An attempt to put constraints on compositionally always expressed in terms of DMRSs. 2001 MRS algebra and the later RMRS version doesn't really correspond to what the grammar is doing. And messy, lots of messing around with variables. Last few years working with DMRS, which is variable free.
A couple of years ago, decided to try writing a grammar that directly produces DMRSs (in a small grammar). Turned out to be easier than expected. In some ways easier than producing MRSs.
Could do that and replicate MRS algebra, but decided to try and produce a set of constraints on what composition means in terms of the operations on the combinations of DMRS graphs.
Intuition: e.g. a long complicated sentence with a clause right down at the bottom, can't attach something to that clause unless you've somehow made it available. Notions of availability of the interior of the semantic structure, can only get hold of things with explicit pointers. Important not only for elegance but also because the generator depends on it.
Looking for examples of tricky things that might test the limits of the algebra.
Dan: That ladder is too tall to climb --- tall, by virtue of being modified by too, it now takes a VP complement. Also tall enough, as tall, and that VP complement is gappy and controlled by the subject of the thing modified. Maybe one step removed from the easy adjectives.
Berthold: Is that like the quasi-modal infinitives, also in German and French, where they show up in tough constructions (which aren't long-distance).
Ann: Let's do the too tall to climb example first.
Dan: The adjective tall by itself doesn't have an ARG2/doesn't take any complements. *This building is tall to climb. Any adjective specified by intensifier too can take a gappy VP complement, where the XARG (SUBJ or MOD) of the adjective is identified with the gap in the VP. (Modifier use: a building too tall to climb.) More complicated than easy adjectives, because the too isn't interested in that argument. If it were a lexical rule from tall to too tall it wouldn't be different from easy, but it has to be syntactic: too tall and heavy to carry.
Guy: Does too need to have its own XARG, or can it identify the XARG of it's SPEC with its own XARG?
Dan: I think that's how I do it.
Emily: And how does the COMPS thing end up on the mother?
Dan: specifier-head rule pulls the COMPS for the mother from the SP-COMPS of the non-head daughter.
Ann: Does the semantics follow the syntax there?
Dan: I think it's unsurprising looking when I'm done.
Alexander: Once you're done with too tall it just looks like easy.
Emily: What is climb the argument of in the semantics?
Dan: The comparative relation, contributed by too --- the degree of tallness is being compared with the VP.
Emily: So externally too tall looks like easy, but internally there's more going on.
Dan: Slight additional wrinkle: Can also put in a for phrase -- That hamburger is too tall for Bernd to devour. So too is actually putting in both the for and VP[to] onto the COMPS list. (Or it's a infinitival clause, underspecified between S and VP.)
Emily: Other examples from the Singapore Summit, do be in English, plus some Japanese and some Wambaya.
Dan: [Sketches do be construction.] That's on the brink of the worst case. The other one, from work with Francis and his students: she craned her neck/*she craned his neck. Want to rule the latter out as ungrammatical---use XARG of the noun to do that and build an ICONS.
Ann: ICONS is separate...
Dan: Doesn't matter if it's ICONS or identity.
Ann: ICONS relationships in general might just do different things in terms of the algebra. You're saying you still need to use the XARG.
Dan: I think so because I need to get number agreement. It's on the border of something that maybe ought to be done with the idiom machinery over in the semantics, but in our papers there are arguments for why we want to do it in the syntax (in the composition).
Ann: We don't do binding, we don't do reflexives... if we did those would be via ICONS. There's various reasons why I might think coindexations are outside this...
Dan: If I just decided to store an ICONS there and hook it up somehow. I still have to do the bookkeeping to find that subject.
Ann: If the only thing you can do with it is do an ICONS, I'm not sure I'm worried.
Dan: This might be an interesting place in the DMRS universe that becomes last vexing. If the three attributes in HOOK are my only affordances for composition, then LTOP and INDEX don't work, XARG is the only hope. If I have any other reason to want to use that XARG (like do be)...
Dan/Ann: *All she has to do is crane his neck. maybe not have enough slots to keep track to rule that out.
Emily: Isn't the do be one weirder --- it's going after it's COMP's MOD's XARG.
Dan: Sure, that's fine.
Guy: No deeper than too above.
Ann: Is there a limit on the depth of that path?
Dan: Typically phrases are COMPS/SPR saturated --- not walking down into the daughters. Anything that the sign continues to carry up is still fair game. Wouldn't expect to get to a modifier's complement's complement.
Emily: I wonder if that makes Wambaya less weird. Digging to a similar depth, but not directly filling a hole with it, so I guess it's weirder.
