Re: is rdf a regular logic? RIF? was: Coherent Logic (a.k.a Geometric Logic) and RDF?

Le 20/01/2020 à 21:14, Patrick J Hayes a écrit :
> 
> 

[skip]
>>
>> Simple entailment can be translated to FOL using either: relations of 
>> arity 2 (where the predicate IRI is used as a binary FOL predicate); 
>> or using a single relation of arity 3 (where <s> <p> <o> becomes 
>> Triple(s,p,o)).
>>
>> If you assume the set D to be empty, then RDF-entailment and 
>> RDFS-entailment can be translated to FOL as well. But as soon as you 
>> add datatypes and literals to the picture, it's a whole different 
>> story. RDF 1.1 Semantics imposes that RDF(S)-entailment MUST recognise 
>> xsd:string and rdf:langString. This totally cripples the RDF-to-FOL 
>> translation.
> 
> Well, as with RDFS, it maps into a FO axiomatic theory (in this case, 
> countably infinite) but the actual reasoning is still simple FO 
> reasoning. It does not require a different /logic/.

Right, but the RDF-to-FOL translation of D-entailment, even with simple 
datatypes like xsd:string, requires some tricks (see below).


> 
> Pat
> 
>>
>> For instance, in RDFS-entailment recognising 
>> {xsd:string,rdf:langString}, is the following graph consistent 
>> (written in Turtle, assuming the obvious prefixes)?
>>
>> rdfs:Resource rdfs:subClassOf xsd:string .
>>
>> (left as an exercise to the reader :)
> 
> :-) I am not sure myself. If a language-tagged string a kind of string?

In D-entailment, the IRIs in D have to be interpreted as the datatype 
they are associated to. For instance, in RDFS semantics, xsd:string has 
to be interpreted as the datatype (LS,VS,L2V) where LS -- the lexical 
space of xsd:string -- is the set of valid XML schema strings, VS -- the 
value space of string -- is the same as LS, and L2V -- the 
lexical-to-value mapping -- is iedentity. So, the universe of all RDFS 
interpretations has to contain the triple (LS,VS,L2V). This triple is 
clearly not a sequence of UNICODE character itself. But the statement:

rdfs:Resource rdfs:subClassOf xsd:string .

in RDFS means that all resources (all things in the universe) must 
belong to the extension of the class denoted by xsd:string. In turn, 
D-entailment says that all datatypes in D are classes whose extension is 
exactly their value space (crucially, this last constraint is removed by 
ter Horst in his D*-entailment [1]).

So, the triple above constrains everything in the universe to be 
character strings, whereas xsd:string is required to denote a triple of 
set-theoretic structures. Obviously, it cannot be the case, so there are 
no RDFS-models of such triple. Thereby, it is RDFS-inconsistent.

D-entailment can be horribly complicated. Consider this example:

rdf:Property rdfs:subClassOf xsd:boolean .

Is this RDFS-recognising {xsd:boolean}-consistent?


--AZ


>>
>> Datatype semantics in RDF is horribly complicated to properly handle 
>> and I doubt there is (and even will be) any reasoner that correctly 
>> and completely implements datatype entailment as defined in the 
>> standard. Notably, in his excellent paper from 2005, Herman J. ter 
>> Horst provides a sound and complete algorithm for RDFS with datatype 
>> entailment, but he dismisses the official D-entailment semantics to 
>> propose a more computable one, that he calls D*-entailment [1]. 
>> D*-entailment is what practical reasoners usually implement, if they 
>> support datatypes at all.
>>
>> However, De Bruijn and Heymans show that, if we are cautious in 
>> selecting supported datatypes, it is still theoretically possible to 
>> reason efficiently with standard D-entailment [2]. But first, they do 
>> not provide an effective algorithm,* and second, it forbids quite a 
>> lot of datatype combinations.
>>
>>
>> * Only indirectly via translation to F-Logic, and it may not be 
>> efficient at all.
>>
>>
>> --AZ
>>
>>
>>
>> [1] Herman J. ter Horst. Completeness, decidability and complexity of 
>> entailment for RDF Schema and a semantic extension involving the OWL 
>> vocabulary. In Journal of Web Semantics, Volume 3, Issues 2–3, October 
>> 2005, pages 79-115.
>> [2] Jos De Bruijn and Stijn Heymans. Logical Foundations of RDF(S) 
>> with Datatypes. In Journal of Artificial Intelligence Research, Volume 
>> 38, August 2010, pages 535-568.
>>
>
> [skip]
>-- 
Antoine Zimmermann
Institut Henri Fayol
École des Mines de Saint-Étienne
158 cours Fauriel
CS 62362
42023 Saint-Étienne Cedex 2
France
Tél:+33(0)4 77 42 66 03
Fax:+33(0)4 77 42 66 66
http://www.emse.fr/~zimmermann/
Member of team Connected Intelligence, Laboratoire Hubert Curien