\section{Introduction}

Lexicographic attempts to cope with verb sense disambiguation often rely on  ``lexical sets'' \cite{hanks1996}, which represent the lists of corpus-derived words that appear as arguments for each distinct verb sense. The arguments are the ``slots'' that have to be filled to satisfy the valency of a verb (subject, object, etc.). For example, \{{\it gun}, {\it bullet}, {\it shot}, {\it projectile}, {\it rifle}...\} is the lexical set of the object for the sense `to shoot' of {\it to fire}. In previous works, e.g. \newcite{montemagni1995}, lexical sets were collected manually and were compared through set analysis. The measure of similarity between two sets was proportional to the extent of their intersection. We believe that possible improvements may stem from deriving the lexical sets automatically and from exploiting the semantic information of the fillers fully. In this work, we devise an extraction method from a huge corpus and use a distributional semantics approach to perform our analyses. More specifically, we represent fillers as word vectors and compare them with spatial distance measures. In order to test the relevance for linguistic theory of this approach, we focus on a case study, namely the properties of verbs undergoing the causative-inchoative alternation. 
Section 1.1. outlines a framework for word embeddings and section 1.2 introduces the case study. Section 2 presents the method and the data, whereas section 3 reports the results of a couple of experiments.

\subsection{Word Embedding}
The full exploitation of the semantic information inherent to argument fillers can take advantage from some recent developments in distributional semantics. Recently, efficient algorithms have been devised mapping each word of a vocabulary into a corresponding vector of \textit{n} real numbers, which can be thought as a sequence of coordinates in a \textit{n}-dimensional space \cite{mikolov2013}. This mapping is yielded by unsupervised machine learning, based on the assumption that the meaning of a word can be inferred by its context, i.e.\ its neighbouring words in texts. This model has some relevant properties: the geometric closeness of two vectors corresponds to the similarity in meaning of the corresponding words. Moreover, its dimensions have possibly a semantic interpretation.

\subsection{Causative-Inchoative Alternation}
A possible testbed for the usefulness of representing the argument fillers as vectors are the verbs showing the so called causative-inchoative alternation.
These verbs appear either as transitive or intransitive. In the first case, an agent brings about a change of state; in the second, the change of a patient is presented as spontaneous (e.g.\ {\it to break}, as in ``Mary broke the key'' vs. ``the key broke''). 

The two alternative forms of these verbs can be morphologically asymmetrical: in this case, one has a derivative affix and the other does not. The first is labelled here as ``marked'', the second as ``basic''. 
Italian verbs with an asymmetrical alternation derive from the phenomenon of anti-causativization. The intransitive form is marked since it is sometimes preced by the clitic \textit{si} \cite{cennamo2011}. \newcite{haspelmath1993} maintain that verbs that show a preference for a marked causative form (and a basic inchoative form) cross-linguistically denote a more ``spontaneous'' situation. Spontaneity is intended by the author as the likelihood of the occurrence of the event without the intervention of an agent. This work is non-committal with respect to whether spontaneity be an actual semantic factor. Rather, it is considered a notion useful for labelling the observed variations in morphology and frequency.

In this way, a correlation between the form and the meaning of these verbs was demonstrated. Moreover, \newcite{samardzic2012meaning} and \newcite{haspelmath2014coding} argue that verbs that appear more frequently (intra- and cross-linguistically) in the inchoative form tend to morphologically derive the causative form, too. This time, the correlation holds between form and frequency. Vice versa, situations entailing agentive participation prefer to mark the inchoative form and occur more frequently in the causative form. 

\section{Previous Work}
In the literature, many methods are available for the automatic detection of verb classes, such as causative-inchoative verbs. They exploit features based on argument alternations, such as subcategorization frames \cite{joanis2008general}. The identification of verb classes displaying a diathesis alternation was also performed through the analysis of selectional preferences. Most notably, the lexical items were compared via distributional semantics \cite{mccarthy2000using}.

