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Re: operational semantics - Fwd: rdf semantics and timelessly true

From: <alexandre.monnin@web-and-philosophy.org>
Date: Fri, 16 Nov 2012 12:28:20 +0100
To: "public-philoweb@w3.org" <public-philoweb@w3.org>, "Henry Story" <henry.story@bblfish.net>
Cc: "ross.horne@gmail.com" <ross.horne@gmail.com>
Message-ID: <op.wnu55iqexo5klo@alexalien-pc>
Hi Henry, Hi Ross, Hi all,

We had a presentation last spring at the Philoweb seminar I was hosting at  
La Sorbonne of a student of Jean-Yves Girard, Samuel Tronçon, who, like  
others, is working on a project whose goal is to study the semantic Web  
 from the perspective of linear logic, ludic and geometry of interaction.  
You can find more information about it here :  
http://www.anr-loci.fr/axes-de-travail/article/tache-4-communication-web-et

Sorry, that's in French!

Best,
A.


Le Fri, 16 Nov 2012 11:55:05 +0100, Henry Story <henry.story@bblfish.net>  
a écrit:

> An interesting e-mail for people doing research in these topics
> with a different view of semantics.
>
> Begin forwarded message:
>
>> From: Ross Horne <ross.horne@gmail.com>
>> Subject: Re: rdf semantics and timelessly true
>> Date: 16 November 2012 11:08:07 CET
>> To: Henry Story <henry.story@bblfish.net>
>> Reply-To: ross.horne@gmail.com
>>
>> Hi Henry,
>>
>> Great email!
>>
>> Modal logics are indeed one option, but they still try to be classical
>> in spirit. What I mean is negation is still interpreted as the
>> complement of a set but this time in term of a Kripke frame allowing
>> possible world connected by a relation.
>>
>> Because you have enthusiasm for logic, I hope you don't mind me
>> sharing another perspective on logic that I feel is relevant to Linked
>> Data. It is possible to work semantically, but remain in a syntactic
>> world, i.e. without building a set theoretic or category theoretic
>> model. This is done in a branch of logic called proof theory, which
>> focuses on the semantics of logic as syntactic proof structures. The
>> key result is the cut-elimination result (first proven by Gentzen for
>> propositional logic). Cut-elimination can be seen in several ways, as
>> an internal soundness and completeness result, or a proof of
>> consistency of the internal dynamics of the proof system.
>>
>> Proof theory opens a door some modern logics including intuitionistic
>> logic, linear logic and the latest twist in modern logic the calculus
>> of structures. These modern logics are highly suited to problems in
>> computer science. E.g. intuitionistic logic matches with typed
>> functional programming and linear logic matches with resources
>> sensitive parallelism. In the last decade, deep inference, has allowed
>> us to treat time or causality in this purely syntactic logical
>> setting. In these logics provability rather than truth are central and
>> negation is no where near as strong as in a classical model theory.
>> For example, given a formula A it negation in linear logic, say ~A is
>> the resource that interacts perfectly with the formula A. This is
>> initially baffling, since you must throw away your classical reading
>> of negation an see things in terms of the dynamic manipulation of
>> syntax!
>>
>> I like your modal logic approach to context. I'm only suggesting that
>> there are other approaches to consider, some of which where the
>> distinction between syntax and semantics is more subtle.
>
>
> Note that David Lewis in all his books proposes a version of possible
> worlds entirely reduced to sets of sentences for pure nominalists.
> There are different consequences for that view, but I don't remember
> the details. I alway found the modal realist approach more fun :-)
> Still that leaves you with Sets I suppose, which he does try to remove
> with his last book on mereology.
>
> My quick initial research on what your pointers leads me to:
>
> Genzen: http://en.wikipedia.org/wiki/Gentzen's_consistency_proof
