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
>
>