- From: Hans Teijgeler <hans.teijgeler@quicknet.nl>
- Date: Wed, 5 Sep 2018 10:54:00 +0200
- To: Simon.Cox@csiro.au
- Cc: SW-forum Web <semantic-web@w3.org>, public-philoweb@w3.org, Pat Hayes <phayes@ihmc.us>, Henry Story <henry.story@bblfish.net>
- Message-ID: <8f4ded14-e542-4b3a-459c-c7d8d8f8bb45@quicknet.nl>
Hi Simon,
In ISO 15926 we don't need any reification because we use N-ary
relations as described by Natasha Noy and Alan Rector, with
contributions of Pat Hayes and Chris Welty, in their 2006 Working Group
Note "Defining N-ary Relations on the Semantic Web
<https://www.w3.org/TR/swbp-n-aryRelations/>".
We make a distinction between Relation and Relationship. Our upper
ontology knows many Relationships and ClassOfRelationships that are
treated as full-fledged classes.
Relationships have two relations, MultidimensionalObjects have N relations.
For instance: MyCar <<< AssemblyOfIndividual >>> MyEngine where
AssemblyOfIndividual is such a Relationship, that can be typed with an
instance of ClassOfAssemblyOfIndividual (e.g. "Any Car has one Engine")
if necessary, so including cardinalities for validation purposes.
or, a bit more complicated, to model the calculation of the head of a
centrifugal pump <http://www.pumpfundamentals.com/what%20is%20head.htm>:
For the full story and code see the topic "Equations and Variables
<http://15926.org/topics/equations-and-variables/index.htm>" and, if you
have the stamina, "Process Design
<http://15926.org/topics/process-design/index.htm>".
I'll get off my soap box :-)
Regards, Hans
------------------------------------------------------------------------
On 5-9-2018 02:35, Krzysztof Janowicz wrote:
> On 09/04/2018 05:27 PM, Simon.Cox@csiro.au wrote:
>>
>> Øthe awkward reification structure survived (sadly, in retrospect).
>>
>> Never replaced by anything better though, so any application that
>> needs to make statements about statements is driven back to it.
>>
>> In the last couple of weeks in my case …
>>
>
> You can also hash a triple and use the resulting URI as the subject of
> the triple about this hashed triple. Of course, this comes with some
> limitations wrt the SPARQL queries you can run.
>
>> *From:*Dan Brickley [mailto:danbri@danbri.org]
>> *Sent:* Tuesday, 4 September, 2018 18:32
>> *To:* Pat Hayes <phayes@ihmc.us>
>> *Cc:* Story Henry <henry.story@bblfish.net>; Semantic Web
>> <semantic-web@w3.org>; Benjamin Braatz <bb@bbraatz.eu>;
>> public-philoweb@w3.org
>> *Subject:* Re: modal logic, rdf and category theory
>>
>> On Tue, 4 Sep 2018, 08:51 Pat Hayes, <phayes@ihmc.us
>> <mailto:phayes@ihmc.us>> wrote:
>>
>> On 9/3/18 3:27 PM, Henry Story wrote:
>>
>>
>>
>> The paper you cite below,
>>
>> 2010 Context Representation on the Semantic Web
>> Bao, Jie, Tao, Jiao, McGuinness, Deborah L. and Smart, Paul (2010)
>> https://eprints.soton.ac.uk/270829/
>>
>> was the earlier work I was thinking of here.
>> >
>> > I started out very early being made aware of Guha's Phd thesis
>> > "Contexts: A Formalization and Some Applications"
>> > http://www-formal.stanford.edu/guha/
>> > But I read it quickly 15 years ago, and should perhaps study it
>> more carefully now. As I
>> > understand he was one of the people at the origin of RDF.
>>
>> True, but...
>>
>> So it looks to me like contexts
>> > are there from the beginning.
>>
>> ...not so. That is, nothing in the genesis of RDF or the first
>> Working Group efforts (resulting in the 2004 standard) considered
>> contexts or tried to get any context mechanism into RDF. RDF
>> might have been more useful if we had, in retrospect.
>>
>> The first first RDF group, fwiw, ran 1997-99 and gave us a Model and
>> Syntax specification with a notion of reification supported both
>> within the abstract graph but also syntactically. It had a ton of
>> problems, hence the rdfcore WG charter which followed. We constrained
>> it to be a cleanup rather than total reinvention, so the awkward
>> reification structure survived (sadly, in retrospect).
>>
>> What pressure there was to 'expand' RDF was in the direction of
>> making it as expressive as conventional FOL rather than a context
>> logic. Guha and I wrote the L-base proposal with this in mind,
>> for example. TimBL's N3 is in the same spirit, with explicit
>> quantifiers and scope markers.
>>
>> >
>> > In fact I always supposed that the semantic web was going in
>> that direction, and
>> > this intuition was confirmed when I discovered Tim
>> Berners-Lee's and Dan Connolly's
>> > N3 language very early one, which already at the time allowed
>> one to be more elegant
>> > about context.
>>
>> ? N3 has no context machinery in it at all. It is basically
>> a(nother!) syntax for FOL.
>>
>> >
>> > Indeed in April 2006, I wrote a blog post showing how one could
>> deal with temporally
>> > constrained graphs by using an N3 rule to rewrite them.
>> > "Keeping track of Context in Life and on the Web"
>> >
>> https://web.archive.org/web/20060626031531/http://blogs.sun.com:80/roller/page/bblfish?entry=it_s_all_about_context
>> <https://web.archive.org/web/20060626031531/http:/blogs.sun.com:80/roller/page/bblfish?entry=it_s_all_about_context>
>> >
>> > I actually show some N3 rules being applied by CWM in that blog
>> post to a context
>> > in order to transform a graph with a temporal relation that
>> depends on the context
>> > into one that does not depend on that temporal context.
