- From: Krzysztof Janowicz <janowicz@ucsb.edu>
- Date: Tue, 4 Sep 2018 17:35:10 -0700
- To: Simon.Cox@csiro.au, danbri@danbri.org, phayes@ihmc.us
- Cc: henry.story@bblfish.net, semantic-web@w3.org, bb@bbraatz.eu, public-philoweb@w3.org
- Message-ID: <b151ad2f-a8c3-ff78-ea74-52f86088c3be@ucsb.edu>
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
Received on Wednesday, 5 September 2018 00:36:09 UTC