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Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the re

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 14 Jan 2008 10:46:33 -0600
Message-id: <p06230900c3b13b4789f9@[]>
At 4:16 AM -0500 1/14/08, John F. Sowa wrote:
>Duality may make two different kinds of operations look symmetrical,
>but that symmetry can hide enormous differences in practice.
>  > The relationship between ist and ist* is symmetrical. They are
>  > duals. We could adopt either as the real meaning of 'true in
>  > a temporal context' and then the other would be defineable:
>  > and only one of these strategies gives McCarthy's axiom (the
>  > other gives the dual axiom, ie transparency under DISjunction.)
>  > So what justifies the choice of one rather than the other as
>  > fundamental? Is there any linguistic evidence for this?
>There is an overwhelming amount of evidence of many different kinds:    (01)

As far as I can see, none of this, below, has any 
bearing on the point at issue. Nothing in context 
logic has anything particularly to do with making 
visual observations, and you yourself define a 
context as a piece of TEXT.    (02)

My point is that there is no particular reason, 
other than aesthetic preference, to interpret 
"true in a time-interval" as meaning 'true 
throughout the interval' rather than 'true at 
some time during the interval'; and that more NL 
uses (at least in Western languages) where a 
proposition is coupled with a reference to a 
time-interval are in fact understood in the 
latter way rather than the former.    (03)

>   1. The only two logical operators that can be directly observed
>      are 'and' and 'there exists'.  You can see A, and B, and C,
>      and D...   That implies that things that cause the percepts
>      (or hallucinations) of things like A, and B, and C, and D...
>      must exist.
>   2. A negation can never be observed.  A failure to observe something
>      might mean that you haven't looked hard enough, you were looking
>      in the wrong direction, it was smaller than you expected, etc.
>      Russell once joked that he could not get Wittgenstein to admit
>      that the statement "There is no hippopotamus in this room" was
>      absolutely certain.  But W. was right.  There is no way to prove
>      that a very tiny hippopotamus -- perhaps an embryo of a hippo or
>      one that had been miniaturized by a reducing ray -- wasn't lurking
>      under the rug or that they weren't at the zoo and merely imagining
>      that they were in an apartment at Cambridge U.  A negation can only
>      be inferred from observation plus many assumptions about what would
>      be the case if the opposite were true.
>   3. Any operator defined in terms of negation is just as problematic,
>      if not more so.  You might be uncertain whether you saw Sam or Joe,
>      but you didn't see their disjunction.  You saw a man whom you
>      couldn't identify for certain.  But that does not mean you
>      saw a disjunction.
>   4. Although 'every' is dual to 'some', you only need one observation
>      to see *some cow* but it's impossible to see *every cow*.
>   5. Implication is impossible to observe.  See Hume, for example.
>   6. In theorem proving, conjunction and the existential quantifier
>      are the easiest to deal with.  But disjunctions in the consequent
>      cause the highly efficient Horn-clause subset of logic to become
>      NP complete.  FOL without universal quantifiers is as easy to
>      deal with as propositional calculus.  But universals require a
>      much more complex approach.
>   7. Finally, every observation sentence can be stated in NL (or in any
>      version of logic) with only conjunctions and existentials.  All
>      languages express those two operators in essentially equivalent
>      ways.  But all other operators are problematical.  Negations raise
>      many different kinds of puzzles (negation as failure, as absence,
>      as denial, as prohibition, etc.).  Some languages have inclusive
>      disjunction, some have exclusive disjunction, some have both, and
>      some are not clear about which is intended.  If-then isn't always
>      clearly expressed in all languages, and when something like it is
>      available, it is more likely to be some kind of "strict" implication
>      rather than material implication.  And various languages express
>      different variations of universal quantifiers in different ways,
>      none of which, of course, represent an observation.
>  > The point however is that the context approach to temporal reference
>  > does not allow tenses: it sets out to replace them by context-
>  > reference....  The actual inner sentences are always in a 'present'
>  > tense (actually, are tenseless.)
>I agree.  That is what I usually do:  attach a relation for point-
>in-time (PTim)    (04)

Ah, Points in time are different. There, indeed, 
it is plausible to claim transparency for all the 
propositional connectives, including negation. 
(see 'context mereology') But that isn't the 
claim that is usually made for contexts: 
intervals, not points, are the basic temporal 
context.    (05)

>  to the outside of a context box and put tenseless
>statements inside.  The problems and paradoxes aren't caused by
>what's inside the context box, but by problematical cases on the
>outside.  This would require more discussion, but I believe that
>problems arise because of inadequate axioms and representations
>on the outside, not the inside of the context box.    (06)

My point is that this all has nothing at all to 
do with contexts. It is all about times, and 
should be understood and discussed in the context 
of the huge body of excellent work already done 
on temporal reasoning and temporal logics.    (07)