>>
>> You keep talking about 'context' here, but that does not make any
>> of this into anything like a context Logic. N3 has no LOGICAL
>> MACHINERY for talking about contexts (contrast McCarthy's context
>> logic, Guha's thesis and its realization in CycL, or the ICL
>> logic developed for use in the IKRIS project.) Just using the
>> C-word when talking about collections of ordinary logical
>> sentences muddles the issue. To reason with and about contexts
>> requires /some/ kind of actual context logic, where contexts are
>> real entities which are described, or at least referred to, in
>> the logic itself. Without that, the word 'context' really has no
>> clear meaning at all. For more on this general topic, see
>>
>> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98.4812&rep=rep1&type=pdf
>>
>> and
>>
>> https://pdfs.semanticscholar.org/4899/493c11d2e803bb86ef6b849fb7b3185be1e3.pdf
>>
>> >
>> > Looking for documentation on N3 I just discovered
>> > that Tim Berners, Lee Dan Connolly, Lalana Kagal, Yosi Scharf
>> and Jim Hendler
>> > wrote a paper that same year
>> > "N3Logic: A Logical Framework For the World Wide Web"
>> > http://dig.csail.mit.edu/2006/Papers/TPLP/n3logic-tplp.pdf
>> >
>> > SPARQL seems to have formalized (in what to me seems often a
>> much less elegant way)
>> > the pattern matching mechanism of N3. It is also known that
>> SPARQL can be used
>> > as a rule language in a way very similar to the log:implies of
>> N3. The nice thing
>> > about N3 is that one always sticks to the triple structure of
>> rdf, which makes it
>> > very elegant.
>> >
>> > There is an interesting question if one can ever escape
>> contexts at all. It certainly
>> > looks like it will be very unlikely that people will work out
>> the right abstractions
>> > that take all contexts into account.
>> >
>> > Thanks to Google Scholar I followed up easily on the article by
>> Guha you mentioned
>> > and found some interesting papers.
>> >
>> > 2010 Context Representation on the Semantic Web
>> > Bao, Jie, Tao, Jiao, McGuinness, Deborah L. and Smart, Paul (2010)
>> > https://eprints.soton.ac.uk/270829/
>> >
>> > Is very interesting not least because it shows how one could
>> build a more
>> > sophisticated notion of contexts on top of N3 or Quad Stores.
>> Most interesting
>> > of all to this thread is that it argues that one could help
>> specify logical
>> > levels using Institution Theory that I mentioned earlier. (And
>> it does so quickly
>> > while explaining in plain english what some of the formulas mean)
>> >
>> >
>> >>> If the semantics of current RDF has not got this part quite
>> right it seems to be there in the syntax from the beginning,
>> since a RDF/XML document can contain another RDF/XML document
>> >> ?In what sense of "contain"?
>> >
>> > Well a predicate can be related to an RDF Literal which of
>> course needs to be interpreted.
>>
>> But RDF literals are typed, and the type - in all cases but one,
>> a datatype - specifies the interpretation.
>>
>> <Later> OK, I see where you might be going with this. If we say
>> that an RDF/XML literal denotes an RDF graph, then a triple with
>> such a literal as object could encode an assertion about that
>> graph. Yes, that could be done. But it hasn't been done, I should
>> perhaps emphasize.</Later>
>>
>> >
>> > <?xml version="1.0" encoding="utf-8" ?>
>> > <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#
>> <http://www.w3.org/1999/02/22-rdf-syntax-ns>"
>> > xmlns:ns0="http://example.com/">
>> > <rdf:Description rdf:about="http://example.com/LauraLane#i">
>> > <ns0:says rdf:parseType="Literal">
>> > <rdf:RDF
>> xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#
>> <http://www.w3.org/1999/02/22-rdf-syntax-ns>"
>> > xmlns:ns0="http://example.com/">
>> > <rdf:Description
>> rdf:about="http://example.com/LauraLane#i">
>> > <ns0:disklikes
>> rdf:resource="http://example.com/ClarkKent#geek"/>
>> > </rdf:Description>
>> > </rdf:RDF>
>> > </ns0:says>
>> > </rdf:Description>
>> > </rdf:RDF>
>> >
>> >
>> >
>> >>
>> >>> , and presumably the point is not to automatically merge the
>> embedded document with the one it is contained in. So what is the
>> meaning of the embedded graph? Well it has to be some
>> interpretation that satisfies the graph. But there could be many
>> full interpretations in part because
>> >>> one can only ever work out Finite interpretations (because
>> the semantic web is incomplete) and these are compatible with
>> very many full interpretations.
>> >>
>> >> I confess to not following your thinking here. AFAIK, the RDF
>> WG discussions never considered the idea of one RDF document
>> "containing" another in any semantically meaningful way.
>> >
>> > It allows a document to contain an XML Literal. If that XML
>> Literal is an RDF/XML literal
>> > it follows that it can be interpreted just the same way as any
>> other document. But if one is
>> > to map that intelligently into a quad store one would map that
>> as a graph linked to from the first one,
>> > such as
>> >
>> > :LauraLane :says { :LauraLane :dislikes :ClarkKent } .
>>
>> But this is nowhere mandated by /any/ RDF standard, and I suspect
>> it never will be.
>>
>> >
>> > At the time there were no quad stores to do this type of
>> transformation, but it would not
>> > be wrong.
>>
>> Well, 'wrong' is a strong word. But it would be unjustified, and
>> not used in any extant RDF tool, and would not transfer to any
>> other RDF surface syntax.
>>
>> And well it would not take a lot to create a literal that had
>> that interpretation
>> > for RDF/XML.
>>
>> There is an issue, though. The same content - same RDF graph -
>> could be represented in, say, Turtle or N-triples or even
>> JSON-LD. But the corresponding literals would look entirely
>> different. They would all have to have different datatypes. Which
>> is possible, but kind of clunky.
>>
>> I suggest that this line of thinking is going to get lost in
>> syntactic weeds. You would do better to just start with quads and
>> try to make them into what you are looking for without going via
>> embedded literals. Or even adopting some version of the named
>> graph convention. Just my 2c.
>>
>>
>> >
>> >>> But also because documents can be published to mislead ("fake
>> news") software into believing the universe is other than it is.
>> >>
>> >> Well, of course. Publication on the Web has never been a
>> guarantee of truth or accuracy, and RDF doesn't change that fact
>> of social life.
>> >>
>> >>> I have a short blog post "Phishing in Context - Epistemology
>> of the Screen" that goes into this
>> >>> where I make clear the importance of context, and how some
>> good salesman arbitrarily named Donald
>> >>> can try to use confusions of context as bait
>> >>> https://medium.com/cybersoton/phishing-in-context-9c84ca451314
>> >>> Another simple logic of Contexts is the well known work by
>> Mike Burrows (who wrote the AltaVista search engine), Martin
>> Abadi, Butler Lampson, Gordon Plotkin from 1993 "A calculus for
>> access control in distributed systems"
>> https://dl.acm.org/citation.cfm?id=155225
>> >>> Quad stores (RDF Datasets) can clearly be used as a
>> foundation to build such things on.
>> >>
>> >> True. However, quad stores have no universally accepted
>> semantics, so it will not be easy to standardize any of this.