These features were usually induced from automatic parses of heterogeneous and wide corpora \cite{im2000clustering}. In particular, the extraction of subcategorization frames was refined including e.g.\ noise filters based on frequency \cite{korhonen2000statistical}. This work is inspired by these attempts to automatically induce lexical information regarding verbs, but its direction of research is reversed. Indeed, rather than classifying verb classes given this information, it analyses this information given a verb class so to shed light on its properties from the perspective of linguistic theory.

\section{Data and Method}
The data are sourced from a sample of ItWac, a wide Italian corpus gathered through web crawling \cite{baroni2009}. This sample was further enriched with morpho-syntactic information through the \textsc{mate}-tools parser \cite{bohnet2010}\footnote{LAS scores for the relevant dependency relations: 0.751 with dobj (direct object), 0.719 with nsubj (subject), 0.691 with nsubjpass (subject of a passive verb).} and filtered by sentence length ($ < 100$). Eventually, sentences in the sample amounted to 2,029,454 items. A target group of 20 causative-inchoative verbs was taken from \newcite{haspelmath1993}. These are listed here from the least spontaneous to the most:

\noindent
\begin{framed}
\noindent
\small
close > open > improve > break > fill > gather > connect > split > stop > go out > rise > rock > burn > freeze > turn > dry > wake > melt > boil > sink
\end{framed}

The extraction step consisted in identifying their argument fillers inside the sentences in the sample. In particular, the arguments considered were the subjects of intransitives (S) and objects (O) \cite{dixon1994}.\footnote{Subjects of forms with \textit{si} were treated as intransitive subjects. Subjects of passive verbs were treated as objects.} These arguments are relevant because they are deemed to share the same fillers \cite{pustejovsky1995}.

These operations resulted in a database where each verb lemma had a single entry and was associated with a list of fillers, divided by argument type. With this procedure, lexical sets were extracted automatically, although they were not divided by verb sense. Afterwards, each of the argument fillers was mapped to a vector relying on a space model pre-trained through Word2Vec \cite{dinu2015}.\footnote{It was generated by a \textsc{cbow} algorithm with negative sampling, 300 dimensions, a context window of 10 tokens, pruning of infrequent words and sub-sampling.}

\section{Experiments}

\begin{figure}[t]
    \centering
    \includegraphics[width=\columnwidth]{boxplot-dividere}
    \caption{Distance of vectors from their centroid.}
    \label{boxwhi}
\end{figure}

\begin{figure*}[t]
    \centering
    \includegraphics[width=\columnwidth]{smeds}
    \includegraphics[width=\columnwidth]{omeds}
    \caption{Medians of S (left) and O (right) distances for verbs ranked by position in Haspelmath's scale.}
    \label{fig1}
\end{figure*}

In order to bring to light the information concealed in the automatically extracted lexical sets, we devised two experiments. One investigates the internal structure of lexical sets. In fact, previous works based on set theory treated them as categoric sets, whose a filler is either a member or not. Research in psychology, however, has long since demonstrated that the members of a linguistic set are found in a radial continuum where the most central one is the prototype for its category, and those at the periphery are less representative \cite{rosch1973,lakoff1987}. Word vectors allow to capture this spatial continuum. 

Once the fillers have been mapped to their respective vectors, a lexical set appears as a group of points in a multi-dimensional model. The centre of this group is the Euclidean mean among the vectors, which is a vector itself and is called centroid. In the first experiment, we calculated the co-ordinates of the centroid of the lexical sets S and O for any given verb\footnote{Every filler was weighted proportionally to its absolute frequency.}. Then we evaluated the cosine similarity of every vector member of the sets from its centroid. The value of this metric goes from 0 (overlap) to 1 (maximum distance) and is useful to evaluate how far a filler is from its prototype. We obtained two sets of cosine similarity values for each verb: these can be plotted as boxes and whiskers, like in Figure \ref{boxwhi}. The example represents those of \textit{dividere} `to split'. The rectangles stand for the values in the second and third quartiles, whereas the horizontal line for the median
value. From all these distance values, we picked the median value for each lexical set. The plot of these medians for the S set and the O set of each verb ordered according to Haspelmath's ranking is shown in Figure \ref{fig1}.

