title: Implicational hierarchy
text: # Implicational hierarchy
  
  Implicational hierarchy, in linguistics, is a chain of implicational universals. A set of chained universals is schematically shown as in (1):
  
  (1) A < B < C < D
  
  It can be reformulated in the following way: If a language has property D, then it also has properties A, B, and C; if a language has a property C, then it also has properties A and B, etc. In other words, the implicational hierarchy defines the possible combinations of properties A, B, C, and D as listed in matrix (2):
  
  | | A | B | C | D |
  | - | - | - | - | - |
  | Type 1: | + | + | + | + |
  | Type 2: | + | + | + | - |
  | Type 3: | + | + | - | - |
  | Type 4: | + | - | - | - |
  | Type 5: | - | - | - | - |
  
  Implicational hierarchies are a useful tool in capturing linguistic generalizations pertaining the different components of the language. They are found in all subfields of grammar.
  
  ## Phonology
  
  (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)
  
  | | /n/ | /m/ | /ɲ/ |
  | - | - | - | - |
  | Type 1: | /n/ | /m/ | /ɲ/ |
  | Type 2: | /n/ | /m/ | - |
  | Type 3: | /n/ | - | - |
  
  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/.
  
  ## Morphology
  
  Number marking provides an example of implicational hierarchies in morphology.
  
  (5) Number: singular < plural < dual < trial / paucal
  
  On the one hand, the hierarchy implies that no language distinguishes a trial unless having a dual, and no language has dual without a plural. 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.
  
  ## Syntax
  
  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.
  
  (5) Person: first < second < third
  
  See also: animacy.
  
  