Ann: This analysis of Wambaya is elegant, but it seems to be only necessitated by the constraints of our parsers. The formalism can allow discontinuous constituents ... we just never developed a parser that does. (Even though the generator can to a certain extent.)
Guy: As a concrete example of going beyond a CFG backbone, there's some work on higher-dimensional trees. TAG & CCG class of languages can be reformulated in terms of 3 dimensional trees.
Dan: But CCG doesn't have much of a theory of constituents.
Guy: The class of languages defined by CCG and TAG can be defined in terms of 2nd order logic over trees.
Ann: And those classes of languages are more constrained that those defined by HPSG.
Guy: CFG languages are 2nd order logic over trees. Mildly context sensitive languages same thing over 3d trees. If we add unification... can see things in terms of a more expressive backbone instead of a CFG backbone.
Dan: I can see that, it surely changes the grammarian's task.
Guy: Just saying this is one way of achieving the goal.
Ann: The more general point I would like to make is that I'm not sure that there's anything that would happen in terms of how discontinuous constituents show up which would absolutely worry me in terms of constraints on compositionality.
Emily: It worries me as a syntactician because if I allow discontinuous constituents, I don't know what my constituents are anymore.
Ann: And many people want to get rid of constituents.
Dan/Emily: And they're not worried about grammaticality.
Alexander: Claims on the upper bound of variables being exposed---is that still what you're talking about? Interacts with discontinuous constituents. If requiring that compositional structure combines constituents that are next to each other, that puts more constraints on the memory/how much has to be carried up.
Dan: Set up the algebra based on English and then allow additional storage if you get discontinuity.
Emily: The typologist in me is grumpy about starting with English for that.
[Discussion of floated quantifiers in Japanese]
Conclusion: If the floated quantifiers are unconstrained as to which NPs they can modify, then the argument could just be left underspecified to be resolved via anaphora resolution. If there are syntactic constraints to model, then it gets more interesting.
Dan: She entered the room a pauper, and left a rich woman. ... those NPs are just underspecified as to what they are identified with.
Ann: Two types of problems---complex combinatorics (easy, too), things in the "wrong" place.
Ann: Memory load is a left-to-right sentence comprehension notion. Not sure whether that adds that much more, already need to do that for things that are semantically straightforward because the relevant thing doesn't come until the end (especially in German). When I talk to non-linguist native speakers, they describe havig a notion of a situation, where the verb just isn't known yet. I can get to 7 things that would be separate bits of DMRS, but if you have a bland situation they are attaching too, it's not so bad. So it's not so bad to assume you have to hallucinate something, since in incremental, temporal order processing you have to do that anyway.
Berthold: Hausa negation comes in two bits -- typical phrasal affixation. If you have a sequence of VPs, you find one ba on the first VP, all the others take the non-negative tone marker and then the final ba. Negation scopes over all of them.
Dan: Doesn't seem scary in terms of bookkeeping of the elements.
Berthold: Yeah okay phrasal affixation analysis does it. So what's scary?
Dan/Guy: When you have to keep track of more than three things in the HOOK.
Berthold: How about partial VP fronting?
Aufräumen hättest du die Küche ja auch schon mal können. clean.up would.have you the kitchen PART also already once can `You really could have cleaned up the kitchen by now'
Guy: I don't think it's too problematic though, because the actual contentful verb goes on the slash list and take over its arguments.
Emily: Examples where it's really a "partial VP" that's fronted?
Berthold: Nerbonne 1994 -- telling your kids a fairy tale.
Dan: I think even one object missing from the fronted VP makes it hard for us. This is a potential candidate other class of examples --- though there is the other debate about topological field-based analyses (more like the shuffle operator).
Dan: Can we get it from embedded clauses? Tell a story I expected my sister to think John should his children.
Antske: It works in Dutch.
Berthold: It works with coherently constructing predicates (those that form verb clusters; not just modals but also many control verbs).
Guy: Quirky case? ("helfen"'s ARG2 is dative, not accusative -- dative plural "-n" highlighted below).
Helfen hättest du den Kind-er-n ja auch schon mal können. help would.have you the.DAT.PL child-PL-DAT.PL PART also already once can `You really could have helped the children by now'
Guy: I take my comment back -- too much depends on the verb to build a structure without it.
Ann: Back to easy adjectives --- do you think the current analysis is algebra compliant?
Dan: Yes, I think so.
Ann: According to my notes, I had made the possible constraints on the DMRS composition weaker than the MRS algebra.
Dan: In order to get these through?
Ann: No, just a consequence of how I set it up.