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Re: OWL 2 profiles

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 23 Nov 2010 22:33:32 -0600
Cc: Cristian Cocos <cristi@ieee.org>, public-owl-dev@w3.org
Message-Id: <3A06C162-F485-480C-A947-58A4EF717FDD@ihmc.us>
To: Bijan Parsia <bparsia@cs.man.ac.uk>

On Nov 23, 2010, at 8:06 PM, Bijan Parsia wrote:

> On 23 Nov 2010, at 19:08, Pat Hayes wrote:
> 
>> On Nov 23, 2010, at 11:46 AM, Cristian Cocos wrote:
>> 
>>>> But do not confuse the OWL 2 RL syntactic profile (which in fact is a
>>>> syntactic fragment of OWL 2 DL) with the OWL 2 RL/RDF rules
>>> 
>>> Thank you. The RL profile I'm talking about is this:
>>> http://goo.gl/PLXRe, which I assume is what you call "OWL 2 RL
>>> syntactic profile," right?
>>> 
>>>> The syntax of OWL 2 Full is the RDF abstract syntax [1], i.e. any RDF graph
>>>> is a valid OWL 2 Full ontology.
>>> 
>>> Thanks, though not being an RDF aficionado, it would help me more if
>>> you used (the binary-relation restriction of) FOL as a term for
>>> comparison. I seem to vaguely recall that via the reification
>>> mechanism, RDF goes beyond FOL,
>> 
>> RDF does not go beyond FOL.
> 
> Not all RDF graphs under the standard semantics can be regarded as notation variants of classic (i.e., name separated) FOL formulae.
> 
> For example, ":a rdf:type :C" does not exactly correspond to C(a) (in a classic, introduction to symbolic logic style FOL).

It corresponds exactly to the formula type(a, C) in a classic, textbook style FOL. It can be written as C(a) in a CL-style formulation of FOL, which is still strictly first-order. 

> 
> However, it does not do so primarily via the reification *vocabulary*, but  via 1) some syntactic liberality (e.g., the signature is not sorted by syntactic role, but the set of  constants and predicates may overlap and, indeed, coincide)

Indeed, they can do so in a CL style FOL. In fact, in CL there simply is no distinction between constants and predicates, or indeed functions and relations more generally; there is simply a set of names, and any name can play any syntactic role. This is not standard textbook FOL, but it is still FOL, and indeed the standard FO inference rules apply to this syntax without change, and are still complete. 

> and 2) additional semantic conditions.

There are no additional semantic conditions in CL. The CL model theory is an exact mirror of 'textbook' FOL if one uses a syntax transcription which maps atomic sentences R(a1 ... an) to Apply(R a1 ... an). 

> 
> However, at least through OWL Full, the particularly ways of doing this do not result in a logic which is e.g., non-compact. It, thus, may be completely defined in (classic, standard) FOL. Thus, it can be (and should be) regarded as a kind of first order logic even though it's not exactly classic, Principa style FOL.

There is a widely accepted criterion for being FO, according to which any logic which is compact and satisfies the downward Skolem-Lowenheim theorem is first order. 

> 
> Note that the mere addition of comments can be regarded, reasonably, as a deviation from standard FOL.

I disagree about the reasonableness. There is no absolutely standard formulation of FOL: there are almost as many syntaxes as there are authors of textbooks. Adding comments does not affect the logic in any way, so to treat this as significant would be unreasonable. 

> 
> I need a name for this. I'll call the specific kind of FOL you find in Introduction to Symbolic Logic text books "Good Old-Fashioned FOL" GOFFOL.

We've been calling it GOFOL, pron. 'go-fol',  for years :-)

> Anything that deviates from that slightly, but remains first order (in a general sense; e.g., can be axiomitized by a finite GOFFOL theory with maybe some axiom schemas) is "New Fangled FOL" or NFFOL. RDF is definitely a NFFOL

I disagree. It depends on how to transcribe the RDF into the logical notation. If you do it uniformly so that each triple a P b is rendered into the formula 
triple (a P b), then you get GOFOL. If you treat properties as binary relations and classes as predicates, you get a CL-style syntax. But that difference is superficial: nothing in RDF requires inferences going beyond classical FO inference. In fact, its a very small subset of FO inference. In fact, this applies to RDFS and all the OWLs also. 

BTW, you can think of the CL version of FOL as being a first-order GOFOL theory which has a signature but no axioms. It is an empty theory, which serves only to achieve a syntactic transformation. That is why the inference rules apply without any change. 

but so is OWL DL at least on the point of having annotations. SHOIN, SROIQ, etc. are clearly GOFFOL. Adding datatypes  is a bit NFFOL, but in a fairly standard way (e.g., of the satisfiability modulo theory sort) (well, except for reals). Adding punning is NFFOL.

Datatypes are NFFOL if you do them properly :-)

> 
>> There is no reification 'mechanism' in RDF, and the RDF semantics of reification are so minimal as to pose no threat to FO expressivity. 
> 
> It's NFFOL but not GOFFOL.

The real point is, its FOL. 

Pat

> 
>> Pat Hayes
>> 
>>> hence OWL 2 Full also does that. Is
>>> that true? If so, I'd be tempted to regard this as the most glaring
>>> distinction b/w OWL 2 DL and OWL 2 Full.
> 
> You can generally break OWL 2 DL/Full expressivity differences (causing, e.g., undecidability) into several parts:
> 
> 1) OWL Full encompasses a larger (undecidable) fragment of GOFFL. Basically, all the syntactic restrictions to keep e.g., the combination of counting quantifiers and transitive decidable are lost. Similarly, you can have aribitrary patterns of BNodes which gets entailment problem to encompass conjunctive query answering with cycles + transitivity + (in)equalities (also undecidable). etc.
> 2) OWL Full has Hilog semantics, which, in the absence of a Unique Role Assumption breaks decidability. This is pretty cheap for OWL Full because the may way that works is by making detecting simplicity of roles impossible to do syntactically. But see 1.
> 3) OWL Full has general syntactic reflection, that is, it doesn't just pun names, but it puns arbitrary (e.g., class) expressions. This can be very dangerous. That is, not only can "C" be both a class and an individual, but so can "C & D".
> 4) OWL Full, wrt general syntactic reflection, allows redefinition of the basic logical vocabulary (in specific ways). See Boris's paper for some consequences.
> 
> Hope this helps.
> 
> Cheers,
> Bijan.
> 

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Received on Wednesday, 24 November 2010 04:34:39 GMT

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