>> >
>> > It's actually quite easy.
>>
>> You misunderstand me. It may be fairly easy to invent a set of
>> conventions for quads which do what you want them to do. But quad
>> stores are an established, even by now an old, technology, and
>> they are out there being used in many different ways. Large
>> amounts of developer time and money have been committed to these
>> uses. To get a STANDARD which assigns a SINGLE semantics to quad
>> stores is now effectively impossible. (It was already impossible
>> in 2012, when the RDF 1.1 WG was chartered.) You will not get the
>> W3C to charter it; and even if someone did that, and it became a
>> W3C Recommendation, nobody would pay that any real attention. It
>> is a social problem, not a technical one; and far from being
>> easy, it is effectively impossible.
>>
>> The semantics of a graph is the set of interpretations for which
>> it is
>> > true. There are a few variables there:
>> >
>> > 1) the set IR of resources can be different. For example in our
>> world the set may contain
>> > books about Superman, and Laura Lane but no agents with those
>> properties.
>> > Whereas in the fictional spaces of those books those Characters
>> do exist as resources
>> > with special properties. But it may also contain resources
>> about Hillary Clinton and
>> > weird pizzarias with basements that in our world don't exist -
>> but that do in the imagination
>> > of quite a few americans, that have lead some to act on those
>> beliefs, and many to vote.
>>
>> Indeed. How, or indeed whether, to deal with imaginary entities
>> in formal ontologies is a much debated topic. My own view - in
>> sharp contrast to the more established view often identified as
>> Quinean - is that the logic must treat all entities similarly, so
>> that to be in the universe of discourse means only that something
>> has been /referred to by someone/, and that this is recognized as
>> not /necessarily/ implying real existence. So we can all talk
>> about what other people are talking about, and even perhaps
>> debate with them, without thereby committing ourselves to agree
>> that what they are talking about is in fact real. (The Horatio
>> Principle: there are more things in heaven and earth than are
>> dreamt of in /your/ ontology.) But I admit this is a
>> controversial position. And I expect that I agree with you that
>> having an explicit treatment of contexts would be a good first
>> step towards a more sophisticated approach to this whole issue.
>>
>> >
>> > 2) the conventional interpretations accepted for the URIs used
>> as subject and object.
>> > A URI could mean anything before it is coined. For example
>> the URL for owl:sameAs could have
>> > been any number of other URIs.
>> >
>> > 3) the various interpretations due to the possibility of blank
>> nodes being assigned to different
>> > resources in each of those universes.
>> >
>> > The set of those interpretations is the meaning of the graph.
>> If the Interpretation considered to
>> > be the actual one is in there then the graph is true.
>> >
>> > So we can understand what
>> >
>> > :HillaryClinton :in :Paris;
>> > :hears { :HillaryClinton :in :Boston }
>> >
>> > And even though the graph quoted contradicts the external one,
>> we know what it would
>> > mean for it to be true, but we (may) also know that it is not.
>> >
>> >>
>> >>> If you think as agents that write RDF graphs as processes,
>> then you can see how this is coalgebraic.
>> >>> Different such processes are writing from partial information
>> situations in different contexts, and
>> >>> with potentially antagonistic aims. Context matters.
>> >>
>> >> I think that you are here using "context" informally, whereas
>> I was using it rather more formally, referring to context logics
>> such as CycL.
>> >
>> > yes, I may have been thinking all one needs is graphs for
>> contexts. It certainly
>> > seems to be an essential ingredient, as the article "Context
>> Representation on the Semantic Web"
>> > argues. And I now see there is a whole literature on more
>> sophisticated notions of context.
>>
>> I think the notion is similar, but the issue is that if you want
>> to have engines drawing conclusions about contexts, you need some
>> actual context /machinery/, and probably some logical context
>> machinery.
>>
>> >
>> >>
>> >>>> Right at the end of the RDF 1.1 semantics document there is
>> indeed a tiny mention of the possibility of some future extension
>> of RDF using a modal interpretation of RDF datasets (basically
>> quad stores). But any such interpretation would require a major
>> change to the semantics (analogous to the extension of Tarskian
>> model theory to the Kripke semantics for modal logics) and some
>> kind of enrichment of the RDF syntax to provide some way to
>> indicate the syntactic scope of any modal operator. RDF graph
>> syntax has no scope marking, a fact that gave the RDF and OWL WGs
>> many technical challenges.
>> >>>> (For further discussion of this point and what could be done
>> about it, see
>> >>>>
>> https://www.slideshare.net/PatHayes/blogic-iswc-2009-invited-talk
>> >>>> starting from slide 15.)
>> >>> Very interesting set of slides. Here are some thoughts from
>> my research in CT.
>> >>> • Slide 10 on names
>> >>> The difference here is between names as syntactic,
>> denotational semantic and operations semantic
>> >>> terms.
>> >>
>> >> If I understand you here (I might well not...) then I
>> disagree. The issue I was trying to describe in that slide is the
>> fact that referring names on the Web are what one might call
>> socially non-arbitrary. They are more like names in natural
>> language than logical identifiers, in this regard. But this has
>> nothing to do with the nature of the entities they refer to.
>> >
>> > yes, David Lewis in "Convention" explains how languages gain
>> their meanings using co-operative Game Theory. It is a very nice
>> read. In the case of the web the game is partly determined by the
>> fact that
>> > one can dereference the URI. That is the fastest, easiest
>> method to find out something about it.
>>
>> Careful. About what, exactly? What an IRI /denotes/ might be
>> completely different from what you get when you dereference it.
>> Google "HttpRange-14" for an amazing amount of debate and
>> discussion about this. Many IRIs - I think most IRIs used in RDF
>> - do not denote time-dependent things.
>>
>> And
>> > practical considerations are not unimportant in helping people
>> choose between equivalent conventions.
>> >
>> >> The syntactic view of names that algebraic views of logic have
>> is the one espoused by the RDF specs. These are indeed
>> interchangeable.
>> >
>> > Well that is also true. At the beginning of the Web any URI can
>> mean anything. Then the process of
>> > convention starts and determines the actual language of the web.
>> >
>> >>
>> >> But they aren't, because the same IRIs get used in non-logical
>> contexts as well, and while a renaming might preserve the purely
>> logical meaning it will not preserve the meaningful relationships
>> to these other uses. But in any case, logical renaming requires
>> ALL uses of the name to be replaced in one step, and the Web -
>> even the purely formal part of it encoded in RDF - is too large
>> and scattered for this to ever be possible.
