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Re: [SCL] same-syntax extensions to RDF

From: Elisa Kendall <ekendall@sandsoft.com>
Date: Sat, 01 Jan 2005 18:20:08 -0800
Message-ID: <41D75A58.6080906@sandsoft.com>
To: Harry Halpin <hhalpin@ibiblio.org>
CC: Pat Hayes <phayes@ihmc.us>, www-rdf-logic@w3.org

Harry,

I haven't seen a reply from Pat to you yet on some of these questions, so
I'll interject a couple of quick answers:

1.  The ISO Common Logic (CL) project is still very much alive -- the latest
draft of the overall standard can be found at:  http://www.jtc1sc32.org/, 
look for document number 1132.  Harry Delugach at the University of 
Alabama,
Huntsville is the editor for the WG2 SC32 working group. 

2.  The document you referenced is the latest XCL surface syntax draft
for SCL -- other relevant documents include the current SCL draft
specification, at: http://www.ihmc.us/users/phayes/CL/SCL2004.html, which
is somewhat more current than Harry's draft, and the latest draft 
mapping from
RDF/S and OWL to SCL, which is at:
http://www.ihmc.us/users/phayes/CL/SW2SCL.html.  The latter may be
very useful to you based on your interest in translating from OWL Full and
OWL DL to FOL.   This latest version of SCL does indeed support guarded
FOL, fyi.

I'm sure that Pat can answer some of your other questions regarding the
translation and language comparison much better than I can.  He has been
very helpful in our work on the OMG's Ontology Definition Metamodel
(ODM), which includes UML2/MOF2 metamodels for RDFS, OWL and
SCL among others, as well as a mapping from the RDFS and OWL
metamodels to the SCL metamodel that relies heavily on Pat's draft.   This
mapping is also only one-way, though we've been talking about how to
represent a lossy mapping going the other way using another emerging
OMG specification called MOF Query/View/Transformation.  MOF Q/V/T
is intended to provide a consistent mechanism for preserving information 
lost
in such transformations, but the specification is not yet sufficiently 
stable for
us to depend on for the ODM at this point. The next revision of the draft
ODM specification, including the one-way mapping from the RDFS and OWL
metamodels to SCL, will be available January 10th for public comment.  We
would appreciate any feedback, so please do take a look if you have the
bandwidth.  We will post the location to this exploder as well as to a
couple of others when it is available.

Best regards,

Elisa

Harry Halpin wrote:

>
>     Obviously since description logic is a fragment of first-order
> logic the conversion of description logic to first-order logic is much
> more solid than trying to embed first-order logic in a description logic
> (or RDF). So from a logic standpoint, is there a good XML notation for 
> first-order logic? Wasn't there a XML-CL "ISO Common Logic" proposal 
> batted about? This is the latest link I can find: 
> http://www.ihmc.us/users/phayes/CL/XCL_sentence_syntax.html.
>
> I noted Peter says OWL Full is equivalent in power to FOL
> (http://www.w3.org/2001/sw/meetings/tech-200303/all-pfps.htm), yet
> given the flow of discussion on this list it's a bit unclear if that's
> true (I can't tell from OWL Semantics), or if the OWL syntax is usable 
> for FOL at all.
>
> Anything newer or any alternatives? I'm somewhat shocked someone didn't
> formulate XML-encoded FOL before SemWeb standards where even made 
> given the prevalence of FOL in the world :)
>
> Another question is there a principled translation between FOL "in the 
> wild" to OWL DL regardless of syntax? This is of utmost importance to 
> myself, as a  computational linguistics kinda guy I work on tools 
> translating natural language to FOL (currently encoded in Discourse
> Representation Theory, a notational variant of FOL), and would like
> to make these tools available to the SemWeb world. Pat Hayes's work on 
> translating from "domestic" OWL -> SCL seems the most extensive, 
> although Bordiga's paper "On the Relative Expressiveness of 
> Description Logics and Predicate Logics." seems to be another good 
> source. I'd like to see at least a nice W3C note on FOL->OWL DL->FOL 
> including the formal semantics - I'd even be willing to help and it 
> would help my own work immensely! Now the translation to FOL->OWL DL 
> is *really* tricky, since most of FOL
> is not expressable in DL, so I've found it difficult to try to find
> a reasonable algorithm to, given a set of FOL statements, find a subset
> of that set that can be expressed in DL.
>
> I've got a quick and dirty XSLT script for translating FOL(DRS 
> notation) in the wild into OWL-DL using the small set of  rules but it 
> uses my own idiosyncratic XML FOL syntax, so it has no use to the 
> wider community, and
> very ad-hoc rules.
>
> This whole translation business would seem to have something to do 
> with the Guarded Fragment, but I haven't found any good theoretical 
> papers motivating the connections between DL (esp an OWL-flavored DL) 
> and the Guarded Fragment. Any work out there?
>
> Again, the motivation behind Sandro's comments is the *utterly real*: 
> People use FOL in the real world for all sorts of thing. People 
> associate the  Semantic Web mentally with logic, AI, "semantics", etc. 
> - and lots of people use FOL to encode "semantics". Thus, it is 
> actually only natural, if mistaken, to try to use whatever SemWeb 
> standards are out there to encode FOL, given the preconceptions most 
> people have about "semantics".
> Pat Hayes's "Catching the Dreamcatcher" paper makes the case well - I
> know this argument has happened on this list before, but maybe now 
> that DL
> is done with the SemWeb standards cadre can move onto FOL, esp. given
> the good work of CL?
>
> So, as someone interested in the SemWeb,  it *might* make the most 
> sense if the W3C and the SemWeb community got together, rallied up a 
> SemWeb standard for FOL ala RDF, and then showed how RDF/OWL DL was a 
> proper subset of FOL. Then people could use
> whatever standard they wanted and translate between the two. I'm pretty
> sure FOL can't fit in the wonderful world of "triples", but vice versa 
> should be true. Then people could use RDF/OWL when decidability/ 
> tractability/"all the nice triple features" were needed, and  FOL when 
> they use naturally use FOL or need it's expressive power. Ala Richard 
> Stallman, the users should be given the  freedom to choose, and part 
> of TimBL's vision has always been universal standards with differing 
> levels of power
> (although XML Schema FSA vs. RELAX NG tree automata debate obviously 
> missed this point as well!).
>
> Or this could just distract everyone from improving and using OWL/RDF, 
> so I see the case against working on FOL directly. But Sandro's 
> comments and my own problems demonstrate the need.
>
>                 Cheers,
>                     harry
>
>
>
>
>
>
>
>
> On Thu, 30 Dec 2004, Pat Hayes wrote:
>
>>> "Peter F. Patel-Schneider" <pfps@research.bell-labs.com> writes:
>>>
>>>>  My understanding of the problem was to write extra semantic 
>>>> conditions on
>>>>  RDF(S) interpretations, and thus generate an embedding/encoding of 
>>>> binary
>>>>  first-order logic into a semantic extension of RDF(S).  You can't 
>>>> extend
>>>>  the syntax at the same time, however, which means that you have to 
>>>> encode
>>>>  formulae as triples somehow, and these triples retain their RDF(S) 
>>>> meaning.
>>>>
>>>>  However, it doesn't seem to me that Sandro has the same 
