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

Le 28/03/2023 à 13:44, Doerthe Arndt a écrit :
> 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>>))∈ 𝓘_EXT (𝓘(/:thinks/))
> while
> 
> (𝓘(:lex), 𝓘(<<:clark :can :fly>>))\not∈ 𝓘_EXT (𝓘(/:thinks/))

Damn, you're right!

So there is another mistake down below.


> 
> 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
> 
> 
> 
> [...]
>>
>> <<:s :p :o>> owl:sameAs :s .
>>
>> az-sameas entails:
>>
>> <<<<:s :p :o>> :p :o>> owl:sameAs :s .


This is wrong too! The entailment does not hold.


If we want it to hold, I guess the following extension of az-sameas 
semantics would suffice:

az-sameas++ semantics:
An az-sameas++ interpretation is an az-sameas interpretation (Δ, 𝓟, 
𝓘S, 𝓘L, 𝓘T, 𝓘EXT, rs, rp, ro) that satisfies the following:
  - for all t1, t2, s, p, o in Δ, if (t1,s) in 𝓘EXT(rs), (t1,p) in 
𝓘EXT(rp), (t1,o) in 𝓘EXT(ro), (t2,s) in 𝓘EXT(rs), (t2,p) in 
𝓘EXT(rp), and (t2,o) in 𝓘EXT(ro) then t1 = t2.


--AZ



>>
[SKIP]


-- 
Antoine Zimmermann
École des Mines de Saint-Étienne
158 cours Fauriel
CS 62362
42023 Saint-Étienne Cedex 2
France
Tél:+33(0)4 77 49 97 02
http://www.emse.fr/~zimmermann/

Received on Tuesday, 28 March 2023 12:55:37 UTC