Applicability of Indexed Grammars to Natural Languages

Abstract

If we take the class of context-free phrase structure grammars (CF- PSGs) and modify it so that (i) grammars are allowed to make use of fInite feature systems and (ii) rules are permitted to manipulate the features in arbitrary ways, then what we end up with is equivalent to what we started out with. Suppose, however, that we take the class of context- free phrase structure grammars and modify it so that (i) grammars are allowed to employ a single designated feature that takes stacks of items drawn from some fInite set as its values, and (ii) rules are permitted to push items onto, pop items from, and copy the stack. What we end up with now is no longer equivalent to the CF-PSGs but is significantly more powerful, namely the indexed grammars (Aho, 1968). This class of grammars has been alluded to a number of times in the recent linguistic literature: by Klein (1981) in connection with nested comparative constructions, by Dahl (1982) in connection with topicalised pronouns, by Engdahl (1982) and Gazdar (1982) in connection with Scandinavian unbounded dependencies, by Huybregts (1984) and Pulman and Ritchie (1984) in connection with Dutch, by Marsh and Partee (1984) in connection with variable binding, and doubtless elsewhere as well.