>>>> understanding.
>>>
>>>
>>> No, that's exactly what I want, too.
>>>
>>> I would also like the whole exercise to be, in the end, simple enough
>>> that the community interested in rule languages and RDF can be
>>> comfortably with the results.
>>
>>
>> If you want simplicity, surely a 'natural' syntax for FOL (or OWL, 
>> for that matter) is simpler than any kind of RDF embedding? If you 
>> don't like recursion, stick to clausal form and use something like 
>> TPTP. FOL syntax is not hard. Its way simpler than, say, Javacode. 
>> What makes everything complicated is this insistence on having it be 
>> simultaneously syntactically embedded in RDF and at the same time a 
>> semantic extension of RDF.
>>
>>> I keep hearing about projects using RDF
>>> encodings of Horn or FOL, and they turn out to have either unclear or
>>> inconsistent semantics.  If we're going to move to a standard here, it
>>> would help to clear up whether it is possible to do this kind of
>>> encoding properly.
>>
>>
>> WHY? Why not get the standard done first, and then argue later about 
>> how to do an RDF encoding? Or, even more radically, why bother with 
>> an RDF encoding? What's wrong with XML? Seems to me that OWL has 
>> pushed this RDF idea about as far as it can be pushed; maybe a bit 
>> further, in fact.  None of the other standardization efforts seem to 
>> feel the need to be encoded into RDF. SPARQL has its own syntax, 
>> completely different in style from RDF (it doesnt even encode RDF in 
>> RDF) . The Rule proposals all use a rule-style syntax. The RDF-in- 
>> HTML embedding guys don't use RDF/XML syntax. Why do you have this 
>> RDF syntax bee in your bonnet? Dont get me wrong. Im all for RDF, and 
>> I like using it for all kinds of things that it can be naturally used 
>> for. But it does have its limitations.
>>
>>> I can't imagine, for instance, that the approach
>>> taken by SWRL 0.6 would ever be approved in a W3C Recommendation, for
>>> the reasons I outlined in the team comment [1].
>>
>>
>> The semantic web can make its own standards without the W3C 
>> imprimateur, if the W3C insists on being insane. But I think you are 
>> wrong, in fact, since the W3C's own WGs are going to be producing 
>> draft recs which don't satisfy these requirements.
>>
>>> If Peter can convince me that it's not possible to write the desired
>>> semantic condition, I can help him convince others that a different
>>> path needs to be taken for rule languages.  If I can convince Peter it
>>> *is* possible
>>
>>
>> You won't be able to convince him that it is, for the very good 
>> reason that it isn't.
>>
>> There is a very general result due to Montague. Here's one way to 
>> state it. Suppose you have a formal system which is capable of 
>> expressing very simple arithmetic (technically, Robinson arithmetic). 
>> FOL would do, for example, but weaker logics would also do. Pretty 
>> much any language in which you can express or use recursion will also 
>> do the job. Now assume that you have some way to encode expressions 
>> of this language into terms (names) in the language itself, ie a 
>> downward reflection principle. Exactly how you do this doesn't 
>> matter: just as long as every expression e has an encoding [e]. 
>> Reification would do this job for RDF, for example, or using quoted 
>> strings, or using XML literals enclosing a chunk of RDF/XML.  Now add 
>> a predicate P to this language which satisfies the condition:
>>
>>  for any e,   P([e]) implies e
>>
>> (so that you can get back from the encoding to 'use' the logic, as 
>> you described in an earlier email) and suppose that you can always, 
>> somehow, perform the 'encoding' inference
>>
>>  from e, infer P([e])
>>
>> (that second one doesnt have to be an axiom; it only requires that 
>> you can somehow get from e to  P([e]) by some inference path or 
>> other. )  Given this, then the system is self-contradictory; you can 
>> derive a paradox from it.  Put another way, any language (good enough 
>> to express basic arithmetic) can't contain an useable meta-theory of 
>> its own notion of truth, or of provability, or even of self-knowledge.
>>
>> One way to get the second rule to hold, by the way, is to have the 
>> axioms
>>
>> P([e]) and P([e implies f]) implies P([f])
>>
>> ie if you can 'mirror' the modus ponens rule in the metalanguage, 
>> then you are dead. This is the form that Montague and Kaplan 
>> originally identified. It was originally thought of as being to do 
>> with self-knowledge, and was called the paradox of the knower.
>>
>> This is a very basic result, and it is kind of robust. People have 
>> tried all ways to wriggle past it, but there aren't any. The 
>> derivation of it is kind of elementary (doesnt use advanced set 
>> theory, etc.) . There really arent going to be any magic bullets 
>> which will slay this dragon: looking for them is like trying to 
>> invent a perpetual-motion machine.
>>
>> You can get past the barrier by weakening the notion of reflection, 
