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.

Morphological systems across languages vary when it comes to the relation between form and meaning. In some languages, a single meaning feature corresponds to a single morpheme, whereas in other languages, multiple meaning features are bundled together into one morpheme. The two types of languages have been called agglutinative and fusional, respectively, but this distinction does not capture the graded nature of the phenomenon. We provide a mathematically precise way of characterizing morphological systems using partial information decomposition, a framework for decomposing mutual information into three components: unique, redundant, and synergistic information. We show that highly fusional languages are characterized by high levels of synergy.