>> >
>> > exactly. That is the process that stabilizes the language -
>> David Lewis uses the word Metastable 3 times in his book. But
>> that is true of all languages, not just the web.
>>
>> Indeed. My point in that slide is that the IRIs used in RDF are
>> now words in a human language in Lewis' sense, but the formal
>> semantics does not face up to the reality of this.
>> >
>> >>
>> >>> But the Semantic web is an evolutionary *process* that
>> starts at a certain stage and develops,
>> >>> where different players have only a partial view on its
>> evolution. Coalgebras represent the mathematics of states (that
>> evolve) and observation as the subtitle of Bart Jacobs' recent
>> book on Coalgebras points out clearly
>> >>>
>> https://www.cambridge.org/core/books/introduction-to-coalgebra/0D508876D20D95E17871320EADC185C6
>> >>> The Web itself is coalgebraic, since resources that URIs
>> refer to are things that change *State*.
>> >>
>> >> Not all of them. And indeed, using a URI to /refer to/ (as
>> opposed to /identify/, using RESTful HTTP) something with a
>> changing state is in many ways non-"cool", in TimBL's phrase.
>> >
>> > URLs (without the hash and ignoring redirects) refer to
>> information resources that have
>> > state and that can change over time. Their referent are states
>> of objects that can be observed
>> > through representations that can change over time.
>>
>> Wrong. Or at any rate, wrong in many cases. This is not true of
>> pretty much any IRI of the form dbpedia.org/resource/.
>> <http://dbpedia.org/resource/>.. for
>> example. It is also not true for any of the XML Schema datatype
>> IRIs. Nor for https://www.ihmc.us/users/phayes/PatHayesAbout.html
>> <https://www.ihmc.us/users/phayes/PatHayesAbout.html>
>>
>> To repeat: what an IRI denotes, and what you get when you
>> dereference it, are two very different things. They might be the
>> same in some cases, but in most cases they are not.
>>
>> That is what I mean by these being
>> > coalgebraic. As such the referent of those names don't change:
>> they refer to the stream
>> > - the changing stream.
>> >
>> > What Tim means by cool URIs don't change is not that the
>> representation does not change - but
>> > that they don't change in ways that change the topic so that
>> people referring to them could
>> > argue that you have changed the meaning of the documents
>> linking to your content. Ie: the identity
>> > criterion for what constitutes representations that are the
>> same as the previous ones is a socially
>> > constructed notion of identity. Seriously changing the meaning
>> is to let down those linking to you.
>> > And it could have legal consequences.
>>
>> Or, in a nutshell, the 'S' in 'REST" means 'state'. Right?
>>
>> >
>> > I have an illustration of how this works here
>> >
>> https://math.stackexchange.com/questions/2896172/how-should-one-model-rdf-semantics-in-terms-of-category-theory
>> >
>> >>
>> >>> These are things that return representations (algebraically
>> interpretable objects).
>> >>> Hence the fight between many logicians and Linked Data
>> folks may just be a case of a categorical
>> >>> misapprehension between people working in a dual category.
>> >>
>> >> Perhaps, but I think it goes deeper than that.
>> >>> Anyway we agree here about names and the importance of
>> reference. And I think the
>> >>> categorical duality here can help give us a mathematical
>> representation of the web that shows how
>> >>> these two sides can work together.
>> >>> • Slide 18 on blank nodes
>> >>> Interestingly here you note that the problem is with a
>> set theoretic definition of blank nodes
>> >>> that are global. Benjamin Braatz in his 2009 thesis
>> >>> "Formal Modelling and Application of Graph Transformations in
>> the Resource Description Framework"
>> >>>
>> https://www.depositonce.tu-berlin.de/bitstream/11303/2617/2/Dokument_29.pdf
>> >>> of which the first half is very readable for someone with
>> knowledge of RDF.
>> >>> gave a Category Theoretic model of RDF where each graph comes
>> with its own blank node set, and
>> >>> the only way to identify such nodes is by morphisms. This is
>> actually an advantage of a category
>> >>> theoretic way of looking things that tends to put less
>> emphasis on identity and a lot more on morphisms.
>> >>> Still it looks like RDF1.1 allows blank nodes across contexts
>> >>
>> >> It doesn't mention contexts but it does allow for graphs to
>> share bnodes, in particular, graphs in a single dataset. So yes,
>> in effect.
>> >>
>> >>
>> >>> (as I gather from 5.1.1),
>> >>> which would be a way to make statements de Re about someone's
>> beliefs, eg:
>> >>> Laura Lane believes of Superman that he cannot fly.
>> >>> _:superman = :SuperMan .
>> >>> :LL believes { _:superman a :NonFlyingPerson;
>> >>> foaf:name "Clark Kent" } .
>> >>> I wonder how much the blank node sharing would require
>> changes to Benjamin Braatz'
>> >>> thesis.
>> >>>>
>> >>>>>
>> >>>>> It is to me very clear that RDF has a modal aspect to it,
>> which comes out very clearly
>> >>>>> with Quad stores.
>> >>>>
>> >>>> That is totally unclear to me. Quad stores can be, and have
>> been, used to represent all kinds of 'extra' content, including
>> graphs with time-stamping or location-stamping or representing
>> states of something or linking information about a person or
>> topic to that person or topic. None of this is modal.
>> >>> Well all of these are thought of as modal logics.
>> >>
>> >> No no no! Please don't get this muddled. A logic with times in
>> it is NOT a modal tense logic, and a logic which mentions belief
>> contexts explicitly is NOT a modal belief logic. The modalities
>> occur, and are required, when the logic does NOT mention the
>> 'parameters' of truth explicitly. So, for example, modal TENSE
>> logic does not have expressions denoting times, but instead has
>> modal operators for future and past tenses. There is an unspoken
>> convention that any plain assertion made without the modalites is
>> supposed to be true 'now'. As soon as you put times into the mix,
>> the modalities become redundant and can be expalined away as
>> simple quantified assertions, so that
>> >>
>> >> PAST(Full-Professor(PatHayes))
>> >>
>> >> would turn into something like
>> >>
>> >> (exists (T)(Earlier(T, NOW) & Full-Professor(PatHayes, T) )
>> >>
>> >> where we mention the 'now' explicitly. And this is no longer a
>> modal logic: it's just conventional logic with an ontology of
>> ties embedded into it. The same kind of thing happens with all
>> the other modalities (though de dicto stuff in quantified belief
>> logics does get a bit hairy.) In fact, context logic can be seen
>> as a general-purpose device for /eliminating/ modalities and
>> reducing all modal constructions to a non-modal framework. For
>> lots more on this, see
>> >> https://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html
>> >> especially ...#ContextsModalities.
