Re: [Sem] Yet another formal semantics for RDF-star

Dear Antoine,

Am 28.03.2023 um 10:44 schrieb Antoine Zimmermann <antoine.zimmermann@emse.fr<mailto:antoine.zimmermann@emse.fr>>:

Le 27/03/2023 à 19:44, Peter F. Patel-Schneider a écrit :
Hmm, yes.  I now think that you are correct.   I was incorrectly treating the T mapping like the blank node mapping.  But now I'm not sure exactly what this semantics is.   I would like to see more examples.

If we stay within az-semantics alone, it's hard to illustrate much. Let us consider an extension with owl:sameAs.

az-sameas semantics extends as-semantics in the following way:

an /az-sameas interpretation/ is an az-intepretation that satisfies this additional constraint:
- I(owl:sameAs) in 𝓟
- IEXT(I(owl:sameAs)) = {(x,x) | x in Δ}

In this case, we have:

:superman owl:sameAs :clark .
:lex :thinks <<:superman :can :fly>> .

az-sameas entails:

:lex :thinks <<:clark :can :fly>> .

Can you elaborate why? I do not see that. Is it not possible that

(𝓘(:lex), 𝓘(<<:superman :can :fly>>))∈ 𝓘EXT(𝓘(:thinks))
while

(𝓘(:lex), 𝓘(<<:clark :can :fly>>))\not∈ 𝓘EXT(𝓘(:thinks))

or to put it differently, I do not see why
𝓘(<<:superman :can :fly>>) should be the same as 𝓘(<<:clark :can :fly>>).

Can you help me here?

Thank you in advance :)

Dörthe




Then,

:lex :assumes <<:superman owl:sameAs :clark>> ;
    :knows <<:superman :can :fly>> .

does *not* az-sameas entail:

:lex :knows <<:clark :can :fly>> .

*nor*:

:lex :assumes <<:clark owl:sameAs :superman>> .

Consider:

<<:s :p :o>> owl:sameAs :s .

az-sameas entails:

<<<<:s :p :o>> :p :o>> owl:sameAs :s .

The RDF-star graph:

<<:s :p :o>> owl:sameAs <<:x :y :z>> .

does *not* az-sameas entail:

:s owl:sameAs :x .


etc.

--AZ


peter
On 3/27/23 13:40, Franconi Enrico wrote:
semantic vs syntactic predication has nothing to do with the existence or not of subject, predicate, and object relationships. It has to do with the identity of the reified object representing the embedded triple.
Is that object “representing” just the syntactic version of the embedded triple, or it represents the “meaning” of the embedded triple?
—e.

On 27 Mar 2023, at 19:36, Peter F. Patel-Schneider <pfpschneider@gmail.com<mailto:pfpschneider@gmail.com>> wrote:

Actually it is unclear what semantic predication should look like.   This proposal is reification plus uniqueness.   Whether that is semantic predication depends on what one thinks the requirements for semantic predication are.  One could argue that semantic predication requires that there are resources that are actually triples, not just that there are resources that are connected to resources via subject, predicate, and object relationships.  I think that it would be possible to add this extra requirement to the semantics.

peter


On 3/27/23 13:28, Peter F. Patel-Schneider wrote:
Are you sure?  My reading is that this is semantic predication without assertion.    Consider the RDF graph { (( s p o ) q n) }.
A model of this graph is
( { t' s' o' n' }, { p', q', rs', rp', ro' }, JS, {}, JT, JEXT, rs', rp' ro' )
with JS mapping s to s', o to o', n to n', p to p', and o to o',
JT( (s p o) ) =  t',
JEXT(q') = { ( t', n' ) }
JEXT(p') = {}
JEXT(rs') = { ( t', s' ) }
JEXT(rp') = { ( t', p' ) }
JEXT(ro') = { ( t', o' ) }
Note that JS has to map to resources or properties as in the RDF 1.1 semantics.
In this semantics there is no entailment from { (( s p o) q n } to { (s p o)}
but there is entailment from { ((s p "42"^^xsd:int) q n) } to
{ ((s p "42"^^xsd:integer) q n) } if xsd:int and xsd:integer are recognized datatypes.
peter
On 3/27/23 13:02, Franconi Enrico wrote:
I looked at it carefully. This seems to characterise more or less the model theory of what I call syntactic predication, which is more or less the current definition of <<.,.,.>>.
Some comments - tell me if I’m wrong.
Some difference I note is that a syntactically embedded triple would still entail the truth of the triple itself, which probably is not intended, and that the reification “implements” the full semantic predication (ie., it would be fully transparent).
Moreover, there is still the open discussion about injectivity, and the interoperation, if desired, with the TEP and/or with the full semantic predication.
cheers
—e,


On 27 Mar 2023, at 18:08, Antoine Zimmermann <antoine.zimmermann@emse.fr<mailto:antoine.zimmermann@emse.fr>> wrote:

Le 27/03/2023 à 17:37, Peter F. Patel-Schneider a écrit :
It would be useful to have some more explanation and some examples.

Yes, it is brutally asserting the definitions and nothing else.

  From my quick read this appears to be very lose to to using RDF reification plus uniqueness of triples.

Yes. The one benefit that I see is that it does not require introducing a vocabulary that would "reserve" some URIs.

In the Satisfaction section it appears that either a nor J[a] is defined for blank nodes.

Damn, I sometimes used bold face T as if it meant the set of all terms, while it is in fact defined as the set of RDF-star triples.

α should be defined on "B ⋃ T ∖ Gnd".
There is an unfortunate copy-paste error before the colon of the 1st paragraph in section "az-Satisfaction"("𝓘[α](t) = : T → Δ" should be "𝓘[α]: T → Δ" and the second item of the first bullet list of this section should have "B ⋃ T ∖ Gnd" instead of "T ⋃ Gnd".

I'll correct that.

--AZ


peter
On 3/27/23 09:09, Antoine Zimmermann wrote:
This is mostly for the semantics task force.

I wrote this:
https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.emse.fr%2F~zimmermann%2FW3C%2FRDF-star-semantics%2F&data=05%7C01%7Cfranconi%40inf.unibz.it%7C628c4c949576455d6c3308db2ee9db12%7C9251326703e3401a80d4c58ed6674e3b%7C0%7C0%7C638155354154223295%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=QsK42%2FvCalgfkj6JBMxNx5l%2Be3zqe9L3LB7yHxL7ek4%3D&reserved=0


The idea is that embedded triples are interpreted as arbitrary resources and the resources denoted by the subject, predicate, and object of an embedded triple are connected (semantically) to the embedded-triple-resource via 3 properties that depend on the interpretation.

Now, please comment and destroy this proposal :)

--
Antoine Zimmermann
ISI - Institut Henri Fayol
École des Mines de Saint-Étienne
158 cours Fauriel
42023 Saint-Étienne Cedex 2
France
Tél:+33(0)4 77 42 66 03
https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.emse.fr%2F~zimmermann%2F&data=05%7C01%7Cfranconi%40inf.unibz.it%7C628c4c949576455d6c3308db2ee9db12%7C9251326703e3401a80d4c58ed6674e3b%7C0%7C0%7C638155354154379524%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=0ngGhIU9nvczkbewEokms0xMi5cYu0ry2%2BuAjO1nml4%3D&reserved=0





--
Antoine Zimmermann
ISI - Institut Henri Fayol
École des Mines de Saint-Étienne
158 cours Fauriel
42023 Saint-Étienne Cedex 2
France
Tél:+33(0)4 77 42 66 03
https://www.emse.fr/~zimmermann/