>  > It is no good quoting dictionaries in discussions like this. There
>  > are FAR more notions of 'context' than this. McCarthy gives the
>  > following examples...
>But all of those examples involve relations and axioms on the
>*outside* of the context box.    (08)

You are entirely missing my point. To say this is to beg the question.    (09)

>  That was the point I was making:
>it is only necessary to have one very simple syntactic mechanism,
>such as a box.  Then the open-ended number of special cases for
>the semantics can be handled with axioms outside the box.    (010)

And my point is that there is no reason at all to 
even suspect that these various, widely 
different, phenomena can even be usefully 
discussed under one heading, let alone adequately 
represented by one simple syntactic device. To 
make this assumption, without any evidence, and 
in the face of decades of research on the various 
topics, none of which remotely suggests any 
tendency to converge, seems like a step backwards 
rather than forwards. Particularly when these 
promised 'outer axioms' which are going to do all 
the work have never actually been exhibited.    (011)

>  > That is not the point. The point is that others use it [the
>  > word 'context'] to justify bad scholarship, claim originality
>  > for old ideas, and repeat old mistakes.
>That's their problem, not mine.  I'm just using the word for one
>very simple syntactic mechanism    (012)

I really don't think you are being entirely 
honest here. If by "context" you really do mean 
simply to refer to the actual syntactic 
mechanism, then you are mis-using the word, 
because that certainly isn't what everyone else 
means by it. But I suspect that in fact, you 
actually intend this syntactic device to mean 
something, and that you have some examples in 
mind: and these are the actual contexts that you 
are talking about.    (013)

>with one simple claim:  all the
>hard stuff goes on outside the box.
>  > There is no such definition, and McCarthy (IMO, correctly) says
>  > so explicitly. The only definition is the context logic itself.
>I quoted a very clear definition from a typical dictionary:
>a context is a piece of text.  Context logic is not inside the
>box, but in whatever axioms anyone wants to write on the outside.    (014)

Then its not context LOGIC. That is the point. 
IKL can express such axioms very handily without 
needing to mention contexts in its metatheory at 
all.    (015)

>As I said before, there are infinitely many axioms that people
>might state about contexts, and they should be allowed to do so.    (016)

Of course, and the same applies to froodles. But 
in order to judge whether their axioms make 
sense, we need to have some intuitions about 
froodles to compare the axioms to. Similarly with 
contexts: and my claim is that there aren't any 
useful intuitions about contexts, as a category 
(because there isn't any category to have 
intuitions about.)    (017)

>  > What have CGs have to do with a discourse?  The NL notions of
>  > context all seem to arise in some kind of conversational or
>  > discourse setting:  but logics aren't used in such settings.
>  > They are used to make assertions, not to have conversations with.
>Discourse and conversations are just text.    (018)

Nonsense. Conversations, in particular, are much more than text.    (019)

>  I might use multiple
>boxes to enclose different turns of the conversation, and put
>relations on the outside of the boxes to relate them.    (020)

You are here describing the conversation, not 
taking part in it. The reasoning that is done 
when we read about a conversation is not the same 
as that which we need to do in order to converse.    (021)

>  A speech
>act can be represented by a statement in a context and an
>intensional verb outside that context.    (022)

I disagree. It can perhaps be described in such a 
way (though you need to be very careful about how 
'directly' the speaker is being quoted), but that 
is not to say that it can be adequately 
represented in that way. A perfect such reasoner 
would be able to follow Jane Austin novels, but 
would be aphasic when required to actually take 
part in a conversation.    (023)

>  See McCarthy's Elephant
>article, for example.    (024)

That article is muddled.    (025)

>  He certainly intended to use logic
>for such things -- I'll admit it's still a wide-open research
>area, but that does not mean logic is irrelevant to it.    (026)

I agree, not irrelevant. But the relationship(s) 
of logic to the topic are complex. Too complex to 
be handled by a single simple syntactic device.    (027)

>  > You havn't said what "true in a context" means.
>Of course not.  That is the purpose of the open-ended range of
>axioms that can be stated outside the context box.    (028)

You miss my point. You havn't said what YOU mean 
by that, informally, so that we might judge 
whether or not any proposed axioms make sense or 
are intuitively reasonable. You write as though 
the meaning was obvious, but it isn't. McCarthy 
makes the same mistake.    (029)

>  > And what are some of those axioms? Or even ONE of them?
>For starters, you can take any axioms that anybody has ever
>proposed for contexts and assert them outside the context box.    (030)

OK, do you know of any? I don't. Lets make an ontology of contexts. You start.    (031)

Pat    (032)

>I don't believe that any finite number can cover all the uses.
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