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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.