>> which breaks the second Montague condition. This is how the KIF 
>> metatheory wriggled past the paradoxes, by putting a syntactic tweak 
>> into the truth predicate so that it doesnt apply to some expressions. 
>> But this is a tricky operation to get right. It works in KIF partly 
>> because KIF does reification very transparently, using direct 
>> quotation, so the syntax of the coded expression can be accessed 
>> straightforwardly when stating the necessary constraint. This would 
>> break if, for example, the language used an encoding mechanism that 
>> allowed identity statements between encoded names (this is Peter's 
>> observation). So if you were to do this for RDF somehow, the trick 
>> might fail when you moved to OWL (because of owl:sameAs).
>>
>>> (and we figure out how onerous it is), then a standard
>>> can use it (or not, but because the difficulty has been actually
>>> weighed).
>>>
>>> Unfortunately, I can't just hand Peter the desired semantic
>>> conditions.  I don't really know how to write them in the formalism of
>>> RDF Semantics [2].  My understanding is that Peter doesn't either and
>>> suspects it's not possible to write them.
>>
>>
>> The problem has got nothing to do with the form in which they are 
>> written.
>>
>>> Meanwhile, it is "obvious" how to write them informally and with
>>> subtle errors.
>>
>>
>> It SEEMS obvious, but appearances are misleading. It seemed obvious 
>> to Frege, until Russell pointed out the problem. Even Russell was 
>> kind of embarrassed by how almost childish the paradox seemed - 
>> nobody took the liar paradox seriously at the time - and was 
>> convinced that there would be a neat, simple-to-understand way to 
>> bypass it. The result of that particular naive enthusiasm was 
>> ramified set theory (abandoned as too complicated to use around 1925) 
>> and Principia Mathematica.  But we know now, almost a century later, 
>> that this apparently simplicity really is an illusion. Don't be 
>> misled by how obvious it seems to be.
>>
>> It really would be a pity if the entire W3C SW standardization effort 
>> were to be warped by this false sense of how "obvious" all this stuff 
>> is. This is like saying that Newtonian physics is kind of obvious, so 
>> transistors shouldn't be based on quantum theory. We KNOW that the 
>> problems of consistency in self-referential languages are a black 
>> hole. We KNOW that none of the techniques that some very clever 
>> people thought might be able to handle it - reification, 
>> substitutional quantification, 3-valued logics, constructive logics, 
>> etc. - will get you past the basic, foundational, snag. We know this 
>> is something very fundamental in the foundations of formal semantics. 
>> So why doesn't the W3C just give up on this insane crusade to reduce 
>> everything to RDF? That idea was a mistake. Get used to it. It is not 
>> usually a good idea to work hard to to try to base a standard on a 
>> howler, particularly when the territory has been so thoroughly 
>> investigated.
>>
>> And particularly when there is in fact, it seems to me, no real 
>> problem here to be solved. It is trivial to embed RDF into full FOL, 
>> corresponding to the fact that RDF is semantically a special case of 
>> FOL. See the RDF-> SCL embedding described in
>> http://www.ihmc.us/users/phayes/SW2SCL.html for example. which is 
>> about as obvious as it can get.  Why wouldn't that be good enough? It 
>> has many advantages: for example, it can allow future extensions to 
>> the language very neatly, it means you can use Xpath to access 
>> sub-expressions, you can use DTDs to check basic syntax, and so on.  
>> Why do you want to be able to push all SWeb languages through an RDF 
>> pipeline? Its not as though it is hard to transmit, parse and use 
>> simple recursive languages, or that there are any real obstacles to 
>> doing it. People have been doing it for years. HTML with embedded 
>> Javascript does it.  And if you start doing things like embedding FOL 
>> expressions in RDF literals, then you have to violate the RDF 
>> conventions to get at the logic anyway; the RDF has just become a 
>> kind of outer crust that is getting in the damn way. Since you will 
>> have to have engines that go 'outside' the RDF conventions in order 
>> to extract the encoded FOL, why not just send the strings to them 
>> directly? You could put the FOL in a file, give it a URI and use RDF 
>> to say that it is a file full of FOL, using an RDF ontology of SWeb 
>> languages, if you really want to have everything triggered by RDF. I 
>> don't think there would be much operational difference between this 
>> and having the FOL encoded syntactically inside the RDF, in fact - as 
>> Peter points out, you still have to parse the FOL expressions 
>> somehow, however they are encoded - but it would enable us to put 
>> this silly issue to rest.
>>
>> An analogy.  Suppose that someone were to say that a construction 
>> like <img 
>> src="http://i.a.cnn.net/cnn/.element/img/1.1/ceiling/gradient.line.gif" 
