Constituent Structure - Part 24 | 150 CONTROVERSIES A third property of X-bar theory is that structures are endocentric. The LCA derives this effect as well. Consider the trees in 29 Assume that L M and P are all maximal categories. L is unheaded in both cases. Regardless of whether P or M for that matter is complex 29b or not 29a M asymmetrically c-commands R and P asymmetrically c-command Q so both q r and r q are in d A . Unheaded structures will necessarily result in cases where a conflicting ordering results. This rules out traditional categories like the unheaded S node and the kind of unheaded structures found commonly in LFG with verb displacement. It also rules out ternary branching structures. Adjunction The discussion in the last section shows that several basic properties of X-bar theory appear to follow from the LCA although they are at least inconsistent with the Speas-Fukui derived notions. But the LCA also has a surprising property that appears to be undesirable. A careful look at 29b also reveals that if we were to interpret L as a maximal category headed by R . R C P C and L CP then such a structure prevents any element M even when phrasal from appearing in the specifier of another phrase. Kayne resolves this by claiming that the things we currently think of as specifiers are better understood structurally as adjunctions which he claims differ in their c-command properties. A word on terminology is in order here. we need to distinguish between adjuncts and adjunctions and among types of adjunct. Many syntacticians use these terms as rough synonyms but I think there are some trends in usage where differences emerge. The term adjunction often refers to the output of a operation. For example for many years SET-THEORETIC CONSTITUENCY 151 Chomskyan grammarians have treated topicalization or heavy NP shifts as a type of adjunction. Conversely adjunct seems to be reserved for those situations where base generation is in effect. Adjunct itself has several distinct usages which .