Minimalist Grammars: The Very Basics

Oh boy, it's been a while... where did we leave off? Right, I got my panties in a twist over the fact that a lot of computational work does not get the attention it deserves. Unfortunately the post came across a lot whinier and accusatory than intended, so let's quickly recapitulate what I was trying to say.

Certain computational approaches (coincidentally those that I find most interesting) have a hard time reaching a more mainstream linguistic audience. Not because the world is a mean place where nobody likes math, but because 1) most results in this tradition are too far removed from concrete empirical phenomena to immediately pique the interest of the average linguist, and 2) there are very few intros for those linguists that are interested in formal work. This is clearly something we computational guys have to fix asap, and I left you with the promise that I would do my part by introducing you to some of the recent computational work that I find particularly interesting on a linguistic level.¹

I've got several topics lined up --- the role of derivations, the relation between syntax and phonology, island constraints, the advantages of a formal parsing model --- but all of those assume some basic familiarity with Minimalist grammars. So here's a very brief intro to MGs, which I'll link to in my future posts as a helpful reference for you guys. And just to make things a little bit more interesting, I've also thrown in some technical observations about the power of Move...

Minimalist Grammars

I have talked a little bit about MGs in some earlier posts already, but I never gave you a full description of how they work. For the most part, MGs are a simplified version of old-school Minimalist syntax before the introduction of Agree or phases. You have your old buddies Merge and Move, and lexical items carry features that trigger operations. There's several technical changes, though:

• features have positive or negative polarity (rather than the interpretability distinction),
• feature checking takes place between features of opposite polarity,
• the features on every lexical item are linearly ordered and must be checked in this order,
• the Shortest Move Constraint (SMC) blocks configurations where two lexical item could both check the same movement feature on a c-commanding head --- for example cases where both the subject and the object may undergo wh-movement to the C head.

If this were a paper rather than a blog post, I would now try to justify these alterations and explain why despite appearance they are not incompatible with mainstream syntax. But for the sake of keeping things short and snappy, I'll just handwave this part and assume that you are all sufficiently eager to hear more about the technical machinery that you do not care about the relation between MGs and Minimalist syntax. If you're really curious, section 2.3 of my thesis includes a thorough discussion of this issue. Anyways, back to Minimalist grammars.

Merge

Here's a very small MG lexicon that we can use to build a simple tree with Merge. Of course we can have bigger lexicons than that, as long as the number of entries is finite.

1. Mary :: D^-
2. likes :: D⁺ D⁺ V^-

Each lexical item has a phonetic exponent to the left of ::, and a string of features to the right. The entries John and Mary each have a single negative D feature, which in linguistic parlance just means that they are of category D. The entry likes has a feature string that starts out with two positive D features, followed by a negative V feature. This means that likes selects two DPs and is itself a verb. That's all we need to build the sentence Mary likes Mary.

First we merge likes and Mary, which gives us the tree below. I'm using X'-style labels for interior nodes, but pretty much any labeling convention will do, including projecting no label at all. Also notice that checked features are grayed out.

Thanks to Merge, the D^- feature on Mary has been checked, so that this instance of Mary does not need to undergo any syntactic operations anymore. But likes still has the features D⁺ and V^-. Another Merge operation is needed to get rid of D⁺. So we merge another instance of Mary, resulting in the tree below.

The only remaining feature is V^- on likes. If V is considered a final category by our grammar, then the tree we built is grammatical. If V is not final, then we have to continue adding new structure, but since there is no lexical item that could check V^-, no further Merge steps are licit and the entire structure is ungrammatical.

Move

Now suppose that we want the object to undergo topicalization, yielding Mary, Mary likes. In Minimalist syntax, this is analyzed as movement of the object to Spec,CP. We can replicate this analysis by adding two more items to our lexicon:

3. Mary :: D^- top^-
4. e :: V⁺ top⁺ C^-

The first entry is just a variant of Mary that can move to a head that licenses topicalization, which is indicated by the negative movement feature top^-. The second entry is an empty head that selects a verb, attracts a mover with feature top^-, and has category C. Let's suppose that we already have the tree below (it only differs from the previous one in the presence of top^- on the object).

This tree is merged with the empty head, which is licensed by the matching V features on likes and the empty head.

The next feature that needs to be checked is top⁺, and lo and behold, the object still has a top^- feature to get rid of. So the object moves to the specifier, the features are deleted, and we end up with the desired tree.

The only unchecked feature is the category feature C^-, so once again the tree is grammatical iff C is a final category.

What would have happened if both the subject and the object had a top^- feature? Which one would have moved then? Well, as I mentioned above, this issue cannot arise because the SMC blocks such configurations. The derivation would have been aborted immediately after Merger of the subject, which makes top^- the first unchecked feature of the subject.

However, the SMC would not block a derivation where the subject rather than the object carries the top^- feature and thus undergoes (string vacuous) topicalization.