>> /> in HTML was inherently faulty because the actual image was not 
>> 'inside' the HTML document, and so the HTML does not properly reflect 
>> the part/whole structure of the final viewed document, in which the 
>> image really does appear inside the document page; and this is a 
>> violation of a Basic Theory of Web Documents.  On this view.,  HTML 
>> needs to be re-designed so that all parts of a web page are 
>> incorporated into the same file as the actual HTML text, not as 
>> external resources referred to by URIs, but actually part of the same 
>> syntax, parseable using HTML (or XHTML) conventions and also be an 
>> HTML semantic extension in the sense that the way that the embedded 
>> image-entity was processed should be the same standard method of 
>> processing as HTML uses for everything else, including text.  There 
>> might be various schools of thought on how to do this. They would 
>> both encode the image bytes as text in some way, lets suppose (which 
>> was decided by a WG which met for 4 years and produced a huge report 
>> explaining the technique of writing the image file as a bitstring 
>> which is split into 16-bit chunks, interpreted as UTF-16 Unicode and 
>> then mapped back into ASCII)  but one school thinks that the text 
>> itself should be simply thrown away, and the image displayed using 
>> image-display conventions; whereas the members of the W3C Team insist 
>> that this amounts to a non-standard semantic treatment, and suggest 
>> instead that images should always be represented using 'Unicode-art' 
>> where each pixel is a Unicode glyph, so as to preserve the standard 
>> HTML meaning of all embedded text uniformly: images in HTML are then, 
>> strictly speaking, just text, but rendered in a very small font.  You 
>> can imagine an entire novella here, all horribly plausible: there 
>> might be special proposals by consortia of commercial foundries, 
>> proposing standardized  minifonts suitable for rendering CMYK images.
>>
>> Now, this little fantasy seems to me almost exactly analogous to the 
>> debates over using RDF syntax for everything. The insistence on 
>> preserving the RDF standard semantics while at the same time 
>> embedding everything into its restrictive syntax is going to produce 
>> exactly the same kind of damn silly time-wasting discussions, and run 
>> the entire process into the same kind of pointless rathole, that 
>> 'true embedded HTML' would have taken HTML.; and for much the same 
>> reasons.  The real issue is not whether or not it can possibly be 
>> done, but whether it is a good idea to even try. Clearly if it can be 
>> done, it will only be by virtue of an enormous amount of work, and 
>> the result will be ugly, hard to use and fragile; and we already know 
>> much better ways to do this, ways that are already in use, known to 
>> be robust and are widely understood.
>>
>> In case you are thinking about CWM as an proof-of-concept, it isn't. 
>> The way that CWM encodes FOL is in direct and stark violation of the 
>> W3C's own recommendations. If the idea is to move forward along those 
>> lines, then please say so now so that we can drop this entire topic, 
>> resign from the W3C WGs and find more productive ways to spend our time.
>>
>>>  Something like "put the FOL expressions in a string
>>> literal and assert it"
>>
>>
>> Or in a reified triple and assert that, or coded as a Goedel number 
>> and assert that. It makes no difference to the Montague result. The 
>> form of the encoding is irrelevant: you could use a binary encoding 
>> of an XML character string, rewritten in musical notation and then 
>> transcribed back through base-7 arithmetic into an XSD integer. You 
>> might as well try to program an uncomputable function by picking a 
>> different programming language. The only way to avoid paradox is to 
>> weaken the connection between language and metalanguage, eg by partly 
>> breaking the reflection inferences. But then you have to be able to 
>> prove that there isn't some hidden way of sneaking past your 
>> restriction.
>>
>>> , as I explored in my previous e-mail [3].
>>>
>>> So I've been trying to write them using a formalism in which I have a
>>> good sense of how to do it and with which I think I can detect most if
>>> not all subtle errors.  It may also show the way in which to do it in
>>> the desired formalism.
>>>
>>> I'll try to return to the substance of this thread shortly.  Peter's
>>> raised to questions I need to explore.
>>
>>
>> There are lots more waiting for you when you get past those.
>>
>> Pat
>>
>>>
>>>        -- sandro
>>>
>>> [1] http://www.w3.org/Submission/2004/03/Comment (in the "RDF" section)
>>> [2] http://www.w3.org/TR/rdf-mt/
>>> [3] http://lists.w3.org/Archives/Public/www-rdf-logic/2004Dec/0022.html
>>
>>
>>
>>
>
>
>     Harry Halpin
>     Informatics, University of Edinburgh
>         http://www.ibiblio.org/hhalpin
>
Received on Sunday, 2 January 2005 02:24:30 UTC

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