> Deep Inference: http://alessio.guglielmi.name/res/cos/
>
> I'd be interested in a good pointer to the definition of causality,
> as I like David Lewis' defintion of causality as a relation between
> two events such that
>
>  e1 causes e2  iff  had e1 not occurred, e2 would not have occurred  
> either
>
> He then needs to tune this definition, because events can be  
> overdetermined
> by multiple causes. Something he looks at in a book Edited by John  
> Collins, Ned
> Hall and L.A.Paul "Causation and Counterfactuals"
>
> Henry
>
>
> Anyway, thanks for the pointers. Those are things I need to study more
> carefully.
>
>
>
>
>>
>> N.B. I'm not posting this publicly. Is this relevant to the philoweb
>> group? I had not been aware of that group before you CC'd the list..
>>
>> Regards,
>>
>> Ross
>>
>>
>>
>> 2012/11/15 Henry Story <henry.story@bblfish.net>:
>>>
>>> On 15 Nov 2012, at 08:25, Ross Horne <ross.horne@gmail.com> wrote:
>>>
>>>> Hi All,
>>>>
>>>> I mentioned this a couple of years ago to Pat, so I know he  
>>>> disagrees..
>>>>
>>>> Many of these problem with context come from assigning truth values to
>>>> RDF triples. Of course, this is possible in classical logic. However,
>>>> if we free ourself from classical logic, assigning truth values
>>>> without a context makes little sense.
>>>
>>> It helps to move to modal logic to solve this problem. David Lewis has
>>> developed a modal logic that works with classical logic and that allows
>>> indeed truth to be contextual: the context being the whole of a  
>>> universe's
>>> life from beginning to end. It is contextual in that the universe could
>>> have been different. RDF Semantics uses this intuition:
>>>
>>> <blockquote cite="http://www.w3.org/TR/rdf-mt/#interp">
>>> The basic intuition of model-theoretic semantics is that asserting a  
>>> sentence makes a claim about the world: it is another way of saying  
>>> that the world is, in fact, so arranged as to be an interpretation  
>>> which makes the sentence true. In other words, an assertion amounts to  
>>> stating a constraint on the possibleways the world might be. Notice  
>>> that there is no presumption here that any assertion contains enough  
>>> information to specify a single unique interpretation. It is usually  
>>> impossible to assert enough in any language to completely constrain  
>>> the interpretations to a single possible world, so there is no such  
>>> thing as 'the' unique interpretation of an RDF graph. In general, the  
>>> larger an RDF graph is - the more it says about the world - then the  
>>> smaller the set of interpretations that an assertion of the graph  
>>> allows to be true - the fewer the ways the world could be, while  
>>> making the asserted graph true of it.
>>> </cite>
>>>
>>>
>>>> Instead, triples are just syntax
>>>> -- a subject, property and object -- that can be processed according
>>>> to our goal (e.g. answer a query), possibly with respect to context
>>>> (e.g. the URI of a named graph or HTTP time stamp as suggested in
>>>> previous posts).
>>>
>>> It is very helpful to think semantically and not syntactically, because
>>> it is what helps us move beyond syntactic fashions, and what allows us  
>>> to
>>> map different systems together.
>>>
>>> In any case here you bring in a new element namely who said what
>>> ( or where you got the  information from ). That is very important for
>>> determining all kinds of elements such as trust, fictionality, etc...
>>> After all since a graph is just the set of possible worlds in which it  
>>> is
>>> true, this means that a graph can describe fictional as well as the  
>>> actual
>>> world. It could describe worlds that have different physical laws than  
>>> ours,
>>> etc... Or it could just describe the world as someone else sees it.
>>>
>>> RDF semantics is completely compatible with all of that btw.
>>>
>>>>
>>>> In this syntactic world, changes can be modelled using an operational
