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

> On 21 Jan 2020, at 09:48, Antoine Zimmermann <antoine.zimmermann@emse.fr> wrote:
> 
> 
> 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).

It looks like literals also add quite a bit of complication to Functorial
Semantics if that is any consolation.
I opened an issue for that with some references 
https://gitlab.com/web-cats/CG/issues/11


> 
> 
>> 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

Received on Tuesday, 21 January 2020 10:19:14 UTC