Projectivity

Overview

An important consideration when writing a dependency grammar is whether or not to allow non-projective trees. To explain the term, consider the following sentence:

``Put the block on the plate in the box by the window.''

It has various different possible interpretations, depending on where exactly the mentioned items are with respect to each other. Perhaps the most probable interpretation is that the block is resting on the plate, and it should be put into the box, which is resting by the window. This is what a dependency tree for this interpretation could look like:

Another interpretation holds that the plate is in the box by the window already, and the block should be placed on it:

There are other, less likely alternatives we do not show here, e.g. that the block should be placed directly by the window. But interestingly, there are some interpretations which appear to be impossible for this sentence although they describe plausible situations. Consider this tree:

This corresponds to the interpretation that the block is in the box, the plate is by the window, and the block should be put on the plate. Although this is a valid scenario, it would never be expressed like this. The reason appears to be that at least two of the dependency relations in the resulting tree need to cross each other, and it is this which forbids the interpretation. In technical terms, the tree is not projective because not all of its nodes can be projected to the base without crossing any dependency.

The dispreference against non-projective structures is very strong; in fact, to express the third meaning, most speakers would agree that the sentence must be reordered:

``Put the block in the box on the plate by the window.''

It is also very common; in fact, it is hard-wired into many parsing methods. For instance, a normal context-free grammar or a standard shift-reduce parser simply cannot produce non-projective structures.

But unfortunately, there are some cases in which normal, perfectly acceptable structures appear to be non-projective. Although they are rare in English, cunning theorists have unearthed sentences such as

``Joan said whatever John likes to decide suits her.''

which provide counter-examples, although they are rather hard to understand. The case is much stronger in languages without the tendency for pure positional grammar that we have in English; thus, Czech and German have many classes clearly non-projective syntax.

I now give an account of the types of non-projective structures that our standard dependency grammar of German encounters and how we deal with them.

Sources

Our grammar of German models three different types of phenomena that give rise to non-projectivity:

1. complex verb phrases
2. moving phenomena
3. semisyntactic relations

1. Complex verb phrases

``Das können wir machen.''

This is the most common source of non-projectivity in German. Many of the other non-projectivities become a problem only because of this one.

The basic problem is that we model verb arguments as modifying the full verb, because existence and compatibility can then be checked with unary constraints. If we attached ``das'' to ``können'', the structure would be much simplified, but the checks would then become impossible. Note that the object can be more than edge remote from the finite verb, so that even binary constraints are not enough:

``Dabei soll auf den Owen-Plan zurückgegriffen werden.''

2. Moving Phenomena

These problems are best viewed as resulting from a transformation performed on a normal sentence -- something that dependency grammar is ill-suited for. Several varieties exist:

2.1 Discontinuous object sentences

Matrix sentences can move into the object sentence if they are short:

``Das, sagte Bruno, sei im Termingeschäft nicht unüblich.''

(was: ``Das sei im Termingeschäft nicht unüblich, sagte Bruno.'')

This construction is rather common in written German because it is considered good style.

2.2 Movable conjunctions

This exception applies to a small group of conjunctions that can move to the right, into the sentence they are conjoining:

``Man habe den Krieg gewonnen, den Frieden aber verloren.''

(was: ``Man habe den Krieg gewonnen, aber den Frieden verloren.'')

2.3 Movable pronouns

This peculiar moving behaviour seems to be unique to ``alle''/``beide''.

``Wir haben es alle gesehen.''

(was: ``Wir alle haben es gesehen.'')

3. Semisyntactic relations

Often particular structures are only allowed in the presence of particular other licensing or signaling structures. Projectivity exceptions occur if we model the relation between signal words and the constructions they signal as a direct dependency. This ensures that the special construction can only occur when the signal word is present, but since the signal word is often structurally distant, non-projectivity ensues.

I call the relationship semisyntactic because the edge really marks the semantic relation between the two concepts. This might indicate that the dependency is not syntactically accurate; we only draw it this way because we lack the formal power to express the dependency in another way.

There are many variants of this problem. In the following examples we mark the signal word and the dependent word. (Interestingly, the signal word always comes first.)

3.4 Repeated elements

Placeholder pronouns signal subclauses with `daß' or infinitives:

``Der Erst-Besitzer muß darauf achten, seine persönlichen Daten zu löschen.''

``Der Erst-Besitzer muß darauf achten, daß er seine persönlichen Daten löscht.''

3.5 Remote conjunctions

A word of category X signals a conjunction that also governs category X:

``Die Dot.Station soll an Geschäftskunden verkauft werden und nicht an Verbraucher.''

(Without that rule, conjunctions would always be maximally ambiguous.)

3.6 Remote object clauses

Deverbal nouns signal object clauses:

``Ich habe das Angebot abgelehnt, schnell Geld zu machen.''

3.7 Remote relative clauses

The relative clause is signaled by its antecedent:

``Ich habe ein Patent angemeldet, das sehr einträglich ist.''