>> >
>> > I will need to look at this more closely.
>> >
>> > But I think there is an indexical element with any
>> statement/graph in RDF, namely it's truth depends
>> > on what the actual world is. This is of course impossible to
>> completely describe, and
>> > furthermore there are important disagreements as to its
>> description. So though I think we
>> > should agree that the actual world is objectively decidable, it
>> won't help to ignore the indexical
>> > role it plays. And this does not alter the meaning of a graph:
>> its meaning is objective
>> > (if we idealise here as before, and ignore potential
>> disagreements as to the meaning of terms),
>> > and is the set of interpretations as argued above.
>> >
>> > The advantage of this is that I can argue and make sense of
>> Sherlock Holmes by taking the
>> > set IR of resources that best describe his partial world as the
>> actual one when he speaks.
>> > That will help me make sense of the story.
>> > See "Truth in Fiction" http://andrewmbailey.com/dkl/
>> <http://andrewmbailey.com/dkl/>
>> >
>> > But it also helps make sense of contemporary politics, as well
>> as of thieves, liars and professional
>> > con men/women, Phishers and others whose aim is to change their
>> victim's perception
>> > of the actual world enough to entrap them.
>> >
>> >
>> >>
>> >>> My guess is that the concept that
>> >>> ties all modal logics together is the concept of context.
>> >>
>> >> That's about as wrong as it can get, in fact. See above.
>> >>
>> >>
>> >>> It would be interesting
>> >>> to see if there is a proof of that...
>> >>>>
>> >>>>> But it looks like this may need proving - or perhaps
>> someone has already
>> >>>>> done so? Modal logic need not I suppose involve possible
>> worlds, and the interesting thing
>> >>>>> is that Category Theories believe to have proven that modal
>> logic is to coalgebras what
>> >>>>> equational reasoning is to algebras. See "Modal Logics are
>> Coalgebraic" for a summary
>> >>>>> https://academic.oup.com/comjnl/article-abstract/54/1/31/336864
>> >>
>> >> That is, unfortunately, behind a rather high paywall. If you
>> have a link to an open published version, please give it.
>> >
>> > Sorry. Here it is available for all
>> > https://eprints.soton.ac.uk/267144/1/ModalCoalgRev.pdf
>>
>> Thanks.
>>
>> >
>> >>
>> >>>>> Coalgebras give us the mathematics of infinite streams,
>> processes, a notion of co-induction,
>> >>>>> and are to semantics what algebra is to syntax.
>> >>>>>
>> >>>>> All RDF semantics tells us is how to merge two graphs when
>> one believes them both
>> >>>>> to be true.
>> >>>>
>> >>>> Not quite "all", but your introduction of "believes" is
>> gratuitous. The RDF (and OWL) semantics saying nothing about
>> believing or beliefs.
>> >>> Yes, that's because I am thinking in terms of using these
>> specs by writing User Agents that need to
>> >>> help the User work with the published graphs encountered on
>> the web in order to arrange meetings,
>> >>> buy products, etc... So I take a pragmatic action oriented
>> view of these specs.
>> >>> Here R. Brandom, a student of David Lewis, whose thesis was
>> on Impossible Worlds, and who went on
>> >>> from there to develop a philosophy of Analytic Pragmatism, is
>> well worth looking at. He uses pragmatism
>> >>> I think to sidestep the idealisation of possible worlds, by
>> instead speaking of the logical consequences an actor is bound to
>> by making a statement. Such statements can of course be
>> contradictory, which is why this is a process oriented view of
>> possibilities, as I understand.
>> >>> But nevertheless, the spec would say that the two graphs have
>> compatible interpretations. Since any graph can have any number
>> of interpretations, this is saying that there some number of
>> models that makes them true. But then if there is set of model
>> that makes them true, that may not be a model the actor dealing
>> with that graph believes to be true
>> >>
>> >> Um... that does not make sense. Models(in this sense) aren't
>> true or not true, they are representations of the way that the
>> world could be arranged so as to make some /sentences/ (RDF
>> graphs) true.
>> >
>> > yes :-)
>> >
>> >>
>> >>> - ie one he would act on. Though he may be keen to use the
>> misapprehension of the actor with that belief to take advantage
>> of that situation.
>> >>> Which is pretty much how Phishing works.
>> >>>>
>> >>>>> But what if one believes that someone else believes them to
>> be true?
>> >>>>
>> >>>> And how is that nested modality to be represented in a form
>> that can be transmitted across the Web? You need to explain how
>> RDF syntax can be extended to cover this kind of assertion.
>> >>> One does not need to transmit it over the web for it to be
>> useful.
>> >>
>> >> But we are here talking about extending RDF (aren't we?) in
>> some way, and that extension /does/ need to be transmittable over
>> the Web. That is the whole point of defining these languages.
>> >
>> > yes. Just pointing out that I can gather a number of simple RDF
>> graphs from the web
>> > and already start using them using evidence logic, which are
>> described in a chapter of
>> > Eric Pacuit's recent book "Neighborhood Semantics for Modal
>> Logics" in 1.4.4 a Logic of Evidence and
>> > Belief. The idea is that every graph should count just as
>> evidence for various propositions and
>> > actions.
>>
>> Well, you CAN do that, but that isn't how the vast bulk of
>> RDF-coded linked data is in fact treated, as far as I know. Maybe
>> this will some to be needed when, if ever, RDF is used to encode
>> something more than simple data.
>>
>> >
>> >>
>> >>> If I have an
>> >>> application that merges different graphs and presents this to
>> the user it should be
>> >>> possible for the user to be surprised about a conclusion
>> reached, ask then where
>> >>> the information came from, and potentially remove some graphs
>> that he finds dubious.
>> >>
>> >> All true, but AFAI can see, has nothing to do with extending
>> RDF to be modal.
>> >
>> > Does the argument that the actual world being indexical makes
>> it interpretable as modal
>> > help convince you?
>>
>> Not really, but then I don't really understand that argument, or
>> in what sense you say that the actual world is indexical.
>>
>> >
>> > David Lewis showed that one can map counterfactual statements
>> to first order logic as
>> > long as one can quantify over possible worlds. Translated to
>> this context this would mean
>> > that we can quantify over interpretations.
