Author Topic: "and" as a nounphrase coordinating conjunction  (Read 489 times)

Offline Andrea245

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"and" as a nounphrase coordinating conjunction
« on: January 23, 2018, 02:28:26 AM »
Hi everyone :)

in one of my uni classes we are currently working on deriving truth conditions. We already dealt with "and" as a conjunction of type <t, t, t> connecting two sentences as in "Jack sings and Lily plays the guitar". We computed the truth-condition using this lambda expression for and: λp ∈ Dt . [λq ∈ Dt . p = q = 1].
But now we have a sentence, where and coordinates two NPs: "Jack and Lilly sing." I got a bit stuck computing the truth-conditions as I don't know what the lambda expression for "and" would look like. It somehow must combine two e type expression and return a noun phrase of either type e or <et, t> so that it can get applied to the verb.
Does anybody know where to look it up?
Kind regards,
Andrea

Offline Daniel

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Re: "and" as a nounphrase coordinating conjunction
« Reply #1 on: January 23, 2018, 09:10:36 AM »
There's actually no good, consistent answer to this question that everyone would agree on. There are some possible answers, but they're all controversial in one way or another and they don't necessarily cover all possible cases. For example, you can also coordinate two adverbs or prepositions, in addition to verbs, clauses, nouns, etc. So some solutions would just address nouns and clauses, while others might attempt a more general solution. (I happen to be writing my dissertation on coordination and related things, by the way.)

From the perspective of syntax, there are broadly speaking two approaches:
1. Treat "and" as if it can link ANY two identical (or similar?) categories. Often this is via "&P", a sort of unusual phrase, which internally takes any two similar XPs and links them up but then acts like that same category (XP) externally. So an &P might act like NP if it's conjoining two nouns. (There's a good recent book that argues for and supports this type of analysis and discusses earlier literature: Zhang, 2009: Coordination in Syntax.)
2. Always assume clausal coordination, and then use a special rule of conjunction reduction to not pronounce all of the parallel words. So your example "Jack and Lilly sing" would actually be "Jack sings and Lilly sings", transformed (by conjunction reduction) to "Jack and Lilly sing", then you can treat "and" as a normal clausal coordination, and the only complex rule is however syntax generates the surface form. This is an older, traditional analysis that doesn't get so much support these days, at least not for all cases. Note that one problem here is any sort of sentence which doesn't work well split up into two parallel parts like that-- notice also the form "sings" vs. "sing" which would somehow need to be derived as a plural once "reduced" as well. Even worse are examples like "John and Mary met", where "John met" isn't a coherent sentence, nor is "Mary met", but only together do they make sense (and they also necessarily met each other, not random other people!).

There is actually some recent evidence that both analyses may be required, for different types of constructions. (One type of evidence is from some languages with optional close-conjunct agreement, where you get things like lit. "John and [Mary sings]" and "John and Mary sings", where the former is derived by conjunction reduction and the latter is derived compositionally with a conjoined noun phrase. That's not uncontroversial but the argument is interesting.) One further argument in support of at least sometimes having conjunctive reduction is non-constituent coordination: "I eat pizza, and you pasta." That seems like it must be generated by some sort of shortening of the full second clause. However, where to draw the line between these two analyses is uncertain at this point, and controversial.

There have been hundreds of papers dealing with the structure of coordination and various types of exceptions. Many of them don't agree with others. So one practical answer is just to pick one approach and use that, unless you want to try to solve this yourself.

(If you're taking a class, see your textbook, or ask your instructor. That's the only way to get the "right" answer in terms of your class!)

So in terms of semantics, there are also two related ways to handle coordination:
1. Treat each type of coordinated constituent separately. Have one type for clauses, another for verbs, another for noun phrases, and so forth. This intuitively doesn't seem like it can be the right answer because you'll just have a list of many types and lambda expressions, but it's relatively straight-forward to do that, making it convenient in another sense. (You could even imagine some sort of general procedure to automatically generated all of these types, although it's unclear how it would fit into a standard formal semantic theory.) One argument in favor of this position is that there are many languages where clausal/verbal coordination and noun coordination are actually done with different conjunctions that can't necessarily conjoin all other categories like is possible so generally in English. In that sense, maybe just making a list and considering "and" to be (many-ways) ambiguous is the best solution. (See: http://wals.info/chapter/64)
2. You can try to come up with a very general solution to the problem involving variable types, of the form <<X,X>,X>, where two Xs are conjoined and also result in an X. But it isn't clear how to integrate that more generally into the theory. (You could alternatively try to bend the types somehow to handle more than one type of phrase, but that probably won't hold up very well.)

Since this sounds like homework, I'm not going to give you 'the answer'. But your question is an interesting one beyond just how to do that one problem. And you've noticed something important by asking the question. For the actual 'answer', you can decide what makes the most sense yourself, or check with your instructor (or textbook) for what the best answer in your case is. Note that for many classes the range or reasoning for possible answers is restricted to make these questions easier, while not necessarily being the same answer that would be used in published research.

In short, yes, that is a complication, and it's not easy to deal with. The simplest answer would be to just treat it like a completely different word (and1, and2), with different types. But that may  not feel intuitively like solving the underlying issue, just patching it until you come across a slightly different sentence.

----

Personally, in terms of a general solution to these things, I'm in favor of I guess what you could call (and some have called) a "3D" approach, where you have layers of sentences which overlap and then merge/switch at the conjunction "and", discussed in some recent papers. (This is similar to the "conjunction reduction" approach above.) But that doesn't seem to work in all cases, so I do like a mix of both types of approaches.

And even more personally/idiosyncratically, at least sometimes, I think that "and" itself has no meaning at all. I wouldn't assign it a node in the tree. Instead I think of it as phonological glue that indicates a conjoined structure, but that isn't itself an element of that structure. (It's part of the tree's trunk/branches, rather than a leaf at the end of a branch, if you want that metaphor.) But that's not a mainstream perspective at all. (I think it's necessary some of the time though.) And it wouldn't cover all cases-- sometimes indeed I think you would need to just treat it as if it's conjoining two nouns.

So "and" is complicated!
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