Why are syntax trees binary trees?

Question

In p.26 of An Introduction to Syntactic Analysis by Sportiche et al. (2013), the authors specify that syntax trees aren't allowed to have more than two children:

We never find morphological trees in which:

i. a given node has more than one mother;

ii. a mother has more than two daughters;

iii. any node lacks a mother

Re the second bullet point, a syntax diagram is given that looks something like this:

  A
/ | \
C D E

So, apparently this is not acceptable when specifying morphological structure; I assume it's the same for syntax trees. This model seems to be exactly the same as a binary tree. Why is this model necessary? I understand that binary trees are very useful structures in computing, but I figured that the use of trees for syntax analysis predated their use in computing. Is there an inherent advantage to using binary trees for syntax diagrams, without considering computing?

Answer 1

My original answer

As I said in a comment I am not completely sure about the meaning/context of your question. I am answering with respect to syntax, though my remarks are so general that they could apply to nearly any context, whether morphological (if you use trees for morphological structure) or syntactic, or other.

Regarding binary trees, anything that can be represented by trees can be represented by binary trees, so it may be a matter of simplification. Another good point of binary trees is that they are the most convenient and effective for factoring structures and information. That can help factor linguistic descriptions of language structures, or factoring ambiguous analyses of a given sentence.

Technically, though you seem uninterested by computational consideration, because binary trees give better factorization, parsing sentences with type 2 grammars (context-free) is faster with binary trees and also takes less space, when you attempt formally to analyse ambiguities. The theoretical complexity is in power of n+1, where n is the maximum number of daughter.

Even though complexity is usually a matter of asymptotic behaviour, this is not completely irrelevant, because the complexity increase is observable even on smallish examples. This means that considering only binary trees might make sense from a psycho-linguistic point of view ... inasmuch as trees are considered relevant for psycho-linguistic models of whatever you are analyzing.

Reply to some comments, including my own.

About the quote

I do not have access to the 2013 edition of the book, but I did find what seems to be an earlier version since it has only 246 pages instead of 470, and the quoted text does not appear on the same page, but on page 21 instead of 26.

The quote I found is slightly different as the third bullet point reads in my version (where it is second):

It seems that we never find morphological trees in which
i. ...
ii. more than one node lacks a mother
iii. ...

That makes more sense than the quote given in the OP's question, since otherwise, the structure should be infinite or looping, which is not compatible with what I know of trees.

But I still fail to understand the reason for excluding morphological trees in which i. a given node has more than one mother. However the authors states a few lines later that:

Trees in general then obey the following conditions: i. Every node but one (the "topmost") has a mother ii. No node has more than one mother

So my guess is only that the first bullet of the text quoted in the question was both tautological, and awkwardly stated. All trees have the property, so that none needs be excluded on that basis.

About morphology and syntax

It is clear from the book that the above quote is about morphology. I have no opinion about its linguistic accuracy. But it is also clear that the extension to syntax trees is only the OP's opinion.

Hence it would be better if the comments or answers were clear on whether they address the book, or the OP's personnal assumptions when stating I assume it's the same for syntax trees, which he does not seem to sustain with arguments.

Again, I am without opinion on the matter, but this part of the book does not seem to me to be related to Chomskyan syntax (maybe because of my ignorance on the matter).

About the use of binary trees in this morphological context

My own, probably limited and simplistic, experience of morphology is that it can most often (with few exceptions) be defined by finite state machines, defining regular sets. Regular sets of morpheme strings can be defined by regular grammars, which are either left or right linear. Representing the sequences as trees rather than strings would be pointless, except for the fact that left and right linearity are not normally not mixed (so as to preserve the regular character), but it seems natural to use one for prefixes and the other for suffixes (though there is surprisingly no explicit tree example in the book to justify that). This then justifies exhibiting the structure with binary trees, that differentiate left and right linearity.

About the use of binary trees in syntax

Once again, I want to make it clear that I do not have the qualification to have an opinion about linguistic theories. But I do have experience and opinions (that I can hopefully sustain) about formalization techniques.

I was clear that my statements are of a very general nature, and thus do not support any linguistic theory over another. It is only my way to give a kind of general support to the idea of binarization, which is more than the OP did, as far as I can tell.

When I state that binary branching structures are more efficient, all I mean, and I said as much, is that it helps factoring. If you use a context-free grammar, you can use the rules:
{ A --> BCF , A --> DEF } or { A --> UF , U --> BC , U --> DE }
If you have for some reason an ambiguity between BC and DE, you can at least share the information regarding the presence of F at the end.

There is at least one situation where this efficiency gain shows as a complexity result, which is context-free parsing. Its complexity is lower on binarized grammars ... or at least binarized parse-tree (to make sure to cover an apparently little known point about Earley's algorithm). If this is not a solid example, I do not know what is. I am however conscious of the fact that asymptotic arguments are of limited value (which some seem to ignore), becahave its valueuse the brain deals only with small examples, but I did try to account for that in my answer.

The wording of my answer (above) was careful. I was expecting reactions about the existence of structures that should be viewed as ternary, or more. I do not deny that, and spoke of representation. The fact is that a representation is chosen for convenience, and can then be abstracted for perspicuity if deemed necessary. Abstraction may mean seeing one ternary node where representation uses two binary ones. And while the ternary view may be essential, there is still the possibility that the binary view is relevant in a different context.

So even if you do consider that the ternary aspect of A --> BCF is essential, you can represent it with A --> UF , U --> BC, while specifying that U --> BC has no meaning on its own.

Once again, my intent is only to see what general arguments can be given for binarization, on an abstract basis, without attempting to consider any specific syntactic theory of language.

Answer 2

There are several different views on the acceptability of trees where a mother has more than two daughters (i.e. non-binary branching). Much current work in the Minimalist Program (e.g. the Sportiche work cited) allows only binary trees. In earlier versions of syntactic theory (e.g. Chomsky 1981), non-binary trees were allowed. And in some alternatives to Minimalist Program (e.g. LFG, HPSG), such non-binary trees are still allowed.

The emphasis on binary trees owes much to the work of Richard Kayne, who has argued that they are the only kind that should be allowed.