As long as you've opened the door to red herrings.....

I don't know that I've ever stated this before in polite company, but I
think that some form of negation (with some sense of intensional class
complements) will ultimately prove to be necessary at the same level of
abstraction as the argument and value links you mention.

The psychological reality is that any time I convince you that there are
basketballs, I've also convinced you that there are non-basketballs.
Therefore, any time I convince you that [X isa basketball], I've prevented
you from also believing that [X isa non-basketball] (or [X not-isa
basketball], which is perhaps the more probable abstraction). You can
follow this as far up the isa-hierarchies you like, of course: By
convincing you that [X isa bird], I've prevented you from also believing
that [X isa lawnmower] because (one way or another) [lawnmower isa
non-bird].

So I think that if I've convinced you that [breakfast before lunch], then
I've prevented you from also believing that [breakfast non-before lunch].

WG handles basketballs, non-basketballs, birds, non-birds and lawnmowers
in a particular way involving isa hierarchies and a default inheritance
algorithm that operates on those hierarchies. It eschews any explicit
representation of non-basketballs or non-birds (or of a not-isa relation)
in favor of a Closed World Assumption (CWA), and is in good company for
doing so.

The way WG currently handles befores and non-befores is different. An
'after' relation exists as well as 'before', but the fact that [after isa
non-before] is not captured. Hence the problem under discussion in this
thread.

So let me now throw a few claims out there:

(a) The CWA is not psychologically plausible. Human reasoners do not
arrive at the conclusion that [lawnmower isa non-bird] by standing *above*
the isa hierarchy and eyeballing the fact that 'lawnmower' and 'bird' are
cousin nodes, i.e. by a chain of inference that is directly dependent on
the CWA. (This is how AI algorithms generally work, though.)

(b) Human reasoners arrive at the conclusion stated above by testing the
hypothesis [lawnmower isa bird] and very quickly and easily falsifying it
on the basis of properties (such as animacy) which are incompatible.

(c) This implies that human reasoners can very quickly and easily convert
between an assertion and its negation.

(d) This applies not only to the negation of isa assertions, but to the
negation of argument-value assertions as well: We know that breakfast
doesn't come after lunch because we've quickly and easily falsified the
assertion that [breakfast not-before lunch].

(e) Inferences such as that in (d) are only possible in *language*
processing if there's a way to get from 'after' to 'not-before'.

(f) WG needs a way to represent the negation of nodes, representing an
intensional complement of whatever the unnegated node represents. The use
with relation nodes has been illustrated here; my gut feeling about the
negation of entity nodes is that the implicit use of the CWA will break
down eventually for certain cases.


Any thoughts?

