Characterizing Idioms: Conventionality and Contingency (2022)

Abstract: Idioms are unlike most phrases in two important ways. First, words in an idiom have non-canonical meanings. Second, the non-canonical meanings of words in an idiom are contingent on the presence of other words in the idiom. Linguistic theories differ on whether these properties depend on one another, as well as whether special theoretical machinery is needed to accommodate idioms. We define two measures that correspond to the properties above, and we show that idioms fall at the expected intersection of the two dimensions, but that the dimensions themselves are not correlated. Our results suggest that introducing special machinery to handle idioms may not be warranted.

## introduction idioms-expressions like rock the boat-bring together two phenomena which are of fundamental interest in understanding language. first, they exemplify non-conventional word meaning @xcite . the words rock and boat in this idiom seem to carry particular meanings-something like destabilize and situation, respectively-which are different from the conventional meanings of these words in other contexts. second, unlike other kinds of nonconventional word use such as novel metaphor, there is a contingency relationship between words in an idiom @xcite . it is the specific combination of the words rock and boat that has come to carry the idiomatic meaning. shake the canoe does not have the same accepted meaning. in the literature, most discussions of idioms make use of prototypical examples such as rock the boat. this obscures an important fact: there is no generally agreed-upon definition of idiom; phrase types such as light verb constructions (e.g., take a walk) and semantically transparent collocations (e.g., now or never) are sometimes included in the class (e.g., @xcite and sometimes not (e.g., @xcite . this lack of homogeneity among idiomatic phrases has been recognized as a challenge in the domain of nlp, with @xcite suggesting that a variety of techniques are needed to deal with different kinds of multi-word expressions. what does seem clear is that prototypical cases of idiomatic phrases tend to have higher levels of both non-conventional meaning and contingency between words. this combination of non-conventionality and contingency has led to a number of theories that treat idioms as exceptions to the mechanisms that build phrases compositionally. these theories posit special machinery for handling idioms (e.g., @xcite @xcite ). an early but representative example of this position is @xcite , who posits the addition of two structures to linguistic theory: (1) an idiom list, where each entry contains a string of morphemes, its associated syntactic structure, and its sense description, and (2) an idiom comparison rule, which matches strings against the idiom list. such theories must of course provide principles for addressing the difficult problem of distinguishing idioms from other instances of non-conventionality or contingency. we propose an alternative approach, which views idioms not as exceptional, but merely the result of the interaction of two independently motivated cognitive mechanisms. the first allows words to be interpreted in non-canonical ways depending on context. the second allows for the storage and reuse of linguistic structures-not just words, but larger phrases as well (e.g., di @xcite @xcite . there is disagreement in the literature about the relationship between these two proper-ties; some theories of representation predict that the only elements that get stored are those with non-canonical meanings (e.g., @xcite , whereas others predict that storage can happen no matter what (e.g., @xcite . we predict that, consistent with the latter set of theories, neither mechanism should depend on the other. this paper presents evidence that prototypical idioms occupy a particular region of the space of these two mechanisms, but are not otherwise exceptional. we define two measures, conventionality-meant to measure the degree to which words are interpreted in a canonical way, and contingency-a statistical association measure meant to capture the degree to which the presence of one word form depends on the presence of another. our implementations make use of the pre-trained language models bert @xcite and xlnet @xcite . we construct a novel corpus of english phrases typically called idioms, and show that these phrases fall at the intersection of low conventionality and high contingency, but that the two measures are not correlated and there are no clear discontinuities that separate idioms from other types of phrases. our experiments also reveal hitherto unnoticed asymmetries in the behavior of head and non-head words of idioms. in idioms, the dependent word (e.g., boat in rock the boat) shows greater deviation from its conventional meaning than the head. ## conventionality and contingency in this section we describe the motivation behind our two measures and lay out our predictions about their interaction. our first measure, conventionality, captures the extent to which subparts of a phrase contribute their normal meaning to the phrase. most of language is highly conventional; we can combine a relatively small set of units in novel ways, precisely because we can trust that those units will have similar meanings across contexts. at the same time, the linguistic system allows structures like metaphors and idioms, which use words in non-conventional ways. our conventionality measure is intended to distinguish phrases based on how conventional the meanings of their words are. our second measure, contingency, captures how unexpectedly often a group of words occurs to-gether in a phrase and, thus, measures the degree to which there is a statistical contingencythe presence of one or more words strongly signals the likely presence of the others. this notion of contingency has also been argued to be a critical piece of evidence used by language learners in deciding which linguistic structures to store (e.g., @xcite . to aid in visualizing the space of phrase types we expect to find in language, we place our two dimensions on the axes of a 2x2 matrix, where each cell contains phrases that are either high or low on the conventionality scale, and high or low on the contingency scale. the matrix is given in figure 1 , with the types of phrases we expect in each cell. low high conv. conv. high idioms common cont. (e.g., raise hell) collocations (e.g., in and out) low novel regular cont. metaphors language use (e.g., eat peas) we expect our measures to place idioms primarily in the top left corner of the space. at the same time, we predict a lack of correlation between the measures and a lack of major discontinuities in the space. we take these predictions to be consistent with theories that factorize the problem into two mechanisms (captured by our dimensions of conventionality and contingency). we contend that this factorization provides a natural way of characterizing not just idioms, but