Two main results can be observed from these plots: the S lexical set is denser, whereas O is more scattered. This is demonstrated by the ranges where their distance values fall. Moreover, the median of the distances in S is normally lower for verbs that are lower according to the Haspelmath's scale. The averages of medians for the ten verbs on the left part of the scale (the most non-spontaneous) and for the ten verbs on the right (the most spontaneous) were compared. The average median in S was 0.696567 for the former and 0.585263 for the latter. The average median in O was 0.556878 for the former and 0.522418 for the latter.

The second experiment consisted in estimating the cosine distance between the centroid of S and the centroid of O for each verb. This operation was aimed at finding to which extent the lexical sets of S and O overlap. In fact, \newcite{montemagni1995} and \newcite{mccarthy2000using} assessed in a corpus some asymmetries between these lexical sets, which in principle should share all their members.

Inspecting our results, the distance between S and O seems to behave as a measure of the cross-linguistic frequency and morphology of a verb: the more the centroids tend to be set apart, the more the verb tends to have a non-derived and more frequent intransitive form. In fact, we compared the ranking of 20 alternating verbs according to the ratio of their cross-linguistic frequency of transitive and intransitive forms \cite{haspelmath2014coding} and a ranking based on the centroid distances of the same verbs. Both these rankings are plotted in Figure \ref{fig2}: every verb is associated with its position in the two scales.

\begin{figure}[ht]
    \centering
    \includegraphics[width=\columnwidth]{scales2014}
    \caption{Ranking based on cross-linguistic form frequencies (green triangles) against ranking based on distance of the centroids of S and O in Italian (blue squares).}
    \label{fig2}
\end{figure}

Both the scales display a common tendency. In particular a Spearman's ranking test was performed over them, yielding a mild positive correlation of $\rho = 0.56391$ with a quite strong confidence, i.e.\ with $p < 0.01$.\footnote{An alternative measure was considered for the ranking: the cardinality of the S-O intersection weighted by the set union. In this case, Spearman correlation was $\rho = 0.42255$, but it was not significant because $p \approx 0.06$.} 

\section{Conclusions}
The representation of lexical sets of Italian causative-inchoative verbs as vectors was demonstrated to provide insights into their internal structure and their relation with spontaneity. The sets of objects appeared to be distributed more uniformly, whereas the sets of intransitive subjects more densely. This difference cannot stem from frequency, since both these arguments share their discursive function of introducing new referents \cite{du1985competing}.

Moreover, the medians of the distances of the subject fillers from their centroid were shown to vary. An interpretation is that they are sensible to the frequency scale: this implies that frequently transitive (hence, non-spontaneous) verbs have semantically less homogeneous sets of referents, since they are farther from the prototype. Possibly this discovery can be related with the fact that non-spontaneous verbs impose milder selectional restrictions on subjects \cite{mckoon2000}.

Probably the most notable result, however, is the fact that a correlation exists between the distance between object and intransitive subject lexical sets of a given verb and its cross-linguistic tendency to appear more frequently as intransitive or as transitive. The lack of a perfect correlation between these measures is maybe due to errors in the automatic extraction and data sparseness for the former, or an insufficient sample of languages in the typological survey of \newcite{haspelmath2014coding} for the latter.

Future work should choose different pre-trained vector models, in order to try and replicate these results. In particular, the new vector models could be optimized for similarity through semantic lexica \cite{faruqui:2015:Retro} or based on syntactic dependencies \cite{seaghdha2010latent}. The experiments in this work may be extended to other languages, either individually or through a multi-lingual word embedding \cite{faruqui2014improving}.

\bibliographystyle{acl}
