Re: A few thoughts on RDF-star, Reification, and Labeled Property Graphs

Hi Chris,

to your last point:

 > Why does RDFMT say "from IP to the powerset of IRxIR" instead of just 
"from IP to IRxIR" [pairs of cartesian product]?

IEXT associates a *set* of pairs to each property, that's why it is 
defined this way.
If we wrote "from IP to IRxIR", it would associate a single pair to each 
property.

For the rest of your email (below), I'm sorry, but I struggle to 
understand the point you are making (even after re-reading the old 
thread you seem be responding to).

   best

On 13/04/2026 10:47, Chris Miller wrote:
> https://lists.w3.org/Archives/Public/public-rdf-star-wg/2024Apr/0019.html
>
> 904 QS- QP- QO- XI- XD .
> 910 QSA QPA QOA XIA XD .
> 920 XIA QSQ QSA XIB XD .
> 928 XIA QSQ QPA --- XD .
> 930 XIA QPQ QPA XIC XD .
> 939 XIA QPQ QPB --- XD .
> 940 XIA QOQ QOA XID XD .
> 951 XIA QPA QBE --- XD .
> 952 XIA QPQ QBE --- XD .
> 953 XIA QPE QOE --- XD .
> 955 QBE QPE QOE --- XD .
> 967 XIC QPE QOE XIE XD .
>
> 904 sets SPOID. XI=rdf:ID (new reifier). XD=named-graph/dataset (default).
> XIA is a reifier of (QSA,QPA,QOA). XIA entails triples from 
> 920,930,940 but not their tokens XIB,XIC,XID. Other XI* reifying 
> statements are entailed but not restated in the table. 928 & 939 are 
> WFF by AAA, which serve as counter-examples to 95*. (QPE,QOE) is an 
> edge-property/property-set. (XIA,QPA) in 951 does not distinguish 
> between 920v928. (XIA,QPQ) in 952 does not distinguish between 
> 930v939. 953 is Example B (see link). 955 fails LPG-interop for EP/PS. 
> 967 corrects LPG-interop for EP/PS. 953 & 967 are each a statement and 
> both about statement 910. Call XIE a 3rd-reifier+12-statements. 
> Enhance RDF/XML with rdf:ID2='XIC' & rdf:ID3='XIE' productions to entail:
> XIC rdf:type rdf:Statement .
> XIC rdf:subject XIA .
> XIC rdf:predicate rdf:predicate .
> XIC rdf:object QPA .
> XIE rdf:type rdf:Statement .
> XIE rdf:subject XIC .
> XIE rdf:predicate QPE .
> XIE rdf:object QOE .
>
> XIC does not need bnode-ns. Counter-examples approximate an argument 
> about how to read translations/rewrites of EP/PS. 953 ought to be 
> typically sufficient when taken with additional rules in an 
> application & it reduces triple count. But there are no operators like 
> implication, negation, nor containment through RDFMT. XIA does not 
> preclude access to any of its linked components. LPG seems to read 
> EP/PS as (~QSA&~QOA)->QPA , which is almost QSA xor QPA xor QOA. But 
> this cannot mean "about QPA" like QP transposed with QS in XD. This 
> must mean QPA within a context of 910->XIA, and hence named-graph 
> (XD*) proposals. A distribution law translates the usage as 
> (~XIA\QSA&~XIA\QOA)->XIA\QPA. Still, RDF does not have a procedure 
> which copies nor relates the infix containment symbol \ of the 
> concatenation XIA\QPA to components XIA,QPA (unless by xml:base). 928 
> & 939 are unlikely to be practical interlocutions, but do show that 
> 951 & 952 cannot translate pairs into triple-queries without assuming 
> a cardinality operator about QO of XIA. RDFMT by AAA does not make 
> that restriction, but OWL could raise inconsistency. 953 reads XIA as 
> possibly inheriting from how QSA or QOA are used in 910. 967 reads XIC 
> as not making any assertion about how QSA or QOA are used in XIA, but 
> only asserts how QPA is used in XIA. XIE equals constant accessor 
> parameters to how a component is used in 910. Therefore rdf:ID2 & 
> rdf:ID3 productions are a general translation for EP/PS, when 
> decisions about reductions of total context are unclear. It ought to 
> have an implementation effort similar to that of rdf:ID. As an 
> objection, it could be said that, like rdf:List, rdf:ID2 & rdf:ID3 
> lead to unwanted verbosity.
>
> Why does RDFMT say "from IP to the powerset of IRxIR" instead of just 
> "from IP to IRxIR" [pairs of cartesian product]?