Continuations and natural language by Chris Barker and Chung-chieh Shan (review)

This book presents the results of a long-term collaboration between the two authors, Chris Barker and Chung-chieh Shan, on the application of the notion of ‘continuation’ in the study of natural language syntax-semantics interface. ‘Continuation’ is a notion originally developed in theoretical computer science. In its application to natural language grammar, it is essentially a tool for explicitly representing the ‘larger (syntactic) context’ in which some piece of linguistic expression is interpreted. As one might expect, this is useful for analyzing linguistic expressions that take scope outside of the immediate syntactic environments in which they occur (such as quantifiers), enabling one to capture explicitly the way they interact with scope-sensitive phenomena such as the binding of pronouns and the licensing of negative polarity items (NPIs).

The book consists of two parts: Part 1 deals with ‘order-sensitive’ phenomena (weak crossover (WCO), superiority, NPI licensing, and donkey anaphora) involving ordinary generalized quantifiers, and Part 2 deals with more complex types of scope taking (parasitic scope) in symmetrical predicates (same, different, etc.) and with sluicing. Both parts present analyses of linguistic phenomena in explicit fragments of English, but, as explained below, the fragments in the two parts are somewhat different.

Part 1 of the book develops a version of combinatory categorial grammar (CCG) called the ‘tower grammar’, which is designed for the analysis of ‘order-sensitive’ phenomena. This fragment is a version of CCG in the sense that it recognizes (generalized versions of) the familiar type-raising (or type-lifting) rule and related rules as axioms. (But it should be kept in mind that it is substantially different from the widely known version of CCG by Steedman (2000, 2012); B&S themselves provide a lucid comparison in Ch. 11.) The fragment is presented using the newly invented ‘tower notation’. This new notation greatly enhances the presentation (to see this, compare Shan & Barker 2006, which presents the same fragment using combinators alone). Part 1 moreover contains many exercises, useful for checking one’s understanding of the material. The key empirical claim in Part 1 is that phenomena such as WCO, superiority, and NPI licensing all involve sensitivity to ‘evaluation order’ (which in many, but not all, cases coincides with surface word order). Familiar contrasts, such as Every student_i loves his_i mother vs. *His_i mother loves every student_i (WCO), are accounted for by the way in which certain linguistic phenomena—binding in this case—are sensitive to the ‘order of evaluation’. Specifically, the fragment is set up in such a way that quantificational binding is possible only if the binder linearly precedes the bindee, signaling, as it were, the presence of the bindee in the rest of the sentence. Technically, this order sensitivity is captured by specifying which of the different ‘combinatory rules’ are posited as licit rules in the fragment (this point becomes important in the comparison with the NL_λ system introduced in Part 2).

An intriguing property of this account of WCO and related phenomena is that an apparent exception to order sensitivity in reconstruction environments (Which of his_i relatives does every man_i admire most?, which is fully grammatical despite the pronoun linearly preceding its binder) is accommodated naturally: one merely needs to assume that the ‘trace’ of wh-movement can be of a higher-order type, inheriting the ‘bindability’ of the fronted expression containing the pronoun (represented explicitly in the syntactic and semantic types of the fronted expression, which the trace inherits via an independently motivated mechanism for extraction).

In Part 2, the tower grammar is no longer used, and B&S instead present a variant of type-logical grammar (TLG) called NL_λ, which by itself does not encode order sensitivity (the dilemma here essentially lies in the fact that the simple option of controlling order sensitivity by admitting only some of the combinatory rules is unavailable in NL_λ, since what correspond to those rules are theorems in NL...