>>
>> Hmm. I don't think this actually makes sense. Try to sketch what
>> such a logic would look like. To quantify over interpretations,
>> you need a way to /refer/ to interpretations. I don't think it is
>> internally coherent to have a logic which has names which refer
>> to the interpretations of that very logic, so that the universe
>> of an interpretation includes ... interpretations? Maybe Aczel's
>> set theory can handle this, but its going to get very strange.
>>
>> Perhaps there is an isomorphism, in which case
>> > it already is modal?
>> >
>> >>
>> >>> But one can even with RDF/XML pass graphs inside graphs since
>> one can pass an rdf literal
>> >>> in an rdf graph, and that can contain an rdf literal too...
>> >>> But there is also some basic ways this has been done since
>> the blogosphere where they
>> >>> invented the nofollow attribute when linking to something,
>> the user wanted to speak about
>> >>> whilst telling Google that he did not want his link to count
>> as a +1 for that web page.
>> >>> Similarly one could have a relation relating an Agent to a
>> content such as :disagrees
>> >>> to keep a distance between that content and ones affirmed by
>> the agent.
>> >>
>> >> Oh sure, one can imagine all kinds of ontologies of
>> propositional attitudes towards content. As well as degrees of
>> belief, numerical confidence scores and so on. But none of this
>> requires any changes to the /logic/. OUr old 'named graph' paper
>> had some ideas in it along these lines, also with detailed
>> semantics worked out: we had to introduce a notion of rigid
>> identifier (for the graph names) into the model theory to do it
>> properly.
>> >
>> > Do you have a link to it?
>>
>> http://wwwconference.org/2005a/cdrom/docs/p613.pdf
>>
>> see especially sections 8 and 9.
>>
>> >
>> >>
>> >>>>
>> >>>>> Then by merging them one can find out what they think is
>> true, and one can model that
>> >>>>> in terms of possible worlds, or for those more
>> syntactically oriented sets of all the
>> >>>>> ways of completing those graphs in ways that are consistent
>> (or sets of maximally complete
>> >>>>> such graphs). There is a clear modal element to that, in so
>> far as one cannot
>> >>>>> merge graphs of what one believes to be true into someone
>> else's belief store without getting
>> >>>>> a wrong idea of what they believe.
>> >>>>
>> >>>> But one can say all of this without mentioning the modal
>> notion of belief. You are here simply talking about truth,
>> consistency and validity (or otherwise) of inference on RDF
>> graphs, but adding 'believes' instead of 'true' throughout.
>> >>> yes, I am speaking of actors that use these graphs in order
>> to act in the world. I don't believe
>> >>> and I don't think anyone here believes that software has to
>> be written that maps an rdf graph
>> >>> to the interpretation in the world. What happens is that
>> software developers map graphs to
>> >>> User Interfaces in a functorial way, and these user
>> interfaces are then mapped by humans in the
>> >>> end to things in the world. The humans complete the
>> interpretation functor by composing with the
>> >>> initial one designed by the software developer.
>> >>
>> >> I don't think the semantic interpretation mapping is a
>> functOR, because I don't believe that the real world is a
>> category :-)
>> >
>> > Does the semantics not require sets? Is the world composed of sets?
>>
>> No, it is composed of things with relations holding between them.
>> Calling this a 'set' is the minimal amount of mathematics
>> necessary to describe it at all; seeing it as having any further
>> structure is a form of mathematical hallucination, IMO. But I
>> know I am out on a lonely limb here.
>>
>> > But seriously I am only putting that forward as a thought
>> experiment to see where
>> > it fails, in order to understand where people coming from
>> category theory may be mislead
>> > by trying to apply categories in an obvious way, but also to
>> see why one may need more
>> > complex structures like Institutions.
>>
>> Fair enough :-)
>>
>> >
>> >>
>> >>> I give a simplistic but at least intuitive view of how such a
>> functorial notion of semantics can
>> >>> be understood to work in the math exchange question
>> >>>
>> https://math.stackexchange.com/questions/2896172/how-should-one-model-rdf-semantics-in-terms-of-category-theory
>> >>> I need to develop that a lot more of course...
>> >>>>
>> >>>>>
>> >>>>> So if this still needs to be proven
>> >>>>
>> >>>> What exactly "needs to be proven" ?
>> >>> I suppose that RDF1.1 with datasets is compatible with modal
>> logic. Though I
>> >>> have a feeling that Kripke modal logic is too simple and even
>> David Lewisian
>> >>> modal logic which is a neighborhood semantics based one is
>> not quite right.
>> >>> In the newly published book "Category Theory for the Working
>> Philosopher"
>> >>> https://books.google.de/books?id=RIM8DwAAQBAJ
>> >>> there are many very intersting articles. One by Abramski on
>> Contextuality and
>> >>> Paradox. But also the one by Kohei Kishida on "Categories and
>> Modalities"
>> >>> which looks a neighborhood semantics with impossible worlds
>> and shows
>> >>> how that can be understood in terms of category theory.
>> >>> I have not yet fully digested all these different pieces. But
>> I hope this
>> >>> gives some idea as to the work one could draw on to further
>> the semantic web
>> >>> and the web in general by placing it on even firmer formal
>> foundations.
>> >>
>> >> Well, good luck. I confess to not, myself, finding Category
>> Theory much use in providing any useful insights; it seems to be
>> a whole lot of jargon describing very little, compared to the
>> simplicity and elegance of the usual set-theoretic picture. The
>> Wikipedia article on Coalgebras (which I looked at to help me
>> understand what you were talking about earlier) is a good
>> example. What in this
>> >> https://en.wikipedia.org/wiki/Coalgebra
>> >> provides ANY useful insight AT ALL into what we are
>> discussing? It defines a coalgebra as a vector space, for a
>> start. What do vector spaces have to do with RDF, modal logic or
>> the Web?
>> >
>> > yes, that is not a very good introduction.
>> >
>> > Corina Cirstea's article is much better and so is
>> > "Universal Coalgebras: A theory of Systems"
>> >
>> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.159.2020&rep=rep1&type=pdf
>> >
>> > as well as Bart Jacobs, Jan Rutten "A tutorial on (co) algebras
>> and (co) induction"
>> >
>> https://pdfs.semanticscholar.org/40bb/e9978e2c4080740f55634ac58033bfb37d36.pdf
>> >
>> > He has a lot of excellent articles from the 1990ies showing how
>> OO programming
>> > is coalgebraic. But he also has an article showing how there is
>> a duality between
>> > OO programming and modal logics with operators
>> > http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.7008
>> > ( much more difficult but it shows how this can help bridge
>> branches
>> > that would seem incompatible)
>> >
>> > Benjamin Braatz' thesis is an algebraic approach to RDF, and
>> the first half
>> > would be close to your heart, as he has blank nodes tied to
>> graphs, which is
>> > a way to make your metaphorical idea of surfaces real.
