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In linguistics, case government is government of the grammatical case of verb arguments, when a verb or preposition is said to 'govern' the grammatical case on its noun phrase complement, e.g. zu governs the dative case in German: zu mir 'to me-dative'. The German term for the notion is Rektion. Case government may modify the meaning of the verb substantially, even to meanings that are unrelated. Analogously in programming, constructing two different functions of identical name but different parameters is called overloading a function.
Case government is a more important notion in languages with many case distinctions, such as Russian and Finnish. It plays less of a role in English, because English doesn't rely on grammatical cases, except for distinguishing subject pronouns (I, he, she, we, they) from other pronouns (me, him, her, us, them). In English, true case government is absent, but if the aforementioned subject pronouns are understood as regular pronouns in the accusative case, it occurs in sentences such as He found me (not for example *He found I).
For example, in Finnish, a verb or sometimes even a particular meaning of a verb is associated with a case the referent noun must be in. "To go for a walk" is expressed as mennä kävelylle (literally 'to go to a walk'), where mennä means 'to go', kävely is 'a walk' and -lle is a postfix that denotes the allative case (usually means 'to' in English). This case must be always used in this context; one cannot say *mennä kävelyyn 'to go into a walk', for example.