Diagnosing Movement via the Absence of C-command Relations

In this paper, we propose a new diagnostic for movement. It has been argued in the computational linguistics literature that some constraints can be formalized by path constraints on the sequence of their c-commanders (Graf and Shafiei 2019), and that some constraints can be formalized by the tree configuration they appear in (Graf and Heinz 2015). It holds that path constraints are a special case of tree constraints. We make the observation that path constraints cannot account for phenomena that have been argued to involve movement of the element requiring licensing, namely for ATB-extraction and parasitic gaps. However, the reverse does not hold: adjuncts islands and freezing effects, which also involve movement, can be formalized by path constraints. We thus propose the following one-way generalization: Whenever a phenomenon cannot be captured by path constraints, and can be captured by tree constraints, this phenomenon involves movement. We contend that this is not surprising given the fact that constraints on the well-formedness of the Move operation cannot be captured by path constraints, and rather must be captured by tree constraints (Graf 2018). This working paper is available in University of Pennsylvania Working Papers in Linguistics: https://repository.upenn. edu/pwpl/vol26/iss1/16 Diagnosing Movement via the Absence of C-command Relations Sabine Laszakovits and Thomas Graf∗ 1 Path Constraints and Tree Constraints Constraints are a core mechanism of many generative formalisms, including Minimalist syntax. Despite their ubiquity, constraints are still poorly understood at a formal level. How should one measure the complexity of constraints? Do the constraints we find in natural languages display uniform complexity? What are the limits of syntactic constraints, and what causes these limitations? A restrictive theory of constraints would make strong typological predictions and provide new diagnostic criteria for syntactic analysis. These questions have recently been explored in subregular syntax. Subregular syntax builds on the notion of subregular complexity, which has been insightfully applied to phonology (see Heinz 2018 and references therein). However, subregular syntax has not yielded a uniform perspective of constraints. Graf and Shafiei (2019) analyze c-command licensing conditions such as Principle A and NPI licensing as constraints on a particular kind of string that lists a node’s c-commanders. Graf (2018), on the other hand, applies constraints directly to a compact tree representation called tree tiers. These constraints are needed to correctly regulate movement, and they cannot be restated in the string-based terms of Graf and Shafiei (2019). This leaves us with a bifurcation of constraints: path constraints apply to strings of c-commanders, whereas tree constraints apply to tree-like structures (phrase structure trees, derivation trees, tree tiers, and so on). This leaves us with the question which class of constraints is more appropriate. In many respects, path constraints are more limited than tree constraints, so on methodological grounds they should be preferred whenever possible. In this paper, we add an empirical dimension to the debate. While the path constraints of Graf and Shafiei (2019) can accommodate a wide range of phenomena, they provably fail in two cases: ATB-extraction, and parasitic gaps. Intuitively, path constraints fail because these two phenomena involve a dependency between elements that occur in independent subtrees and thus do not stand in a c-command relation to each other. Both phenomena are intrinsically tied to movement, though, which is already known from the work of Graf (2018) to be beyond the purview of path constraints. We thus conjecture that phenomena that cannot be captured by path constraints invariably involve movement. If this is correct, then non-definability in terms of path constraints provides indirect evidence for movement. This paper is organized as follows. In Section 2 we look at examples of path constraints by investigating formalizations of Principle A of Binding Theory in English (Section 2.1), adjunct islands (Section 2.2), and freezing effects (Section 2.3). Whereas the first two build on existing work on the literature, the account of freezing effects is a novel contribution. In Section 3 we show that ATB-extraction (Section 3.1) and parasitic gaps (Section 3.2) cannot be formalized with path constraints, but can be formalized with tree constraints. We proceed to draw a connection between tree constraints and movement in Section 4, which leads us to our generalization that phenomena that cannot be expressed via path constraints invariably revolve around movement. We conclude in Section 5. 2 Phenomena with Path Constraints As the concept of path constraints is both fairly new and fairly abstract, we cover several examples that illustrate just how much of syntax can be reduced to this simple piece of formal machinery. We start with sketches of how one would formalize anaphora binding (Section 2.1) and adjunct islands (Section 2.2), based on work in Graf and Shafiei (2019) and Shafiei and Graf (2020), respectively. Section 2.3 then presents a novel analysis of freezing effects to illustrate that at least some complex ∗For helpful comments and discussion, we thank the members of the Math Ling Reading Group at Stony Brook University and the audience and the reviewers of PLC 43. U. Penn Working Papers in Linguistics, Volume 26.1, 2020 136 SABINE LASZAKOVITS AND THOMAS GRAF conditions on movement can also be captured with path constraints. 2.1 Anaphor Binding in English The first phenomenon concerns the licensing of reflexives (anaphor binding, Condition A) in English. According to the standard analysis (Chomsky 1981), reflexives need to be c-commanded by their antecedent within a certain locality domain. In (1), this is fulfilled: the reflexive herself is licensed by the c-commanding local φ -matching antecedent Janet. This contrasts with (2), where a domain boundary intervenes between herself and Janet. It also differs from (3), where the antecedents Bill and Janet are both local but Bill does not φ -match the reflexive and Janet does not c-command the reflexive. (1) Janet likes herself. (2) * Janet thinks that Bill likes herself. (3) * Bill invited Janet before liking herself. Chomsky’s (1981) proposal can directly be translated into a path constraint in the sense of Graf and Shafiei (2019). For each node in the tree, one first computes a string that consists of the node followed by all its c-commanders, ordered from lowest to highest. Strictly speaking, Graf and Shafiei (2019) use a slightly different command relation that is sometimes called d-command in the computational literature. D-command differs from c-command in that I) a head commands both its specifier and its object, and II) a specifier does not command its head, and III) only heads can stand in d-command relations, not phrases (so if XP c-commands YP, the head X d-commands the head Y). The minor differences between c-command and d-command are immaterial for this paper, but to avoid confusion we will use the term d-command whenever we refer to the formal command relation, whereas c-command may still be used as a descriptive term. In (4) we show the paths for all lexical items in the depicted tree ($ explicitly marks the start and end of a string, which is done for mathematical reasons).