>>>> semantics, which is just a relation over syntax that describes how the
>>>> system evolves e.g. [1]. Again, there are no truth values in this
>>>> situation, just rules for manipulating syntax. (n.b. this is a
>>>> simplification since we really need to take a suitable "weak memory
>>>> model" [2] into account.)
>>>
>>> You get to truth when you want to merge graphs, and when you want to
>>> pass to an action. So if you want a minimal definition of truth
>>> you can take Donald Davidson's ( Truth and Interpretation ) take on
>>> Tarski's formula
>>>
>>>  S is true in language L if and only if p
>>>
>>> where p expresses the proposition that S in L expresses. You can  
>>> rewrite
>>> this in N3 as
>>>
>>>  { { ?s ?r ?o } a log:Truth }  <=> { ?s ?r ?o }
>>>
>>> What is the function of truth? Well it is a disquotational function.
>>> It is what allows you to take something within a quote and merge it
>>> with other information in the context in which you are speaking.
>>>
>>> So this should help you now to understand what is happening on the
>>> Web, and the relation between syntax and semantics ( a major theme
>>> in Donald Davidson's work was that of interpretation ). Let's go back
>>> to Donald Davidson's example
>>>
>>>  "Schnee ist weiß" is true in German <=> Snow is white .
>>>
>>> If you can produce a theory that can map all such sentences from
>>> German to  in this case English, you have a theory of meaning of
>>> German. Doing this in terms of possible worlds I think just allows
>>> you to generalise this to all possible translation systems.
>>>
>>> In any case if you are more pragmatic you may ask: how does this
>>> affect action? Cause you know we have got things to do here!
>>>
>>> So here goes when you say that some graph is true, you are saying that
>>> that sent of possible worlds contains the actual world. Which means you
>>> can merge that information with the other graphs you consider to  
>>> describe
>>> the actual world.
>>>
>>> Assume you believe ( your data store contains ).
>>>
>>>  :george a foaf:Person .
>>>
>>> and now assume a friend of yours has written on his profile
>>>
>>>   { :tim foaf:knows :george . } saidBy :tim .
>>>
>>> Assume you have a rule such that
>>>
>>>   { { :tim foaf:knows ?p } saidBy :tim } => { { :tim foaf:knows ?p } a  
>>> log:Truth }
>>>
>>> it follows from the disquotational rule of truth you can then assert
>>>
>>>   :tim foaf:knows :george .
>>>
>>> If it happens that :george visits your site, you can for example make
>>> it easy for  :george to communicate with :tim   ( simplifying a lot )
>>>
>>> That is truth is important because it allows you to merge information
>>> in order to then be able to act on it. And yes, reality may then show
>>> you that your reasoning about which possible world you were in was  
>>> mistaken.
>>>
>>>
>>>> Provenance can also be tracked also using
>>>> only syntax, perhaps proving historical information about the context,
>>>> then used to "quantify" triples; but you all know this!
>>>>
>>>> Andy Seaborne and the Data Access WG has been smart in avoiding asking
>>>> questions about the truth of RDF statement when producing the SPARQL
>>>> specs. In the SPARQL specs, RDF triples are just syntax.
>>>
>>> They are looking for patterns in a graph, and so don't need to
>>> go beyond what you term syntax.
>>>
>>>>
>>>> However, I agree with Pat that the URIs themselves should be
>>>> "intuitively" timeless . Will it ever be possible to avoid using the
>>>> word "true" in this open world setting?
>>>
>>> People over time got very anxious about Truth, because they thought  
>>> that
>>> they were forced into one overarching truth. Such thinking makes
>>> it impossible to do psychology correctly. It is wide spread, since most
>>> programming languages don't make the notions of context clear.
>>>
>>>  https://blogs.oracle.com/bblfish/entry/are_oo_languages_autistic
>>>
