Linguistics and Philosophy

, Volume 29, Issue 1, pp 91-134

First online:

Explaining Crossover and Superiority as Left-to-right Evaluation

  • Chung-Chieh ShanAffiliated withDepartment of Computer Science and Center for Cognitive Science, Rutgers, the State University of New Jersey Email author 
  • , Chris BarkerAffiliated with0108 Department of Linguistics, University of California San Diego

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We present a general theory of scope and binding in which both crossover and superiority violations are ruled out by one key assumption: that natural language expressions are normally evaluated (processed) from left to right. Our theory is an extension of Shan’s (2002) account of multiple-wh questions, combining continuations (Barker, 2002) and dynamic type-shifting. Like other continuation-based analyses, but unlike most other treatments of crossover or superiority, our analysis is directly compositional (in the sense of, e.g., Jacobson, 1999). In particular, it does not postulate a level of Logical Form or any other representation distinct from surface syntax. One advantage of using continuations is that they are the standard tool for modeling order-of-evaluation in programming languages. This provides us with a natural and independently motivated characterization of what it means to evaluate expressions from left to right. We give a combinatory categorial grammar that models the syntax and the semantics of quantifier scope and wh-question formation. It allows quantificational binding but not crossover, in-situ wh but not superiority violations. In addition, the analysis automatically accounts for a variety of sentence types involving binding in the presence of pied piping, including reconstruction cases such as Whose criticism of his i mother did each person i resent?