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Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

To: "Barker, Sean (UK)" <Sean.Barker@xxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 1 Jun 2007 12:06:34 -0700
Message-id: <p06230919c286193faf2f@[192.168.1.4]>
>Duane,
>       unfortunately, once I get into a 2d environment, I'm not sure
>that "!exists 3d" is meaningful, though it might be in a meta-world
>embedding the 2-d world.
>
>Sean Barker
>0117 302 8184
>    (01)

This message, and indeed this sub-thread, 
illustrate perfectly what seems to me to be the 
key advantage of using a 'context ontology' (as 
IKL does: that is, treating contexts as objects 
and making non-contextual assertions about them) 
as opposed to a 'context logic' (that is, a logic 
in which assertions are understood as being made 
in a context and interpreted there using 
contextually local criteria). In a word, contexts 
in a context logic make meaningful things 
meaningless.    (02)

Ask yourself: does it make sense to talk of 3-d 
things? Yes, of course it does. Are 3-d things of 
interest when talking of 2-d things? Yes, of 
course they are: they are often the things that 
have 2-d surfaces or 2-d projections, for 
example. An adequate description of a knife 
cutting a block of cheese involves entities of 
all dimensions from 4 down (the cutting process 
is 4-d; the block is 3-d; the newly revealed 
surface of fresh cheese is 2-d and the location 
of where the knife edge meets the cheese, where 
the action is, is 1-d.) So what advantage or 
utility is there is a framework which, when it 
talks of 2-d things, makes it incoherent to also 
talk of 3-d things? True, we might want to 
consider a 'local universe' of purely 2-d 
entities: but we can do that (or perhaps, if one 
is being a logical purist, can *model* it) by 
simply talking about the set of 2-d things - 
which amounts, in a classical logic, to having a 
property of 2-dimensionality and predicating it 
of things in our quantifiers:
(forall ((x 2-D-thing)) ... ) instead of (forall (x) .... )
- and then can make any local assertions about 
the 'universe' of 2-d entities that we want. 
Nothing is gained by pretending that when we are 
"in" (whatever that means) a 2-d context, that 
all non-2-d things have some how vanished or 
become inaccessible. To think about 2-d entities 
is not to enter Flatland: it is simply to be able 
to make assertions about a subset of the universe 
of discourse.    (03)

Pat    (04)


>
>>  -----Original Message-----
>>  From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>>  [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
>>  Duane Nickull
>>  Sent: 31 May 2007 17:10
>>  To: [ontolog-forum]
>>  Subject: Re: [ontolog-forum] Ontology,Information Models and
>>  the 'Real World': Contexts
>>
>>  Sean:
>>
>>  Assuming you have modeled correctly, there should logically
>>  !exists 3d entity in a 2d environment, should there?
>>
>>  Duane
>>
>>
>>  On 5/31/07 1:35 AM, "Barker, Sean (UK)"
>>  <Sean.Barker@xxxxxxxxxxxxxx> wrote:
>>
>>  >
>>  > What happens if a context/possible world is such that the
>>  proposition
>>  > ceases to be a proposition? That is, it ceases to evaluate
>>  to true or
>>  > false? For example, "the volume of a cube is the cube of
>>  the length of
>>  > its side" is meaningless in a 2-D world, since there is no
>>  concept of
>>  > volume. Similarly (A/B > 1) is meaningless in a context
>>  where A and B
>>  > are both zero.
>>  > The tricky part is that there is no order of evaluation in
>>  classical
>>  > logic, so, in the latter case, adding guards on the
>>  context, such as
>>  > (A != 0) AND (B != 0), still leaves the combined
>>  proposition meaningless.
>>  >
>>  > Sean Barker
>>  > 0117 302 8184
>>  > 
>>  >
>>  >> -----Original Message-----
>>  >> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>>  >> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf
>>  Of John F.
>>  >> Sowa
>>  >> Sent: 31 May 2007 02:54
>>  >> To: [ontolog-forum]
>>  >> Subject: Re: [ontolog-forum] Ontology,Information Models and the
>>  >> 'Real World': Contexts
>>  >>
>>  >>
>>  >>                *** WARNING ***
>>  >>
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>>  >>      Keep this in mind if you answer this message.
>  > >>
>>  >> Wacek, Ken, Pat, Ingvar, et al.,
>>  >>
>>  >> I agree that one should use technical terms in a way that stays
>>  >> fairly close to traditional usage.  But the tradition has a lot of
>>  >> branches.  In some branches, a proposition is fairly close to a
>>  >> sentence, but with the option of considering a restatement in a
>>  >> different language to be "the same" proposition.
>>  >>
>>  >> I take that to mean that a proposition is the language-independent
>>  >> "meaning" or "intension" of a sentence, and that the truth
>>  value is
>>  >> evaluated in terms of some "extension" or universe of discourse.
>>  >> If somebody changes the extension or universe of
>>  discourse, then the
>>  >> truth value may change.  But the intension remains fixed.
>>  >>
>>  >> That interpretation is consistent with most 20th-century work on
>>  >> modal and other kinds of intensional logics.  Montague,
>>  for example,
>>  >> defined the intension of a sentence to be a function that maps
>>  >> possible worlds to truth values.
>>  >> Different possible worlds are different extensions, but
>>  the function
>>  >> (intension) remains fixed.
>>  >>
>>  >> Although I prefer Dunn's semantics of laws and facts to a
>>  >> Kripke-Montague version with possible worlds, Dunn's approach
>>  >> produces exactly the same truth values for the same sentences.
>>  >> That implies that the same sentence with the same intension
>>  >> (proposition) may have different truth values in different
>>  >> circumstances.  (I don't care whether anyone chooses to
>  > use the terms
>>  >> 'possible worlds', 'universes of discourse', or 'contexts'
>>  for those
>>  >> circumstances.)
>>  >>
>>  >> As Ingvar pointed out, Quine requires propositions to have fixed
>>  >> truth values.  But that follows from the fact that he does
>>  not allow
>>  >> different possible worlds or contexts.
>>  >>
>>  >> Although I do not like the notion of possible world, I would agree
>>  >> with the modal logicians that any theory of modal logic
>>  should permit
>>  >> the same intension (proposition) to have different truth values in
>>  >> different extensions (universes of discourse).
>>  >>
>>  >> I also agree with Pat that the word 'context' has been used in too
>>  >> many confused and confusing ways.  But I don't like either of the
>>  >> following ways of talking:
>>  >>
>>  >> KC>> In that sense, a change in context BECOMES a
>>  >>>> change in meaning of a proposition
>>  >>
>>  >> PH> No, that is muddled. That is exactly what does NOT happen.
>>  >>> A proposition never changes its meaning. The SENTENCE  >
>>  >> expresses different propositions.
>>  >>
>>  >> I wouldn't say that a proposition changes its meaning
>>  because I would
>>  >> prefer to say that a proposition *is* the meaning of a
>>  sentence.  I
>>  >> also would not say that a sentence whose indexicals were
>>  resolved to
>>  >> specific referents could express two or more different
>>  propositions.
>>  >>
>>  >> I'm sure that one can find logicians such as Quine who
>>  would disagree
>>  >> with this interpretation.  But I believe that it is
>>  consistent with
>>  >> those logicians who are more tolerant of modal logic.  And since I
>>  >> want to represent modal sentences in NL, I prefer to accommodate
>>  >> their usage (even though I use Dunn's semantics rather than
>>  >> Kripke's).
>>  >>
>>  >> John
>>  >>
>>  >> 
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