[developers] Defaults in TDL

Guy Emerson gete2 at cam.ac.uk
Wed Sep 5 18:56:58 CEST 2018

I'm going to adapt Alex's extended Nixon diamond example from
http://moin.delph-in.net/StanfordDefaults , because it's a minimal working
example that captures the essence of Emily's example.

We have:

a := *top* &
  [ F /#1,
    G /#1 ].

x := *top* &
  [ P *top*,
    Q *top* ].

c := *top*.
d := *top*.

b := a &
  [ F.P c,
    G.P d ].

I take it that the behaviour we would like to have is that the default
re-entrancy between F and G is pushed down (in b) to a re-entrancy between
F.Q and G.Q.  As I understand, YADU (
http://www.aclweb.org/anthology/J99-1002 ) would discard the re-entrancy,
because it's not compatible with the hard constraints.  (Also, note that I
have deliberately left the features P and Q outside of the definition of a,
to mimic valence-min in Emily's example -- we can't represent the
re-entrancy between F.Q and G.Q in a, but only in b.)

I have a tentative proposal -- and I say tentative, because Ann has already
warned that YADU can blow up, and what I'm about to suggest would be
probably be even more likely to blow up.  So here be explosive dragons!

But with that warning aside... YADU represents a defeasible feature
structure in two parts - a normal feature structure (containing the hard
constraints), and a "tail" of default constraints.  In the above example,
only a has a non-empty tail, which just has one thing in it (the
re-entrancy).  With YADU, unifying two defeasible structures involves first
unifying their hard structures, combining the tails, and then discarding
anything in the tail that's incompatible with the hard structure.  My
proposed extension of YADU is not to discard incompatible constraints in
the tail, but rather "expand" them and keep whatever compatible constraints
are in this expanded set.

This "expansion" of constraints doesn't require new algebraic operations,
because we can use what's already in YADU -- in particular, the DefFS
operation (Definition 12 on page 70, which is page 16 in the pdf).
Essentially, DefFS takes a hard structure and a set of possibly
contradictory default constraints, and adds as many of the default
constraints as possible without creating a contradiction.  My proposal is
to apply DefFS *backwards* -- if we unify two hard structures and find that
some default constraint in the tail is now incompatible with the unified
hard structure, we can use DefFS to "expand" the default constraint.  We
treat the default constraint as the hard structure in DefFS, and we treat
the unified hard structure as the tail in DefFS.  This tells us how much of
the unified hard structure is compatible with the default constraint -- in
other words, we have "expanded" the default constraint in the context of
the unified hard structure.  We can now decompose this expanded structure
into individual constraints, and add them to the new tail, as long as they
don't contradict the new unified hard structure.

This might be clearest looking at the above example.  We would like to
unify b's feature structure with a's feature structure.  This gives us the
following hard structure, and tail (I am ignoring the types of tail
elements, for simplicity, because we aren't considering when one default
overrides another default):

[ F x & [ P c,
          Q *top* ],
  G x & [ P d,
          Q *top* ] ].
tail: { F=G }

To apply DefFS, we first credulously add the hard structure's constraints
to the tail element.  This gives a pair of structures (which differ in the
value of F.P):

[ F #1 & x & [ P c,
               Q *top* ],
  G #1 ].

[ F #1 & x & [ P d,
               Q *top* ],
  G #1 ].

DefFS gives us the generalisation of these two structures, which is:

[ F #1 & x & [ P *top*,
               Q *top* ],
  G #1 ].

We can break this up into individual constraints: { F:x, G:x, F=G, F.P=G.P,
F.Q=G.Q }

Of these five constraints, the first two are already part of the unified
hard structure, and the second two are incompatible with it.  So we are
left with a single element to keep in the tail: F.Q=G.Q.  So, expanding
elements in the tail rather than discarding them gives:

[ F x & [ P c,
          Q *top* ],
  G x & [ P d,
          Q *top* ] ].
tail: { F.Q=G.Q }

Finally, the last step (as with YADU) is to apply DefFS, which would give
the following compiled structure used at runtime (supposing I've understood
what is supposed to happen at compile time -- I wasn't sure where to look
for this documentation):

[ F x & [ P c,
          Q #1 ],
  G x & [ P d,
          Q #1 ] ].

