This thesis investigates the mechanisms applying in the interpretation of syntactic chains. The theoretical background includes a translation of syntactic forms into semantic forms and a model theoretic explication of the meaning of semantic forms. Simplicity considerations apply to all three stages of the interpretation process: syntactic derivation, translation into semantic forms, interpretation of semantic forms. Three main results are achieved. The first is that trace positions can have semantic content beyond what is needed for the semantic dependency of trace and binder. This extra content is some or all of the lexical material of the head of the chain, as expected on the copy theory of movement. Two independent arguments support this conclusion. One, discussed in chapter 2, is based on the distribution of Condition C effects, where novel interactions between variable binding, antecedent contained deletion and Condition C are observed. The second, developed in chapter 3, is based on conditions on the identity of traces observed in antecedent contained deletion constructions. Both arguments lead to the same generalizations about what lexical material of the head is interpreted in the trace position. The second main result is that lambda calculus is superior to both standard predicate logic and combinatorial logic as the mathematical model for the semantic mechanism mediating the dependency of trace (or bound pronoun) and binder. Chapter 4 argues this on the basis of the distribution of focus and destressing in constructions with bound pronouns. The third main result is that quantification must be allowed to range over pointwise different choice functions. Chapter 5 shows that quantification over individuals is insufficient, and that pointwise different choice functions are required. The result entails that the syntactic difference of A-chains and A-bar chains predicts a semantic difference in the type of the variable involved, which is argued to explain weak crossover phenomena. Chapters 6 argues that the interpretation procedures developed in the preceeding chapters account for all cases. It is shown that only traces of the type of individuals arise, and that scope reconstruction is a phonological phenomenon. The latter result also supports the T-model of syntax.