>>> But you don't need to worry about Truth being problematic for this.
>>> And you need not worry that logic cannot work with context. Or that
>>> syntax and semantics are not related. It all works nicely together,
>>> but one has to see how and in what way.
>>>
>>> Modal logic did it is true take a lot of time to be convincing ( the
>>> 1970ies it seems was the breakthrough period ). So you have to be  
>>> careful
>>> when reading philosophers, logicians to see if their criticism comes
>>> before or after that time.
>>>
>>>
>>>
>>> back to work.
>>>
>>>>
>>>> Best Regards,
>>>>
>>>> Ross
>>>>
>>>> [1] http://www.sciencedirect.com/science/article/pii/S0304397512006020
>>>> [2] http://www.cl.cam.ac.uk/~pes20/weakmemory/
>>>>
>>>>
>>>> 2012/11/15 Pat Hayes <phayes@ihmc.us>:
>>>>>
>>>>> On Nov 14, 2012, at 9:56 AM, Nathan wrote:
>>>>>
>>>>>> Pat Hayes wrote:
>>>>>>> On Nov 14, 2012, at 8:42 AM, Nathan wrote:
>>>>>>>> Pat Hayes wrote:
>>>>>>>>> On Nov 14, 2012, at 8:03 AM, Nathan wrote:
>>>>>>>>>> Hi Pat,
>>>>>>>>>>
>>>>>>>>>> Pat Hayes wrote:
>>>>>>>>>>> Its not impossible, and in a strong sense this is required by  
>>>>>>>>>>> the current RDF semantics, which treats all RDF assertions as  
>>>>>>>>>>> timelessly true.
>>>>>>>>>> Can you refine / expand on this please? I'd presumed RDF to  
>>>>>>>>>> have no consideration of time - e.g time-less; as opposed to  
>>>>>>>>>> being true for all time (timeless).
>>>>>>>>>>
>>>>>>>>>> TIA,
>>>>>>>>>>
>>>>>>>>>> Nathan
>>>>>>>>> Yes, time-less is a better way to put it. But it is so because  
>>>>>>>>> URIreferences are assumed (and I know this is an idealization,  
>>>>>>>>> but...) to be timeless in how they refer. Section 1.2 says:   
>>>>>>>>> "... the semantics simply assumes that ... a single URI  
>>>>>>>>> reference can be taken to have the same meaning wherever it  
>>>>>>>>> occurs. Similarly, the semantics has no special provision for  
>>>>>>>>> tracking temporal changes. It assumes, implicitly, that URI  
>>>>>>>>> references have the same meaning whenever they occur."
>>>>>>>>> In other words, no counters allowed.
>>>>>>>> What about any data that changes? if <http://webr3.org/nathan#me>  
>>>>>>>> refers to "me", and I change my name from Nathan to Bob, then I  
>>>>>>>> cannot update my RDF to reflect this? or perhaps more  
>>>>>>>> realistically, my email address?
>>>>>>> Its fine to coin a new URI for yourself. The issue arises if you  
>>>>>>> want to re-use your old URI to refer to something different. What  
>>>>>>> you *ought* to do, according to the strict RDF rules (and TimBL's  
>>>>>>> idea of "cool URIs") is to coin a new URI for the new thing and  
>>>>>>> keep the old one meaning the same thing as it always did. But  
>>>>>>> note, it is fine for this "thing" to be something that is dynamic,  
>>>>>>> ie which has states that change with time. LIke a daily newspaper,  
>>>>>>> for example. But then you need to be careful to distinguish this  
>>>>>>> thing from one of its states...
>>>>>>
>>>>>> That makes sense, however I'd still like to clarify further,  
>>>>>> specifically on the distinction between something which changes  
>>>>>> states, and something who's properties may change over time.
>>>>>
>>>>> OK, let me interrupt with a quick disclaimer. I DONT want to defend  
>>>>> this distinction. There is a huge metaphysical/ontological sinkhole  
>>>>> here that some very clever people have fallen into, trying to  
>>>>> distinguish between things that have states and things that simply  
>>>>> endure while their properties change. All that matters for the  
>>>>> present discussion is that, however you describe this, to do so  
>>>>> properly requires that you relate this thing to a property and a  
>>>>> time: *three* entities that all have to be involved in the data  
>>>>> record. [*1] As opposed to just relating two of them, the thing and  
>>>>> its property, and relying on the "actual time" (AKA "now" or "the  
