Proof - at the end of last Spring we agreed on these points:
#1: +x/$has/+y INFERS:
#1A: +x+y INFERS
therefore, supposing $has is a left associative operator, +a+b+c reads as :
i.e. node +a+b, which is a "specialized" +b, has an outgoing arc +c
When instead you have +a(+b+c) you read:
i.e. node +a has an outgoing arc, +b+c, which is a "specialized" +c
Def. Quota "Drummond Reed" <firstname.lastname@example.org>:----------------------------------------------------------------
After our discussion on last Thursday’s telecon I wanted to post a note
about the $has predicate and the XDI expressions it produces.
The rule we established last spring that is that any XDI $has statement can
be simplified into two other XDI statements:
1) A single XRI cross-reference (an XRI in parentheses) containing exactly
two XRI segments—the first being the subject of the original $has statement
and the second segment being the object of the original $has statement.
+a/$has/+b <==> (+a/+b)
2) A single XRI segment by directly concatenating the subject of the
original $has statement and the object of the original $has statement.
+a/$has/+b <==> +a+b
All three express the same underlying semantics, i.e.:
+a/$has/+b <==> (+a/+b) <==> +a+b
This example is straightforward because the XDI statement +a+b represents
only one $has statement and therefore has only one expansion. XDI statements
consisting of more than two XRI subsegments represent multiple $has
statements and so the number of expansions increases. Let’s take the
My understanding is the semantics we want for $has statements is
associativity (http://en.wikipedia.org/wiki/Associativity). By that I mean
that sequence matters, but not the placement of the $has operation between
multiple XRI subsegments that have been associated with $has statements. If
so, this means our example +a+b+c+d expands into all of the following XDI
+a+b+c/$has/+d <==> (+a+b+c/+d) <==> +a+b+c+d
+a+b/$has/+c+d <==> (+a+b/+c+d) <==> +a+b+c+d
+a/$has/+b+c+d <==> (+a/+b+c+d) <==> +a+b+c+d
Note that this rule does NOT constrain the use of cross-references to
perform explicit grouping (reification) of XDI statements. For example:
…is different from +a+b+c+d because +a+b(+c+d) is a three-subsegment XRI
that has two expansions outside the cross-reference…
+a/$has/+b(+c+d) <==> (+a/+b(+c+d)) <==> +a+b(+c+d)
+a+b/$has/(+c+d) <==> (+a+b/(+c+d)) <==> +a+b(+c+d)
…and two variants on these if you also expand inside the cross-reference:
+a/$has/+b(+c/$has/+d) <==> (+a/+b((+c/+d))) <==> +a+b(+c+d)
+a+b/$has/(+c/$has/+d) <==> (+a+b/((+c/+d))) <==> +a+b(+c+d)
Again, my interpretation is that this is exactly what we want—the same
associativity between $has statements that we have with left-to-right
sequences of English adjectives before a noun:
engine cowling color
Boeing plane engine
Boeing plane engine cowling
Boeing plane engine cowling color
Boeing plane engine cowling color
In these five examples, the final word in each column (left and right) is a
noun, and all the words before it are adjectives. If you then take any
combination from the left and then concatenate it with the right (without
changing the sequence), the result is that all but the last word is turned
into an adjective, and “color” is the noun they all describe.
I hope this clears up any confusion about $has statements. I definitely see
the need to include some additional clarification about this in the XDI RDF
Graph Model spec.
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