Oups! There's a typo, should be [R' is-a R] of course.

2008/9/5 Lukasz Stafiniak <[log in to unmask]>:
> Dear Richard,
>
> On Wed, Sep 3, 2008 at 10:44 PM, Richard Hudson <[log in to unmask]> wrote:
>> But my approach is monotonic because it always starts at the
>> bottom, so instead of retracting older propositions, you never inherit those
>> propositions because the younger ones always come first.
>>
> Actually no, our approach is deterministic: G(A) = G'(A) for any
> saturated derivations G and G', but not (generally) monotonic: A < B
> (B contains A) doesn't imply G(A) < G(B); unless there's a structural
> constraint over A and B (which you state as starting at the bottom).
>
>> The problem that worries me is the one you mention in your last sentence,
>> where you suggest adding 'disjoint' links to relations that are mutually
>> exclusive such as 'after' and 'before'. This is very similar to Lyne's
>> suggestion, and I feel uncomfortable with it for the same reasons. One of my
>> main objections is that this problem only arises when two relations link the
>> same pair of entities, as in:
>> [1: word dependent X]
>> [2: word before X]
>> [3: word subject Y]
>> [4: word after Y]
>> [5: subject is-a dependent]
>> Here the conflict only arises because of [5], whereas most inheritance
>> conflicts arise because one entity is-a some other entity. This is why I'm
>> trying to re-frame the problem in terms of how relations (in contrast with
>> entities) inherit properties. I haven't got there yet, but I'm still
>> hopeful!
>>
> I thought that we've been talking about how relations are being
> inherited based on their hierarchy (so that the "subtyping" is checked
> on all three dimensions of relation triples). So that [W is-a word]
> implies [W subject' Z] which overrides [W dependent' Z] (dependent' is
> retracted, or if you prefer, not inferred in the first place). Then [W
> after' Z] and not [W before' Z]. (Notation: for relations R, [R is-a
> R'].)
>
> The problematic situation is when (forgive me my ignorance and
> artificial example):
>
> [6: word topic V]
> [7: word before V]
> [8: topic is-a dependent]
>
> If it so happens that [W topic' Z], then again both [W after' Z] and
> [W before' Z]. Only now if this situation is undesirable, we have to
> introduce properties for relations.
>
> Kindest Regards, Łukasz
>