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Re: [ontolog-forum] Context, at last!

To: nicolas.rouquette@xxxxxxxxxxxx, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Fri, 17 Jun 2005 13:52:43 -0500
Message-id: <20050617185243.GH64829@xxxxxxxx>
On Wed, Jun 15, 2005 at 04:46:42PM -0700, Nicolas F Rouquette wrote:
> Which field of study talks about "intensional" contexts?    (01)

There are very large (distinct but overlapping) bodies of literature on
intensional contexts in linguistics, the philosophy of language, and
philosophical logic.  There is in particular a very active area of
formal research falling under the rubric "intensional logic" -- very
roughly, logics in which standard extensional semantical rules break
down (or appear to break down).  Modal logic is a prime example of an
intensional logic.  Notably, "it is necessary that" is a
non-compositional operator, that is, the truth value of a sentence of
the form "It is necessary that p" is a determinate function of the truth
value of p (unlike, say "It is not the case that p").  Consider cases
where p is, for example, "2+3=5" and "George Bush is president",
respecitvely.  Both propositions are true.  But in the one case "It is
necessary that p" is true and in the other it isn't.  So the necessity
operator is not truth-functional.    (02)

A famous example of intensionality from the 19th C. philosopher/logician
Gottlob Frege (who was the first to clearly recognize the significance
of intensionality) involves identity.  A standard law of identity is
that     (03)

ID: if x = y, then anything true of x is true of y.     (04)

This law appears to break down in intensional contexts.  For example,
the Morning Star and the Evening Star are the same thing, viz., the
planet Venus.  So we have    (05)

(1) the MS = the ES    (06)

Hence, from the unproblematic claim:    (07)

(2) George believes the MS is identical to the MS    (08)

it follows from (1) and ID that    (09)

(3) George believes the MS is identical to the ES    (010)

But George might not know much about astronomy; while he is aware of the
MS and the ES, he may not know they are one and the same.  So the
inference to (2) appears to be unsound, and so ID appears to break down
in belief contexts.    (011)

> >One of the interesting things about intentional (hence de re and de
> >dicto) contexts that can be seen here is that their proper
> >representation often seems to require reifying *propositions* -- the
> >things worried about, believed, feared, desired, etc.  For this reason
> >worry, belief, etc are often called "propositional attitudes".  I've
> >used square brackets above as a mechanism for forming a
> >proposition-denoting term out of a sentence.  (There are other ways to
> >do represent intentional contexts, but this one is clear and pretty well
> >studied.)
> >
> Coincidentally, your point about reifying propositions sounds very
> close to the point DOLCE makes in their approach to formalizing the
> notions of "description" and "situation" in their ontology.     (012)

This could be; I don't know all the details of DOLCE very well.    (013)

> I mentioned the dr/dd distinction because there is some relationship to 
> context I couldn't quite explain.
> Would it be fair to say then that precise reasoning over an ontology
> w.r.t. "context" would require :
> a) reifying the propositions whose interpretation is potentially subject 
> to a context of some kind    (014)

It is my view that a proper treatment of context involves reifying
propositions.  This is borne out by several treatments of the idea,
notably McCarthy's.    (015)

> De re: (exists (?x) (IsWorried Menzel [IsWatching ?x Menzel]))
> De dicto: (IsWorried Menzel [exists (?x) (IsWatching ?x Menzel]))
> we could say that the interpretation of "IsWatching" is subject to a
> context of some kind, namely, an individual (?x in de-re), or another
> proposition (IsWorried) which could itself have a larger "context"
> sensitvity of its own.    (016)

I'm not sure I'm following you here.  I don't see that the particular
example requires a notion of context.    (017)

> b) specifying the attribution of the modality of such "context"
> properties
> Perhaps you said it best with:
> > Typically (and very informally), a de dicto proposition involves the
> > attribution of a modal property (notably, necessity or possibility) to
> > a general proposition, whereas a de re modality involves the
> > attribution of a modal property to a specific individual. 
> Without (a) and (b) done across an entire ontology, then we have an
> over-hanging ambiguity w.r.t. a given proposition has any context
> sensitive interpretation at all and if so, relative to what.
> Once we have (a) and (b), then, we could further require that the
> modality of "context" properties should be a well-defined concept,
> kind of like what you hinted at w.r.t.  (1b) as a "dubious" context
> compared to (1a) which is reasonably well-defined.
> Does this make sense?    (018)

I'm afraid I had trouble following it.    (019)

> What kind of worries me is the idea that people who have studied
> "modal propoerties" for dr/dd purposes seem to be content w/ the view
> that "context" is about the scope of the quantifiers and that we have
> to be careful in placing these quantifiers.     (020)

I don't really see that anyone is committed to the idea that context is
about the scope of the quantifiers.  And the reason we are careful about
placing them is that we simply want to be able accurately to represent
an important difference in meaning.    (021)

> Ok, I can appreciate that and understand that these things matter
> w.r.t. automated reasoning and the sensibility of the inferences we
> get from it.    (022)

And simply for getting the meanings right.    (023)

> However, there is a larger concern at the level of using ontologies as
> a way to facilitate knowledge capture and representation in which it
> would be helpful to have some awareness about the relevance of
> clarifying what quantification scopes are meant and whether the
> dependencies between quantifiers and propositions and individuals or
> something else are really what is "meant" with the way an ontology is
> actually written.    (024)

Well, sure -- but isn't that just to point out that we have to be
careful about scope ambiguities when we are writing ontologies?    (025)

> Would you have suggestions w.r.t. where these concerns have been
> already discussed in the litterature or perhaps analyzed w.r.t. how to
> reason about them?    (026)

Nothing specific; there are many many books and articles (including a
lot on the web) on these topics.    (027)

-chris    (028)

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