This paper presents a roadmap to deliver tools able to model and predict the behaviour of neologisms in the form of nominal compounds. Quite often these compounds yield meanings (in our case, word associations) that are not related to the components of the compounds taken individually. Classical probabilities cannot handle this e ect, thus a framework based on quantum probability to model the phenomenon is proposed.
Most people agree that the combination pet tree is likely a bonzai and that a pet human is probably a slave, although none of these combinations exist in the English language, there is no connection between pet and the interpretations of the compounds, bonzai is a quite rare type of tree and slave is a rather rare type of human. Words that are connected to a combination but are not connected to the single constituent words of the combination are termed \emergent associates". This capacity that humans have to share a creative understanding of novel combinations has been at the centre of several studies in psychology and cognitive science trying to understand what are the processes conducting to their interpretation. In particular, we have evidence that some novel combinations yield to associates that cannot be predicted from the associates of the words taken separately nor from a collection of documents containing both words together.
Information Retrieval (IR) systems can deal with combinations only if
they occur in the documents, but they are still largely ignoring novel
combinations and emergent associates. In IR, novel combinations not
only can be encountered within queries and documents, but also are
essential to capture the intentions of authors or users. Multilingual users
may express queries using novel combinations assuming a consensus on
their interpretation when either they don't know the correct words
(paraphrasing) or they translate literally from their native language a concept
expressed as a combination. For example, a Chinese user may search
? The research leading to these results has received funding from the European Union
Seventh Framework Programme (FP7/2007-2013) under grant agreement N. 247590.
documents relevant to hippopotamus after literally translating it river
horse, and lobster would be literally translated dragon shrimp. This
strategy could work in human to human communication, but automatic
systems are to date not able to infer such new meanings as early work on
cross-lingual information retrieval using dictionary based translation has
proven [
The previous examples of usage of novel combinations re ect the main problems (among others) QONTEXT (EU funded contract N. 247590) is striving to address: (i ) can we predict whether a combination will yield to an emergent associate? (ii ) can we predict what will be the meaning of an novel combination? 2
The key to solve these problems is to nd a representation that allows
for the modelling of the emergence of unexpected associates from novel
combinations. Classical representations of words and their meaning are
either based on semantic networks (formal relations) or semantic spaces
(based on co-occurrences). Composition is then expressed as a function of
the neighbours or the dimensions of each word taken individually within
a single space [
Quantum Theory (QT) has been previously shown to be the only way
of going beyond the classical interpretation of compositionality to solve
the problem of typicality of combinations [
In the classical probabilistic model, events (e.g., associates or
combinations) are represented as sets and the probability measure is based on
a set measure, e.g., set cardinality. In contrast, in quantum probability,
events are represented as subspaces and probabilities are generated by
density matrices3, the most simple case being vectors. Suppose that the
vectors jwi, jbi represent an event and a density, respectively.4 The
probability that w occurs given b is provided by the quantum probability rule,
that is, jhwjbij2 = jawbj2 where awb is termed amplitude and jhxjxij2 = 1
for every jxi.5. In general, the probability measure is given by the trace
of the product between the density matrix which corresponds to the
probability distribution, and the matrix representing an event. A
quantum probability space is then given by a set of subspaces and a density
matrix. [
Suppose that b = b1b2 is a combination (e.g. pet tree) and v is an associate (e.g., slave or bonzai ). Using classical probability, these events are sets and then b b1; b2 (if b occurs, then both b1 and b2 occur but the viceversa does not hold). Suppose also that b1 and b2 are quite common words, thus their probability is not negligible. Moreover,
P (v; b1)
P (v; b1; b2)
P (v; b)
P (v; b2)
P (v; b1; b2)
P (v; b) If v (e.g., bonzai ) rarely occurs with b1 (e.g., pet ) or with b2 (e.g., tree), it is also rare within b and thus it cannot be an emergent associate, which cannot be detected by classical probability.
Using quantum probability, instead, jbi = aibjbii + aibjbii jaibj2 + jaibj2 = 1 hbijbii = 0 where the sum of the rst two terms of the right-hand side is the classical probability P (vjb) and
I = jaibjjaivjjaibjjaivj cos (1) (2) is the interference term. The conditions for emergence can be studied using (1) and (2). As 1 I +1, (1) can be lower or higher than P (vjb) and then can be used for predicting emergent associates. The estimation of I is thus crucial. In particular, whereas the the jaijj2's are 3 In general, density operators. 4 The Dirac notation is used in QT. 5 hxj is the transpose of jxi.
empirical probabilities, the estimation of cos is the most di cult step because it is mainly due to the interpretation of , which is the angle of the complex number aibaivaibaiv { further investigation are then needed. The vector formalism allows us to build the quantum probability space. Suppose that the empirical probabilities jaijj2 are estimated for n associates w1; : : : ; wn with respect to the bi's, i = 1; 2. If the jaijj2's are arranged in a 2 n matrix, (jw1i jwni) = jbii jbii ain ain Through SVD of the 2 n matrix, the jwji's and the jbii's can be built, thus obtaining the space and the probability jhb1jb2ij2 which measures the distance between the constituent words of the combination b. 5
A single representation of the events is obtained so that the empirical probabilities can be reproduced by the quantum probability rule. The modeling results are still quite preliminary, however, we are con dent that the ongoing research may provide the useful theoretical framework for detecting emergent associates.