We discussed Pullum & Rawlins' discussion of the X-or-no-X construction in English. Their 'denotational identity' account of the well-formedness of the X-or-no-X construction was able to interestingly generalize across superficially different constructions involving 'or', but the fix for the concommittant overgeneration (that 'speakers interpret any distinction as semantically relevant') seemed problematic. We identified a range of X-or-no-X sentences with systematically syntactically different parts that seemed not too bad.

For reference, here is an accepted but unpublished (I wasn't happy with it and never submitted the final version) commentary on Pullum and Rawlins' paper.

Reading

Next time we will discuss

• Hagstrom (2005) A-not-A Questions

primary (but unavailable) sources include:

• Huang (1991) Modularity and Chinese A-not-A Questions
• Ernst (1994) Conditions on Chinese A-Not-A Questions
• McCawley (1994) Remarks on the Syntax of Mandarin Yes-No Questions

We investigated copying in Yoruba.

Reading

Next time we will discuss

• Pullum & Rawlins (2007) Argument or no argument?

We restated the empirical questions about copying that our formal considerations had led us to want to ask:

1. is this real copying?
2. is the copying unbounded?
3. can the copies be syntactically complex?
4. can the copies themselves be of other copies?
5. can the copies be non-identical?

We then compared three analyses of the language \(\{w,w0w : w \in \{a,b\}^{\ast}\}\), one using TAGs, one MGs, and one MGs with copy movement. Our subjective intuitions about simplicity/elegance/capturing generalizations lined up with objective measures of grammar size:

• how many lexical items are needed
• how many new lexical items must be added to account for the introduction of a new word
• Next time we will begin talking about Yoruba
  • Stahlke (1970) Serial Verbs
  • Bamgbose (1973) Relative clauses and nominalized sentences in Yoruba

We added an operation of copying to our MCFGs, via reuse of variables in the rules. We saw that we could immediately derive the copy language, as well as languages beyond the power of MCFGs; like the arbitrary number of copies language - w⁺, and the language \(a^{{2^{n}}}\), which involves recursive copying.

We discussed the limitations of M(CF)Gs, wrt copying. For example, while they can generate any fixed number of copies (wᵏ), they cannot generate all numbers of copies (w⁺). Furthermore, while they can generate copies with internal structure, they cannot generate recursive copies (ad infinitum). The latter of these limitations is subsumed by the fact that M(CF)Gs are semilinear.

We introduced (a logic grammar presentation of) multiple context-free grammars, and showed how they provided a faithful implementation of MGs, thus identifying movement with tupling.

We introduced minimalist grammars (Stabler 97, Stabler 10), a formalization of the essence of Chomsky's minimalism. We saw how to construct a grammar for the copy language. It worked by maintaining two identically pronounced subtrees, and at each 'step', choosing to merge either an a or a b, moving one of the subtrees to the specifier, merging another instance of the same letter, and moving the other subtree to its specifier. This results again in two identical subtrees.

We discussed the limitations of grammars with adjunction (i.e. macro grammars) with respect to their copy generating potential. The discussion was (informally) based on this paper by Kanazawa and Salvati, which loosely showed that, while grammars with adjunction can generate copies, the underlying grammar of the copied material must be simple in a precise sense.

We introduced Tree adjoining grammar (Frank 2006, Kroch and Joshi 1985, Kroch 1989), and reasoned about how to derive the copy language using adjunction.

Building on our discussion from last time, we noted that a fundamental question regarding copying is:

Q1

Is copying unbounded?

This question has been largely ignored in the Chomskyian syntactic literature, where much discussion has revolved around the relative positions in the clause of the two copies. (See section 4.3 of this paper.)

We 'relaxed' our criterion for being a copy construction, requiring not literal copies, but only that the construction be viewable as involving copying if you squint; if by systematically changing the identities of words you could arrive at copies, then it counts. As an example, we considered the set of sentences of the form:

• Paul, Paula, Paul, … are a widower, a widow, a widower, … respectively

which, if you map both Paul and widower to the letter a, and Paula and widow to b, and erase all other words, you obtain a sentence of the form ww.

Part of the reason for this more liberal criterion is so as not to prejudge the issue of copying, leading to the following question:

Q2

Can copying be non-exact?

In looking for answers to Q1, we looked the English X-or-no-X construction, which has been discussed in the literature (see Manaster-Ramer for an overview of some copy constructions, Pullum and Rawlins for discussion of the X-or-no-X construction, and Finkbeiner of the German X-hin,X-her construction).

We looked at sentences in (a dialect of) Swiss German, and saw that they were inherently non-local, in that no local grammar could be given which generated all and only these sentences.¹ This was a recap of an argument published by Stuart Shieber (official version, publicly available version).

I suggested that a useful heuristic for determining whether a set of sentences could be given a local description was whether their dependencies were crossing or not. We saw that wh-movement did indeed involve crossing dependencies, but, that if there were an upper bound on the number of such crossing dependencies, we could eliminate them altogether, by encoding them into the category system. Thus, it is not just crossing, but unbounded crossing that we should be on the lookout for.

We began by defining a local syntactic property to be one which could be verified by looking at only the local relationships in a tree (i.e. mother and daughters). This nomenclature comes from the literature on tree languages in computer science, and provides a good (imho) approximation of the linguist's intuitive usage of the term.

We defined a local grammar to be one with rules of the form A → α. A a non-terminal symbol, and α any (finite) sequence of words and/or non-terminal symbols.²

We saw that many linguistic constructions involving seemingly non-local dependencies (wh-movement, single word predicate copying) can be given local characterizations by enriching the set of categories we use. (e.g. S[NP] is the category of sentences containing an unbound noun phrase trace.)

This led us to ask the question: are all linguistic constructions local? I.e. is there a local grammar generating exactly the grammartical sentences for each human language?

We saw that it was easy to give a local characterization of any finite set (one rule per sentence). In order to derive infinite sets of sentences, a local grammar must use recursive rule application. Such recursive rule applications can be iterated ad infinitum, and thus on the basis of one structure we can infer the existence of infinitely many other structures differing from this one only in the number of iterations of the recursion. This is visible at the level of sentences (i.e. sequences of words), where it becomes: if p and q are the symbol sequences introduced in the recursive step in the derivation of the sentence upwqv, then for every natural number n, the sentence upⁿwqⁿv is grammatical.

This allows us to reason (by modus tollens) from strings to the (lack of) grammars generating them. If, given some infinite language L, there is no pumpable class of strings, then this language cannot be described by any local grammar. As a concrete example, we looked at the set of strings aⁿbⁿcⁿ, where every grammatical sentence has the same number of the symbols a, b, and c, and moreover all symbols a precede all symbols b which in turn precede all symbols c. Here we saw that there was no way to pick two non-empty substrings p and q in a sentence of this language which could be grammatically pumped. Thus, we were able to conclude that there was no local grammar which could generate exactly the sentences of this language, irrespective of the categories used, or the structures assigned.

A more precise description of these properties can be found here.