-- Mark




jasper holmes wrote:
> Finally, the red herring:
>
> I originally thought that the problem would disappear in the face of the
relatively new (or anyway only recently formalised) treatment of
relationships as just more concepts (this is all in Language
> Networks), but I discovered that it just gives you a clearer way to
express the problem.
>
> Under this treatment, the triples [X subject Y] etc are lists of the
three associates (argument, function, value) of some (unnamed) concept
which forms the grammatical representation of the dependency, so [word
before X] and [word after Y] mean word<argument-before-value>X and
word<argument-after-value>Y. Now we see the problem: Y isa X (because
[word dependent X] and [word subject Y] and [subject isa dependent]), so
word<argument-after-value>Y and word<argument-before-value>Y. The
problem is there's no limit on the number of things you can be the value
of.
>
> Jasp
>
> In that case, since Y isa X (because both are variables and subject isa
dependent),
>
> On 9/4/08, jasper holmes <[log in to unmask]> wrote:
>> So the question is, if both of these solutions can be made to work,
>>  which should we prefer. The answer to that is, of course, that it
depends what you want it for. You might take the view (I do) that the
second is the most psychologically real. But then you might feel at
one and the same time that the first would be easier to implement in
an algorithm, especially if you were already using [x before y] and [x
after y] in your computer application to save hassle (and I know it
does save hassle: when you start counting every little arc they soon
add up). You may or may not (I do) want to bear in mind that this is
and remains a hack.
>>  So what do you want? Psychological reality or a working computer
model? Mark, I guess, would argue that if your hacks don't correspond
to psychological reality then sooner or later you are going to come up
against something that you can't model any more without going back and
undoing the hacks. Dick might also say that the whole point of the
computer model is to represent what we really think grammar is like
(to test our theory of grammar as much as anything else). The
>>  principles of WG plus the correct grammar structures should always
give the correct result; and if they don't then you need to revisit
the grammar (or the principles!).
>>  Japs
>>  On 9/4/08, jasper holmes <[log in to unmask]> wrote:
>>  > I don't mean by cutting in at the beginning like this to discount
the
>>  >  very useful discussion that has already taken place. It's just I
couldn't find anywhere else to sensibly come in.
>>  >
>>  >  This is a tricky one, isn't it and I remember we struggled with it
when we were in the same situation before. I think, though, that we
largely solved it, or caused it to disappear.
>>  >
>>  >  I think we looked at possible ways of putting two relationships
into
>>  >  conflict without one (transitive)isa-ing the other, rather as Lyne
>> has
>>  >  been suggesting, so that 13 would block 14 because of 'after'
overriding 'before'. We tried to state this in terms of some common
ancestor, as Dick is doing below. I think my favourite solution
>> along
>>  >  these lines was to say that there are some relationships that you
>> can
>>  >  only have one of: you can have as many dependents as you like so [X
extractee Y] doesn't override [X object Y], but you can only have
>> one
>>  >  'ordering' (let's call it that for now, until the next paragraph
anyway), so [X after Y] does override [X before Y].
>>  >
>>  >  Can't remember exactly why this didn't work out, but I don't think
>> it
>>  >  did. Fortunately, however, there is another solution, and this
>> follows
>>  >  Lynes other suggestion: [X after Y] and [X before Y] are not the
>> right
>>  >  way to represent the ordering relationships. I'd say something more
like this:
>>  >  [91: word dependent X]
>>  >  [92: word time Pw]
>>  >  [93: X time PX]
>>  >  [94: Pw < PX] ('less than')
>>  >  [95: subject isa dependent]
>>  >  [96: word subject Y]
>>  >  [97: Y time PY]
>>  >  [98: Pw > PY] ('greater than')
>>  >
>>  >  Then, for what it's worth, 97 overrides 93, since Y isa X.
>>  >
>>  >  I've been trying to think of other examples, in case they aren't
amenable to this kind of solution, but I can't. Perhaps there are
some; it's a bit of a hostage to fortune I guess to rely on none
turning up.
>>  >
>>  >  I think I've presented two almost solutions. I evaluate them (very
briefly) in the next message. Then there follows a message with a
>> red
>>  >  herring.
>>  >
>>  >
>>  >  Jasper
>>  >
>>  >
>>  >
>>  >  On 8/28/08, Richard Hudson <[log in to unmask]> wrote:
>>  >  >
>>  >  >  Dear All,
>>  >  >  After a long silence on this list, here's a question for you
all.
>> It's
>>  >  > about how to make default inheritance work properly. We (at
least,
>> Mark Line
>>  >  > and I) have an algorithm which promises to work reasonably
>> smoothly in a
>>  >  > computer system that Mark is building (and that should work more
>> generally
>>  >  > as well, of course), but only for one of the two kinds of
>> situation that
>>  >  > default inheritance has to deal with. My question is whether
>> anyone has any
>>  >  > bright ideas for handling the other kind. Here goes with the
>> problem.
>>  >  >
>>  >  >  DI has to take as input a proposition [1: A R V], where A is the
>> argument,
>>  >  > R is the relation and V is the value, and apply it to some
>> instance of A,
>>  >  > called A'. "Applying it" means deciding whether or not to inherit
>> [2:A' R'
>>  >  > V'], a copy of [1], in the light of  the store of propositions P
>> already
>>  >  > stored for A'; and the crucial question is whether P contains a
>> proposition
>>  >  > which overrides [2].
>>  >  >
>>  >  >  For example, assume this database:
>>  >  >  [3: Bird locomotion flying]
>>  >  >  [4: Penguin locomotion swimming]
>>  >  >  [5: Penguin is-a bird]
>>  >  >
>>  >  >  Store of propositions about Penguin', some particular penguin:
[6: Penguin' isa Penguin]
>>  >  >  [4': Penguin' locomotion' swimming']  {inherited from [4]},
where
>>  >  > [locomotion' is-a locomotion]
>>  >  >
>>  >  >  Question: can Penguin' also inherit [3']?
>>  >  >  [3': Penguin' locomotion' flying']
>>  >  >
>>  >  >  The question assumes a potentially inheritable stored
proposition
>> IP and
>>  >  > some potential overriding proposition OP - e.g. in the above IP =
>> [3] and OP
>>  >  > = [4'].
>>  >  >
>>  >  >  Type 1 inheritance:
>>  >  >  Where IP and OP have the same relation but different values.
This
>> is easy,
>>  >  > because we can define 'the same relation' as being where:
>>  >  >
>>  >  > IP = [A1 R1 V1]
>>  >  >  OP = [A2 R2 V2]
>>  >  >  and [R2 is-a R1].
>>  >  >  There's not even any need to check the relation between V1 and
>> V2, because
>>  >  > it doesn't matter whether or not they're related; either way, the
inheritance system ignores IP.
>>  >  >
>>  >  >  Type 2 inheritance:
>>  >  >  Where IP and OP have the same value but different relations.
This
>> is the
>>  >  > hard one, and I'm embarrassed to say that although I've been
aware
>> of the
>>  >  > problem for years, I've also managed to avoid thinking about it.
>> It's
>>  >  > painfully easy to illustrate from word order rules:
>>  >  >  [7: word dependent X]
>>  >  >  [8: word before X]
>>  >  >  [9: word subject Y]
>>  >  >  [10: subject is-a dependent]
>>  >  >  [11: word after Y]
>>  >  >
>>  >  >  Precisely what is it that prevents some word W from inheriting
>> the
>>  >  > following?
>>  >  >  [12: W subject Z]
>>  >  >  [13: W after Z]
>>  >  >  [14: W before Z]
>>  >  >  I've had various thoughts, but none that I really like, so I'd
be
>>  >  > interested to hear other ideas.
>>  >  >
>>  >  >  Best wishes, Dick
>>  >  >
>>  >  >
>>  >  >
>>  >  > --
>>  >  >
>>  >  >
>>  >  > Richard Hudson, FBA. Emeritus Professor, University College
London
>>  >  >
>>  >  > My web page: www.phon.ucl.ac.uk/home/dick/home.htm
>>  >  > Why I support the academic boycott of Israel:
>>  >  > www.phon.ucl.ac.uk/home/dick/home.htm#boycott
>>  >  > My latest book: Language Networks. The New Word Grammar
>>  >  >
>>  >  >
>>  >
>
>


-- Mark

Mark P. Line
Bartlesville, OK