Am Di., 4. Sep. 2018 um 23:10 Uhr schrieb Emily M. Bender <ebender at uw.edu>:

> Dear Mike,
> Thanks for bringing up this issue.  At the 2010 DELPH-IN Paris Summit, Ann
> and I had a further conversation about this, from which I took the homework
> of typing up what it is I'd like to have (as a grammar developer, and
> especially from the point of view of the Matrix) wrt to defeasible
> constraints.  Here's what I wrote down later that year (Oct 27):
> Dear Ann,
> Here, with much more delay than I intended, is the write up
> I promised of my (reconstruction of my) understanding of where
> we ended up in our discussion of defeasible identity constraints
> over crepes in Paris.
> First, why I want it:
> In lexical rules, we want to be able say (like in SWB) that
> the value of certain features (HOOK, CAT, ARG-ST) is shared
> between the mother and the daughter unless the rule contradicts
> this.  If the rule does contradict it, then we want only the information
> specifically stated as such to change, and the rest "around" it,
> to be shared.
> For a concrete example, take a hypothetical lexical rule that
> changes the case on the first complement from acc to dat.
> First, here's the general lex rule type:
> lex-rule := phrase-or-lexrule & word-or-lexrule &
>   [ NEEDS-AFFIX bool,
>                              LAST #last ],
>                         HCONS [ LIST #hfirst,
>                                 LAST #hlast ] ],
>     DTR #dtr & word-or-lexrule &
>         [ SYNSEM.LOCAL.CONT [ RELS [ LIST #first,
>                                      LAST #middle ],
>                               HCONS [ LIST #hfirst,
>                                       LAST #hmiddle ] ],
>           ALTS #alts ],
>     C-CONT [ RELS [ LIST #middle,
>                     LAST #last ],
>              HCONS [ LIST #hmiddle,
>                      LAST #hlast ]],
>     ALTS #alts,
>     ARGS < #dtr > ].
> And a subtype with the defeasible identity indicated
> (using /# for now):
> defeasible-identity-lex-rule := lex-rule &
>   [ SYNSEM.LOCAL.CAT <http://synsem.local.cat/> /#cat,
>     ARG-ST /#arg-st,
>     C-CONT.HOOK /#hook,
>     DTR [ LOCAL [ CAT /#cat,
>                            CONT.HOOK /#hook ],
>              ARG-ST /#arg-st ]].
> The lex rule definition itself would just look like this:
> acc-to-dat-obj-lex-rule := lex-rule &
> The intended behavior is for that to compile into a rule that
> includes constraints like these (I'm sure I'm missing some here):
> acc-to-dat-obj-lex-rule (expanded):
>  [ SYNSEM.LOCAL.CAT <http://synsem.local.cat/> [ HEAD #head,
>                                       VAL [ SPR #spr,
>                                                SPEC #spec,
>                                                SUBJ #subj,
>                                                COMPS [ REST #rest,
>                                                              FIRST [
> NON-LOCAL #non-local,
>   LOCAL [ CONT #cont,
>                 CAT [ VAL #val,
>                           AGR #agr,
>                           HEAD.CASE dat ]]]]]],
>   C-CONT.HOOK #hook,
>   ARG-ST #arg-st,
>                                        CAT [ HEAD #head,
>                                                  VAL [ SPR #spr,
>                                                           SPEC #spec,
>                                                           SUBJ #subj,
>                                                           COMPS [ REST
> #rest,
>  FIRST [ NON-LOCAL #non-local,
>             LOCAL [ CONT #cont,
>                           CAT [ VAL #val,
>                                    AGR #agr,
>                                    HEAD.CASE acc ]]]]]]],
>            ARG-ST #arg-st ]].
> What I remember from Paris is that we decided it would be best to
> encode these constraints not directly in the type definition as
> I did above in defeasible-identity-lex-rule but in a collateral file that
> instructs the LKB to do something special with certain feature paths
> on instances of certain types at compile time.
