3.1 Methods

11Previous studies about negation of adjectives described its effect as a meaning shift from the adjective towards the antonym, that can be measured in terms of semantic similarity (Fraenkel and Schul, 2008). Distributional Semantics offers us a data-driven method of quantifying this: we can represent expressions as vectors summarizing their large-scale patterns of usage and then interpret their proximity relations in terms of similarity.

12To this aim, we build a distributional semantic model with standard techniques, but whose vocabulary includes, besides word units, also negated adjectives. In practice, each occurrence of a negated adjective (adjacent occurrence of not and an adjective without intervening words; e.g., we exclude cases like not very cold) is treated as a single and independent token (e.g., not cold not_cold). With this pre-processing, we train a word2vec CBOW model (Mikolov et al., 2013)3 on the concatenation of UkWaC and Wackypedia-En corpora (2.7B tokens; Baroni et al., (2009)), setting parameters as in the best performing model by Baroni et al. (2014).4 We do not carry out any hyperparameters search, nor we employ any ad hoc techniques aimed at, for example, amplifying the distances between antonyms in the semantic space (such as that of Nguyen et al. (2016) or The Pham et al. (2015)). Indeed, we are interested in investigating characteristics of antonyms and negated adjectives in a standard distributional model, that is not fine-tuned to a particular task and where no assumptions about the structure of its space are incorporated. However, we assess the quality of the induced model through a similarity relatedness task, where we find that it achieves satisfying performances.5

13For our analyses, we consider triples as those described in Section 2. Given a triple (e.g., cold, hot, not cold), we define the following score:

(3) Shift := Sim(not ) − Sim(not )

14where , and Sim(not ) and Sim(not ) are the cosine similarities of the negated adjective with the antonym and the adjective, respectively. This measures how much closer a negated adjective is to the antonym than to the adjective (i.e., how much closer not cold is to hot than to cold), and hence how much negation shifts the meaning of an adjective towards that of the antonym. Due to the well-known tendency of antonyms to be close in a distributional space (Mohammad et al., 2013), the absolute value of Shift is not expected to be high (a vector close to one is likely close to the other too). However, we can test whether a higher proximity is registered towards one of the two adjectives.

15From the data introduced in Section 2, we only consider triples where each of the three elements occurs at least 100 times in the training corpus of the distributional model. Table 1 shows the number of triples considered for each class and the average frequency of adjectives and negated adjectives.6 The number of contradictory triples is small due to the choice of keeping only antonyms for which we had full agreement in the annotation; double negations triples are few due to the limited frequency of these expressions in the corpus.7

3.2 Results and discussion

16Table 2 shows the scores across the different categories mentioned in Section 2. Example triples for each category are given in Table 3, together with the nearest adjectives of each element in the triple.

17Lexical vs. morphological antonyms The average Shift scores of both classes are negative, showing that a negated adjective is typically closer to the adjective than to the antonym. Indeed, as shown in Table 3, the nearest neighbor of a negated adjective is often the related adjective. On one hand, this could be seen as supporting the idea that negated adjectives express an intermediate meaning between that of the adjective and the antonym (e.g., not small is close to normal-sized). More in general, it shows that negated adjectives have a profile of use that is more similar to that of the adjective than to the antonym.

18The two classes of antonyms differ significantly in the extent of this effect: negated adjectives are closer to a morphological antonym than a lexical one (e.g., not perfect vs. imperfect, not wide vs. narrow). Such similarity in distribution can be explained by the similarity in structure, and hence possibly in meaning, of negated adjectives and affixal negations. Yet, in spite of the higher similarity in use, affixal negation still does not seem equivalent to negation by not, due to the negative average Shift value.

19Contrary vs. contradictory antonyms In contrast to the results from the linguistic literature (see Section 2), the behavior of contrary and contradictory antonym pairs is not significantly different in our analysis. When we look into a distributional space, even for contradictory antonyms, the negated adjectives tend to be more similar to the adjective itself than to the antonym.

20This result points at the fact that distributional similarity is capturing a different type of similarity from that considered in the experiments of Fraenkel and Shul (2008). We cannot thus directly interpret our results as just a product of the mitigating aspect of negation. Distributional information may discriminate between the negation of an adjective and the antonym, even when the two seem intuitively equivalent (e.g., not dead is closer to dead than to alive): indeed, the use of one or the other may serve different functions (e.g., contradicting an expectation, politeness, etc.), leading them to appear in different contexts. Moreover, we find that, since continuous representations are able to capture nuanced differences, the alleged dichotomy between contrary and contradictory antonyms may become a continuum in distributional space: for example, one of the closest adjectives to not dead is half-dead. This further underscores the difficulty in distinguishing between contrary and contradictory antonyms which we had already encountered in the annotation.

21Simple vs. double negations There is not a significant difference between negated adjectives that are instances of simple and double negations: crucially, it is not the case that double negations are very close to the antonym as a result of the two negations canceling each other out (e.g., not unhappy is closer to unhappy than to happy).

22As before, the result cannot be interpreted only in terms of mitigation (though, e.g., not unhappy is close to unimpressed, hence a mid-value between happy and unhappy). In general, it suggests that the contexts of use of double negations are more similar to the ones of the adjective that is negated than to those of its antonym. Indeed, double negations typically appear in contexts where the use of the “logically” equivalent alternative (i.e., the antonym) is to be avoided for pragmatic reasons, as possibly too strong or direct (e.g., not unproblematic vs. problematic; Horn, (1984)).

4 Conclusion

23We have investigated negated adjectives using the tools of Distributional Semantics, which allows us to quantify the similarities between expressions on the basis of how they are used. Our analyses show that, when considering contexts of occurrence, negating an adjective does not make it closer to the antonym than to the adjective itself. This can be seen as a result of the various functions of negation (e.g., mitigation, contradiction to an expectation, politeness) that may lead to different patterns of use for negated adjectives and antonyms. Further research may shed light on which type of contexts actually discriminate them, for example through a corpus study, and which other properties negated adjectives have in a distributional space, such as their interaction with scalar dimensions (e.g., not hot vs. freezing, cold, lukewarm, hot etc.; Wilkinson and Tim (2016)). Finally, while for the purpose of this study we opted for a standard word2vec model, one could test for the same effects with differently obtained distributional vectors.

24Despite its current limitations in covering truth-related aspects of meaning, Distributional Semantics was shown by Kruszewski et al. (2017) to be apt to model at least some aspects of negation, especially if graded in nature, such as alternativehood. Our study provides supporting evidence for this line of research and in addition points at the utility of using Distributional Semantics to uncover nuanced differences in use between a negation and other expressions, even when logically equivalent. Moreover, we regard our results to be of general interest for the NLP community, since effects of negation like the ones we studied and how they are represented in a distributional space can be critical for tasks like sentiment analysis (e.g., what does it imply that a costumer is not happy or not unhappy with a product?; Wiegand et al, (2010)).