>> >
>> > One of the key things of Category Theory is that it emphasizes
>> structure above
>> > elements. And most amazingly it is based on the same notion of
>> a graph that
>> > RDF uses. That is what is so weird about it. Category theory is
>> less interested
>> > in identity as it is in translation or isomorphism. So that is
>> why it is very good
>> > at finding deep symmetries between very different parts of
>> mathematics, as well
>> > as showing how the same structure is found across mathematical
>> and logical domains.
>>
>> OK, I know it is foundational in mathematics, but Web logic isn't
>> primarily a mathematical topic. The actual metamathematics of
>> logic (certainly of RDF) is very simple, almost trivial. It
>> doesnt need anything high-powered to grasp it. And the
>> subject-matter of Web logic isn't mathematical at all. The worlds
>> that linked data describes have essentially no generalizable
>> mathematical structure.
>>
>> But whatever, I don't mean to have an argument about this. If you
>> can find insight in category theory, good luck with it :-) Thanks
>> for the pointers, in any case.
>>
>> Pat
>>
>> > For example it turns out that one can think of programming with
>> types in ways
>> > that are very similar to basic algebras one learns in high
>> school. It used to be
>> > abstract nonsense. Now category theoreticians are doing
>> keynotes at programming
>> > language conferences:
>> https://skillsmatter.com/skillscasts/10179-the-maths-behind-types
>> >
>> >>
>> >> But YMMV, as I am sure it does.
>> >
>> > :-)
>> >
>> >>
>> >>>>
>> >>>>> it seems like Institution theory may help to do
>> >>>>> so. In a very interesting paper from 2006 by Dorel Lucanu,
>> Yuan Fang Li, and Jin Song Dong
>> >>>>> entitled "Semantic Web Languages – Towards an Institutional
>> Perspective" show how one can
>> >>>>> use the theory of institutions to show how RDF, RDFS, OWL
>> (light, DL,...,Full), ... that
>> >>>>> seem to have very different semantics can in fact be seen
>> to be consistent.
>> >>>>
>> >>>> The OWL specification documents show this already, in almost
>> painful detail. (Well, insofar as it is correct. Some RDFS
>> tautologies are not valid in any OWL dialect, for example.)
>> >>> Thanks for pointing that out.
>> >>> In fairness, the article "Semantic Web Languages - Towards an
>> Institutional Perspective" was
>> >>> published in 2006 while the document "OWL 2 Web Ontology
>> Language Mapping to RDF Graphs"
>> >>> https://www.w3.org/TR/2012/REC-owl2-mapping-to-rdf-20121211/
>> >>> came out in Dec 2012 so over 6 years later.
>> >>
>> >> Well, sure, but the same job was done in 2004 for the earlier
>> versions of OWL and RDF.
>> >>
>> >>> I remember in the early days people doubting that these
>> languages could have the same
>> >>> semantics, and using that as an argument for the
>> infeasibility of the semantic web.
>> >>
>> >> Yes. It was a very contentious matter for quite a while. The
>> split between OWL-DL and OWL-Full was the product of those
>> energetic debates.
>> >>
>> >> Pat
>> >>
>> >>>>>
>> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.119.5368&rep=rep1&type=pdf
>> >>>>> So if someone tells you that these are incompatible
>> semantics point them to that paper.
>> >>>>
>> >>>> Or read the specifications themselves :-)
>> >>> Yes, now I can point people to two such documents, and most
>> interestingly for me
>> >>> is I can see how the two methodologies overlap or diverge.
>> >>>> Pat
>> >>>>
>> >>>>>
>> >>>>> It looks like work needs to be done to show that these are
>> also compatible with
>> >>>>> modal logics (with neighborhood semantics is my guess: ie
>> coalgebras of the form
>> >>>>> S -> S^2^2
>> >>>>> a.k.a
>> >>>>> S -> 𝒫𝒫(S)
>> >>>>> where 𝒫(S) is a predicate and 𝒫𝒫(S) is a set of
>> predicates. Now if one thinks
>> >>>>> of a graph as a predicate on possible worlds, one sees why
>> this is similar to quad
>> >>>>> stores. Those are known as a hyper-system as explained in
>> "Universal Coalgebra: A Theory
>> >>>>> of Systems"
>> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.159.2020&rep=rep1&type=pdf
>> >>>>>
>> >>>>> As for good introductions to CT, since that was part of the
>> topic 4 years ago,
>> >>>>> I think the best online intro (and more) for programmers
>> are Bart Milewski's
>> >>>>> ( https://bartoszmilewski.com/ ) videos on youtube
>> >>>>> https://www.youtube.com/user/DrBartosz/playlists
>> <https://www.youtube.com/user/DrBartosz/playlists>
>> >>>>> I really recommend it. He is extremely clear without being
>> boring.
>> >>>>>
>> >>>>> I also liked a lot "Category Theory for Computing Science"
>> by Michael Barr and
>> >>>>> Charles Wells (online
>> http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf )
>> >>>>> because they make the relation of categories to Graphs so
>> clear.
>> >>>>>
>> >>>>> Indeed just because the relation is so striking I asked a
>> question on Math
>> >>>>> Stackexchange to illustrate how one could be (mis?)lead
>> into a simple pattern
>> >>>>> of thinking of the relationship
>> >>>>>
>> >>>>>
>> https://math.stackexchange.com/questions/2896172/how-should-one-model-rdf-semantics-in-terms-of-category-theory
>> >>>>>
>> >>>>> Has anyone come across further developments in this space
>> since then?
>> >>>>>
>> >>>>> Henry Story
>> >>>>>
>> >>>>>
>> >>>>>
>> >>>>>> On 17 Apr 2014, at 20:02, Obrst, Leo J. <lobrst@mitre.org
>> <mailto:lobrst@mitre.org>> wrote:
>> >>>>>>
>> >>>>>> Back a few years, emerging from the old IEEE Standard
>> Upper Ontology group’s work was Bob Kent’s Information Flow
>> Framework, an ontology framework (a meta-level framework) based
>> on Barwise & Seligman’s Information Flow Theory, itself an
>> application of Category Theory. See, for example:
>> http://arxiv.org/pdf/1109.0983v1 <http://arxiv.org/pdf/1109.0983v1>.