It is also perfectly fine to have top^- features on both the subject and the object as long as they are not active at the same time. Let's look at an artificial example since I can't think of a good real world scenario (if you have any suggestions, this is your chance to be today's star of our prestigious comments section).

Suppose that there are actually two topic positions, with TP sandwiched between the two. Furthermore, the object has a top^- feature, whereas the subject has the movement features nom^- and top^- so that it has to move to Spec,TP first before it can undergo topicalization. In this case the two topic features are never active at the same time and the derivation proceeds without interruption.

Special Movement Types and Generative Capacity

Since Minimalist grammars put no particular constraints on movement except the SMC, they allow for a variety of movement configurations, including roll-up movement, remnant movement, and smuggling.

Imagine a tree where UP contains ZP, which contains YP, which in turn contains XP.

• In roll-up movement, XP moves to Spec,YP, followed by movement of YP to Spec,ZP (which might also undergo roll-up movement to Spec,UP).
• In remnant movement (popularized by Richard Kayne²), XP moves out of YP into Spec,ZP before YP undergoes movement itself to Spec,UP.
• In smuggling (a term coined by Chris Collins³), YP moves to Spec,ZP, which is followed by extraction of XP from YP to Spec,UP.

Each movement configuration corresponds to a particular distribution of movement features over the lexical items X, Y, Z, and U.

	X	Y	Z	U
roll-up	f-	f+ g-	g+ h-	h+
remnant	f-	g-	f+	g+
smuggling	f-	g-	g+	f+

If you're at all theoretically inclinded, your curiousity should peak immediately when faced with such a beautiful typology. The first thing to notice is that this list is complete; if X, Y, Z, U stand in a containment relationship and are the only sources and/or targets of movement, then any (phrasal, cyclic) movement configuration that comprises at least two movement steps belongs to one of the three types above. Now the obvious question is whether the three types differ in some important respect. For instance, is one type more powerful than the others? We might expect roll-up movement to be more complex because it involves more features than smuggling or remnant movement. But as Greg Kobele showed a few years ago,⁴ remnant movement is the most powerful movement type. In fact, roll-up movement and smuggling are pretty weak --- they do not add anything over Merge!

Let's make this claim a little bit more precise (Caution: the discussion may reach critical levels of jargon density; proceed with care). Minimalist grammars that only use Merge have the same generative capacity over strings as context-free grammars, while the set of phrase structure trees generated by such an MG is a regular tree languages. We have also known for a long time that adding movement to MGs increases their weak generative capapcity to that of multiple context-free grammars (see the discussion in this post for some background), which also entails that not all phrase structure tree languages are regular.

Greg showed that if movement must respect the Proper Binding Condition (PBC), which requires that every non-initial element of a movement chain is c-commanded by the head of the chain, the increase in weak generative capacity does not occur --- MGs still generate only context-free string languages. Building on some recent results about the equivalence of Merge and monadic second-order logic (which was the topic of this lovely series of blog posts), one can also show that strong generative capacity is not increased by PBC-obeying movement. Now if you take a look at the three movement types above, you will see that remnant movement is the only one that does not obey the PBC. Hence remnant movement is the only (cyclic, overt, phrasal, upward) movement type that increases the power of MGs beyond what is already furnished by Merge.

Summary

A Minimalist grammar is given by a finite list of lexical items, each of which consists of a phonetic exponent and a string of features. Each feature is either a Merge feature or a Move feature, and it has either positive or negative polarity. The grammar generates every phrase structure tree that can be obtained by Merge and Move such that

1. all features have been checked off except the category feature of the highest head,
2. said category feature is a final category,
3. the SMC has not been violated at any step of the derivation.

As you can see, MGs are a very simple formalism. Of course we can add new constraints and operations, but the basic variant here covers a surprising amount of empirical ground. As a matter of fact, vanilla MGs can handle almost all known syntactic phenomena under the proviso that we only consider weak generative capacity, i.e. the surface strings rather than the derived tree structures (copying constructions, scrambling and multiple wh-movement are problematic even under these conditions). But even when structural descriptions are part of the picture, MGs are far from inadequate --- Greg Kobele, for example, develops an MG grammar for a decently sized fragment of English in the first chapter of his thesis.

Greg's thesis is also a good starting point if you'd like to know more about MGs, as are the first two chapters of my thesis and Ed Stabler's survey paper in the Oxford Handbook of Linguistic Minimalism.

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1. Kudos to Norbert for keeping his blog open to these formal topics and discussions.↩
2. Kayne, Richard (1994): The Antisymmetry of Syntax. MIT Press↩
3. Collins, Chris (2005): A Smuggling Approach to the Passive in English. Syntax 8, 81--120. Manuscript here↩
4. Kobele, Gregory M (2010): Without Remnant Movement, MGs are Context-Free. MOL 10/11, 160--173. ↩