In other words, the implicational hierarchy defines the possible combinations of properties A, B, C, and D as listed in matrix (2): Implicational hierarchies are a useful tool in capturing linguistic generalizations pertaining the different components of the language.
(3) is an example of an implicational hierarchy concerning the distribution of nasal phonemes across languages, which concerns dental/alveolar, bilabial, and palatal voiced nasals, respectively: (3) /n/ < /m/ < /ɲ/ This hierarchy defines the following possible combinations of dental/alveolar, bilabial, and palatal voiced nasals in the phoneme inventory of a language: (4) In other words, the hierarchy implies that there are no languages with /ɲ/ but without /m/ and /n/, or with /ɲ/ and /m/ but without /n/.
On the other hand, the hierarchy provides implications for the morphological marking: if the plural is coded with a certain number of morphemes, then the dual is coded with at least as many morphemes.
Implicational hierarchies also play a role in syntactic phenomena.
For instance, in some languages (e.g. Tangut) the transitive verb agrees not with a subject, or the object, but with the syntactic argument which is higher on the person hierarchy.