>> >>>>>>
>> >>>>>> Mainly folks have used Information Flow Theory or Goguen’s
>> notion of institutions as springboards from category theory to
>> ontologies, especially for so-called “lattice of theories”,
>> ontology mapping, and semantic interoperability applications.
>> Work includes Mossakowski’s various papers:
>> http://iws.cs.uni-magdeburg.de/~mossakow/
>> <http://iws.cs.uni-magdeburg.de/%7Emossakow/>.
>> >>>>>>
>> >>>>>> For a short “position” paper, see:
>> >>>>>> Markus Kr¨otzsch, Pascal Hitzler, Marc Ehrig, York Sure.
>> 2005. Category Theory in Ontology Research: Concrete Gain from an
>> Abstract Approach. http://www.aifb.kit.edu/web/Techreport893.
>> >>>>>>
>> >>>>>> For RDF and category theory, the only paper I know of
>> addresses graph transformations for RDF:
>> >>>>>> Benjamin Braatz; Christoph Brandt. 2008. Graph
>> Transformations for the Resource Description Framework.
>> Proceedings of the Seventh International Workshop on Graph
>> Transformation and Visual Modeling Techniques (GT-VMT 2008).
>> http://journal.ub.tu-berlin.de/eceasst/article/view/158/142.
>> >>>>>>
>> >>>>>> Admittedly most of the above are applications beyond logic
>> itself and RDF, but might shed some light on how category theory
>> is being used for ontologies.
>> >>>>>>
>> >>>>>> Thanks,
>> >>>>>> Leo
>> >>>>>>
>> >>>>>> From: henry.story@bblfish.net
>> <mailto:henry.story@bblfish.net> [mailto:henry.story@bblfish.net
>> <mailto:henry.story@bblfish.net>]
>> >>>>>> Sent: Wednesday, April 16, 2014 6:09 PM
>> >>>>>> To: Gregg Reynolds
>> >>>>>> Cc: Antoine Zimmermann; SW-forum Web;
>> public-philoweb@w3.org <mailto:public-philoweb@w3.org>
>> >>>>>> Subject: Re: rdf and category theory
>> >>>>>>
>> >>>>>>
>> >>>>>> On 11 Apr 2014, at 16:32, Gregg Reynolds
>> <dev@mobileink.com <mailto:dev@mobileink.com>> wrote:
>> >>>>>>
>> >>>>>>
>> >>>>>> On Fri, Apr 11, 2014 at 8:30 AM, Antoine Zimmermann
>> <antoine.zimmermann@emse.fr <mailto:antoine.zimmermann@emse.fr>>
>> wrote:
>> >>>>>> There're a lot of resources available online and for free
>> about category theory.
>> >>>>>>
>> >>>>>> Some examples:
>> >>>>>> - Jirí Adámek, Horst Herrlich, George E. Strecker.
>> Abstract and Concrete Categories: The Joy of Cats (524 pages).
>> http://katmat.math.uni-bremen.de/acc/acc.pdf
>> >>>>>> - Maarten M. Fokkinga. A Gentle Introduction to
>> Category Theory: the calculational
>> approach.http://wwwhome.ewi.utwente.nl/~fokkinga/mmf92b.pdf
>> <http://wwwhome.ewi.utwente.nl/%7Efokkinga/mmf92b.pdf> (80 pages).
>> >>>>>> - Jaap van Oosten. Basic Category Theory (88 pages).
>> http://www.staff.science.uu.nl/~ooste110/syllabi/catsmoeder.pdf
>> <http://www.staff.science.uu.nl/%7Eooste110/syllabi/catsmoeder.pdf>
>> >>>>>>
>> >>>>>>
>> >>>>>> One of the best is Robert Goldblatt's Topoi : The
>> Categorial Analysis of Logic . He pays special attention to
>> linking CT concepts to both classic math and ordinary intuition.
>> >>>>>>
>> >>>>>> I looked through Robert Goldblatt's Topoi quickly [1] and
>> indeed it is the book that covers the subject probably most
>> relevant to the semantic web community, since it aims to show how
>> logic can be derived from Category Theory. In this area I found
>> reading through the first part of Ralf Krömer's "Tool and Object:
>> A History and Philosophy of Category Theory" to also be very
>> interesting, as it gives an overview of the foundational debate
>> in Mathematics started by CT.
>> >>>>>>
>> >>>>>> It's so odd that RDF is entirely about relations just as
>> CT is ( except that RDF is one to many whereas CT arrows are
>> functions). So I really look forward to understanding how these
>> two domains fit together, and perhaps how they complement each other.
>> >>>>>>
>> >>>>>>
>> >>>>>> Henry
>> >>>>>>
>> >>>>>> [1] Having read through half of "Conceptual Mathematics"
>> by Willima Lawvere and done most of the exercises there, I am
>> starting to be able to read a lot of these books much more easily.
>> >>>>>>
>> >>>>>>
>> >>>>>>
>> >>>>>>
>> >>>>>> -Gregg
>> >>>>>>
>> >>>>>> Social Web Architect
>> >>>>>> http://bblfish.net/
>> >>>>>
>> >>>>>
>> >>>>>
>> >>>>>
>> >>>>>
>> >>>> --
>> >>>> -----------------------------------
>> >>>> call or text to 850 291 0667
>> >>>> www.ihmc.us/groups/phayes/ <http://www.ihmc.us/groups/phayes/>
>> >>>> www.facebook.com/the.pat.hayes
>> <http://www.facebook.com/the.pat.hayes>
>> >>
>> >> --
>> >> -----------------------------------
>> >> call or text to 850 291 0667
>> >> www.ihmc.us/groups/phayes/ <http://www.ihmc.us/groups/phayes/>
>> >> www.facebook.com/the.pat.hayes
>> <http://www.facebook.com/the.pat.hayes>
>> >
>> >
>> >
>> >
>> >
>>
>> --
>> -----------------------------------
>> call or text to 850 291 0667
>> www.ihmc.us/groups/phayes/ <http://www.ihmc.us/groups/phayes/>
>> www.facebook.com/the.pat.hayes
>> <http://www.facebook.com/the.pat.hayes>
>>
>>
>
> --
> Krzysztof Janowicz
>
> Geography Department, University of California, Santa Barbara
> 4830 Ellison Hall, Santa Barbara, CA 93106-4060
>
> Email:jano@geog.ucsb.edu
> Webpage:http://geog.ucsb.edu/~jano/
> Semantic Web Journal:http://www.semantic-web-journal.net
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