Beyond concatenation

In formalisms such as PATR II the string associated with a derivation is the sequence of terminal nodes of the corresponding derivation tree in left-to-right order. For example, the sentence

$\begin{exam} Kim is easy to please \end{exam}$
may be analyzed in some PATR grammar in a way that gives rise to the derivation tree in figure 4.1.

**Figure 4.1:** A possible PATR derivation tree, for the sentence `Kim is easy to please'
$\begin{figure} \begin{center} \leavevmode \unitlength1pt \beginpicture \setplot... ...ion \put{\hbox{please}} [Bl] at 64.11 18.00 \endpicture \end{center}\end{figure}$

In sign-based approaches such as in UCG and HPSG the string is part of an attribute of each feature structure (sign). The attribute is usually called `phon', `string', `graph' or `orth' (I will use `phon' in the following). Hence, the string associated with a construction is simply the value of the `phon' feature of the sign that is assigned to the construction. In UCG there is a condition, called `adjacency', which says that signs can combine only if they are adjacent. In other words, the value of the `string' feature of a mother node in a parse tree is always the concatenation of the `string' features of the daughter nodes. Hence, the UCG parse tree for the foregoing example presumably would be something like figure 4.2.

**Figure 4.2:** Possible UCG parse tree, restricted to the value of the `phon' attribute, for the sentence `Kim is easy to please'
$\begin{figure} \begin{center} \leavevmode \unitlength1pt \beginpicture \setplot... ...on \put{\hbox{please}} [Bl] at 183.26 18.00 \endpicture \end{center}\end{figure}$

The two approaches are formally equivalent, but the second approach has the advantage that it at least becomes easier to think of other `modes' of combination of the value of the `phon' attribute. As an example consider

$\begin{exam} Kim is an easy person to please \end{exam}$
Suppose that there is linguistic motivation that in this sentence, as in sentence 1, the sequence `easy to please' should be regarded as a (discontinuous) constituent. Such an analysis cannot be defined directly in PATR or UCG. If no adjacency condition applied we could have a parse tree of `easy person to please' as in figure 4.3.

**Figure 4.3:** Hypothetical parse-tree (restricted to phonological information), for a discontinuous analysis of the sentence `An easy person to please'
$\begin{figure} \begin{center} \leavevmode \unitlength1pt \beginpicture \setplot... ...n \put{\hbox{ please}} [Bl] at 212.96 18.00 \endpicture \end{center}\end{figure}$

In the next subsections I describe some proposals which allow such a direct implementation of discontinuous constituents.