Abstract 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.