> We also worked out that we would only be able to "push down" the identity
> constraint to features that were necessitated by the types invoked
> in the rule.  Thus in the example above, we know that SPR, SPEC and SUBJ
> need to be identified because the value of VAL is necessarily "valence"
> (and not valence-min) as we've mentioned COMPS. But if CASE were
> appropriate
> for both noun and comp (for example), then we wouldn't be able to know to
> put in identity constraints for any other features of noun (or comp).  If
> the daughter in fact had a constraint on one of these other features,
> it wouldn't be copied up to the mother.  Relatedly, we lose the actual
> value because we can't identify HEAD while changing CASE.  (So here, the
> grammar
> writer would need to stipulate [HEAD noun], say, on the mother.)
> In Paris, I remember being convinced that the added simplicity in defining
> lexical rules would out-weigh the lack of transparency noted above.  And
> I'm still pretty sure I agree with that.  One thing in favor of that view
> is that if a rule
> defined using the defeasible identity type didn't have the expected behavior,
> the
> grammar engineer could always either add constraints or side-step
> that type and hand-specify all the desired identities.
> A further complication I noticed while writing out this example is the
> interaction between defeasible and indefeasible identity tags.  Two
> conditions
> to consider:
> 1) The rule inherits a constraint (e.g., from the type of the DTR value)
> that
> the REST of the ARG-ST is the same as the COMPS list.
> 2) The rule doesn't inherit such a constraint, but the constituent that
> serves as the daughter identifies its ARG-ST.REST and its COMPS.
> I think (2) isn't a problem (this is very similar to things that confused
> Tom, Ivan and I as we designed the lex rules in the textbook, though, so
> I'm
> not feeling very confident just now!).  As for (1), it could entail a
> similar
> push down of identity inside the ARG-ST.  But what if the ARG-ST to
> DTR.ARG-ST identification were a non-defeasible identity constraint?
> Maybe that's just a broken grammar that either shouldn't compile or would
> just have surprising behavior.
> I hope you are still interested in this problem. Let me know if/when it
> would
> be useful to have a grammar to play with.
> Thanks!
> On Tue, Sep 4, 2018 at 10:42 AM, goodman.m.w at gmail.com <
> goodman.m.w at gmail.com> wrote:
>> Hello everyone,
>> I appreciate the feedback I've received in previous messages in my
>> attempts to dust off neglected corners of TDL syntax, and I'd now like to
>> bring up "defaults", or "defeasible constraints" (I believe these refer to
>> the same thing). Are we prepared to start supporting
>> defaults/defeasible-constraints in our processors and using them in our
>> grammars? Or should we discard them as an undesired experimental feature
>> (i.e., declare them to *not* be part of DELPH-IN TDL)?
>> Further information:
>> Currently, only the LKB supports them (and maybe PET?). As I understand,
>> they are a compile-time feature, meaning that they change how the grammar
>> is compiled and that there is no longer a notion of "defaults" during
>> run-time. I don't think the use of defaults causes any change in the
>> competence or performance of a grammar.
>> The benefit of defaults is for the grammar engineer as it can reduce the
>> amount of boilerplate code and make the grammar source code more intuitive.
>> I think any result that makes grammar writing easier is a big win. The
>> differences it creates between the source-code form of the grammar and the
>> compiled hierarchy, however, can complicate debugging (e.g., interactive
>> unification).
>> Some links:
>>   - http://www.aclweb.org/anthology/J99-1002
>>   - http://moin.delph-in.net/ParisDefeasibleConstraints
>>   - http://moin.delph-in.net/StanfordDefaults
>> --
>> -Michael Wayne Goodman
> --
> Emily M. Bender
> Professor, Department of Linguistics
> University of Washington
> Twitter: @emilymbender
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