Constituent Structure - Part 24 | 160 CONTROVERSIES representations start at the bottom with the first merge operation and then progresses upwards. a stands for a p stands for portrait s stands for of someone and t stands for the relative clause that Rivera painted. 45 a p p s a 4 p pi p p s t 5 a - Merge p p s - Pair merge t 3 2 p Merge s 0 Simple merge combines p and s portrait of someone into the set p p s in step 1 . This set is the input into two distinct operations which are not ordered with respect to each other nor interact with each other. In 21 the adjunct that Rivera painted t is merged with p p s resulting in p pi p p s t portrait of someone that Rivera painted. Simultaneously p p s is identified in 3 as a member of the set a p p s a a portrait of someone. It is this later set that merges into the derivation with the potential c-commander that should trigger but fails to trigger a condition-C effect. The set containing t that Rivera painted 3 intersects with 4 accounting for the compositional meaning but is not part of it explaining the Lebeaux effects. The set-theoretic notation then amounts to a tiered three-dimensional representation much like that found in autosegmental phonology except that the tiers are not linked geometrically but through set intersection. We return to multidimensional representations in Chapter 10 but it is worth noting that this explanation fails in one crucial regard it does not explain why sentences such as 44d are ungrammatical. If adjuncts are on a different dimension and do not interact with the c-command relationships in the non-adjunct portions of the representation then 44d is predicted to be fully grammatical. One possible solution which lies beyond the scope of this book can be found in Stepanov 2001 . Bottom-to-top and top-to-bottom derivations Another consequence of the BPS system is the strictly upwardly cyclic nature of the phrase structure derivation. The merge operation works from the terminals to the root. This is of course true of all .
