Abstract
Indexed grammars are shown to correspond to an existential monadic second-order logic over phrase structure trees, extended with a single existential quantifier ranging over a certain type of unary function. Indexed grammars are also shown to correspond to contingency grammars, a strengthening of context-free grammars that makes use of such unary functions.
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Langholm, T. A Descriptive Characterisation of Indexed Grammars. Grammars 4, 205–262 (2001). https://doi.org/10.1023/A:1012228321223
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DOI: https://doi.org/10.1023/A:1012228321223