Two closely related types of context-free grammars called X-bar and strong X-bar grammrs are presented along the lines of Jackendoff (1977). The family E of languages generated by strong X-bar grammars is properly included in the family K of languages generated by X-bar grammars, which, in turn, is a proper subset of the context-free family L_2. E and K cannot be compared to the regular, OL, and TOL families, and both are anti-AFLs.
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