>>>>> present") to play the role of the missing time reference.
>>>>>
>>>>>>
>>>>>> To persist with the name example, a good percentage of females will  
>>>>>> have their surname change over time - so what do we do when today  
>>>>>> we have:
>>>>>> { <#mary> foaf:lastName "Thompson"@en . }
>>>>>> and tomorrow:
>>>>>> { <#mary> foaf:lastName "Davids"@en . }
>>>>>>
>>>>>> How do we distinguish mary from one of her states?
>>>>>
>>>>> Well, to be strict about it, we ought to say that names that are  
>>>>> liable to get changed are names *at a time*, or perhaps in this case  
>>>>> names *up to a time*, and that the name after that time (of  
>>>>> marriage, in our culture) is a different name. OK, thats being very  
>>>>> strict, because this kind of change is comparatively infrequent (in  
>>>>> a single lifetime, I mean) and it is often assumed that such data is  
>>>>> indeed intended to be "about the present", and that it will get  
>>>>> updated from time to time. We even have special constructs, eg the  
>>>>> "neé" relation to indicate a previous name, for this case. But try  
>>>>> doing this for something which changes its state compartively  
>>>>> rapidly, such as the noon temperature at a certain location, or the  
>>>>> headline in the NYTimes.
>>>>>
>>>>> In your example, what happens to the first Thompson triple on the  
>>>>> day after Mary gets married? Is it just deleted, and forgotten  
>>>>> about? (But what about all the copies of it that may be cached in  
>>>>> RDF stores anywhere on the Web?) Or does it get modified using a  
>>>>> "neé" kind of property? And is the date of the change-over recorded?  
>>>>> What about this new Davids triple: it wasn't always true: shouldn't  
>>>>> the data record the date when it started being true, in case someone  
>>>>> wants to check something historical, not just about what is true  
>>>>> "now"? The more you ask quesitons like this, the more it seems that  
>>>>> time information should have been in this kind of data from the  
>>>>> get-go.
>>>>>
>>>>> Pat
>>>>>
>>>>> [*1] The metaphysical debate is between those who want to associate  
>>>>> the time with the property, and those who want to associate it with  
>>>>> the thing. The former would say Mary's properties change, the latter  
>>>>> would say that Mary changes her state. After years of arguing about  
>>>>> this, I no longer care which you say: the basic logic is the same in  
>>>>> both cases.
>>>>>
>>>>>
>>>>>>
>>>>>> TIA,
>>>>>>
>>>>>> Nathan
>>>>>>
>>>>>>
>>>>>
>>>>> ------------------------------------------------------------
>>>>> IHMC                                     (850)434 8903 or (650)494  
>>>>> 3973
>>>>> 40 South Alcaniz St.           (850)202 4416   office
>>>>> Pensacola                            (850)202 4440   fax
>>>>> FL 32502                              (850)291 0667   mobile
>>>>> phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>
>>> Social Web Architect
>>> http://bblfish.net/
>>>
>
> Social Web Architect
> http://bblfish.net/
>


-- 


Responsable Recherche Web et Métadonnées à l'Institut de Recherche et  
d'Innovation du Centre Pompidou (IRI)
Doctorant en philosophie à Paris 1 (PHICO, EXeCO)
Collaborateur extérieur de l'INRIA (Membre associé de l'EPI Wimmics,  
Centre de Recherche de Sophia-Antipolis)
Doctorant associé au CNAM (équipe DICEN)

Responsable du séminaire "Digital studies, Metadata studies : les enjeux  
de la contribution", 2012-2013 (Ministère de la Culture, IRI)
Co-organisateur des "Rencontres du Web de données" au Centre Pompidou
Membre du comité de rédaction de la revue Implications Philosophiques

Twitter : @aamonnz & @PhiloWeb
Philosophy of the Web, http://web-and-philosophy.org/
PhiloWeb on Dailymotion, http://www.dailymotion.com/PhiloWeb
Philosophy and Web discussion list @INRIA,  
https://lists-sop.inria.fr/sympa/info/philoweb
Received on Friday, 16 November 2012 11:28:55 GMT

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