also collocations and novel metaphors, alongside regular language use. ## methods in this section, we describe the creation of our corpus of idioms and define measures of conventionality and contingency. given that definitions of idioms differ in which phrases in our dataset count as idioms (some would include semantically transparent collocations, others would not), we do not want to commit to any particular definition a priori, while still acknowledging that people share somewhat weak but broad intuitions about idiomaticity. as we discuss below, our idiom dataset consists of phrases that have at some point been called idioms in the linguistics literature. ## validation of conventionality measure our conventionality measure provides an indirect way of looking at how canonical a word's meaning is in context. in order to validate that the measure corresponds to an intuitive notion of unusual word meaning, we carried out an online experiment to see whether human judgments of conventionality correlated with our automatically-computed conventionality scores. the experimental design and results are described below. (note that our contingency measure directly computes the statistical quantity we want, so validation is not necessary.) ## analyses in this section we present analyses of our two measures individually, showing that they capture the properties they were intended to capture. we then investigate the interaction between the measures. section 5.3 evaluates our central predictions. we predict that the target phrases will score lower on conventionality than the matched phrases, since we expect these phrases to contain words with (often highly) unconventional meanings. we further predict that the target phrases will have higher contingency scores than the matched phrases, due to all of the target phrases being expressions that are frequently reused. putting the two measures together, we expect idioms to fall at the intersection of low conventionality and high contingency, but not to show major discontinuities that qualitatively distinguish them from phrases that fall at other areas of intersection. ## asymmetries between heads and dependents our experiments revealed an unexpected but interesting asymmetry between heads and their dependents. based on conventionality scores, the head word of the target phrases was more conventional on average than the primary non-head word. a two-sample t-test revealed that this difference was significant (@xmath0.029, @xmath1.45, @xmath2.0027). the matched phrases did not show a significant difference between heads and non-heads (@xmath3.506, @xmath4.42, @xmath5.1332). figure 5 presents the data in a different way, with target and matched phrases plotted together. the plots show that the variability in overall phrase conventionality, which helps to distinguish idioms and non-idioms, is largely driven by the dependent word (as indicated by the steeper slopes for the non-head effects). this interaction between phrase conventionality and head/non-head is significant (see row 10 of in addition, figure 5 illustrates that this discrepancy between heads and non-heads is largest for verb object phrases. we confirm this by fitting a linear model of word conventionality with predictors for phrase conventionality (average of the component words), head versus non-head word, and syntactic class, plus all interactions, using sum coding to compare factor levels of syntactic class. 7 the effect of headedness on conventionality scores is significantly greater for verb object phrases than the global effect of headedness (see panel 4 of figure 5 ; row 14 of we note that there is disagreement in the literature about whether binomial phrases (which are coordinate structures) contain a head at all. some proposals treat the first conjunct as the head (e.g., @xcite @xcite , while others treat the conjunction as the head or claim that there is no head (e.g., @xcite . we find that in the binomial case, the first conjunct patterns like the heads of the other phrase types, though how much of this effect may be driven by linear order remains unclear. this may provide suggestive converging evidence for the first-conjunct-as-head theory, though further exploration of this idea is needed. ## related work many idiom detection models build on insights about unconventional meaning in metaphor. a number of approaches use distributional models, such as @xcite , @xcite , sa-pereira (2016), and @xcite , the latter of which was one of the first to implement a fully unsupervised approach for encoding relationships between words, their contexts, and their dependencies. a related line of work aims to automatically determine whether potentially idiomatic expressions are being used idiomatically or literally, based on contextual information @xcite @xcite . our measure of conventionality is inspired by the insights of these models; as described in section 3.2, our measure uses differences in embeddings across contexts. meanwhile, approaches to collocation detection have taken a probabilistic or informationtheoretic approach that seeks to identify colloca- nn vo an b -4 -2 0 2 -4 -2 0 2 -9 -6 -3 0 3 -9 -6 -3 0 3 phrase conventionality (rescaled) word conventionality (rescaled) word type head non-head figure 5: change in head versus non-head conventionality scores as phrase conventionality increases, for all phrases (target and matched), separated by phrase type (adjective noun, binomial, noun noun, and verb object). while much of the literature in nlp recognizes that idioms share a cluster of properties, including semantic idiosyncrasy, syntactic inflexibility, and institutionalization (e.g., @xcite @xcite , our approach is novel in attempting to characterize idioms along two orthogonal dimensions that correspond to specific proposals from the cognitive science literature. our measures may offer a new avenue for tackling automatic idiom detection. ## discussion & conclusion we investigated whether idioms could be characterized as occupying the intersection between contingency and conventionality, without needing to appeal to idiom-specific machinery that associates the storage of multi-word expressions with the property of unconventional meaning, as has been proposed in previous work. when we plotted conventionality and contingency scores against each other, we found that idioms fell, on average, in the area of low conventionality and high contingency, as expected. regular, non-idiomatic phrases fell in the high conventionality, low contingency area, also as expected. the lack of correlation between the two measures provides support for theories that divorce the notions of conventionality and contingency. our results suggest that idioms represent just one of the ways that conventionality and contingency can interact, analogous to collocations or metaphor. we also presented the novel finding that the locus of non-conventionality in idioms resides primarily in the dependent, rather than the head, of the phrase, a result that merits further study.