1.1 Focus-sensitive coordination

Focus-sensitive coordination structures are a class of constructions that contain a coordinator like let alone, much less, and to some extent never mind, in the scope of explicit or implicit negation,² which impose a suite of syntactic, pragmatic, and prosodic constraints on their conjuncts. Following current literature (Hulsey 2008; Toosarvandani 2010; Harris 2016), we assume that the second conjunct is the remnant of ellipsis, rather than a simple constituent. For example, Harris (2016) proposes that the overt conjunct vodka in (6a) corresponds to the remnant of ellipsis, which moves into a focus position FocP above the elided clause (I drink t₁) as in (6b). This derivation is on par with other move-and-delete accounts of clausal ellipsis, such as those for stripping/bare argument ellipsis (Frazier et al. 2012; Sailor & Thoms 2014), sluicing (Merchant 2001), or fragment answers (Merchant 2004; Weir 2014).

Though not reviewed in detail here, the ellipsis account of focus-sensitive coordination structures is supported by many distributional tests that align it with so-called small conjunct ellipsis (see Hulsey 2008 for a gapping account, and Harris 2016 for a move-and-delete account similar to those proposed for stripping/bare argument ellipsis). Consequently, we will continue to use key terminology from the ellipsis literature to describe the components of the structure: a “remnant” (vodka) that represents the non-elided material in the clause containing the ellipsis, and a “correlate” (beer) in the antecedent clause that contrasts with the remnant.

Focus-sensitive coordination is similar to stripping/bare argument ellipsis and sluicing ellipsis in that the correlate and the remnant bear pitch accent in the most felicitous pronunciation, typically with accents that mark contrastive focus (Harris & Carlson 2018). In the examples below, contrastive accent is indicated with CAPS. Note that the contrastive element in the remnant corresponds to a contrastive correlate in the antecedent, regardless of whether the constituents are nouns (7a), verbs (7b), verb phrases (7c), or modifiers (7d).

However, research on a range of ellipsis structures has found that overt prosodic marking on a noun increases the likelihood of it being selected as a correlate, but does not entirely disambiguate the sentence (e.g., Carlson 2001; Carlson et al. 2009; Carlson, Frazier & Clifton 2009; Harris & Carlson 2018). Listeners still can and do choose unaccented nouns as correlates, potentially due to a preference for local correlates, or an expectation about the default position of focus. For example, Rooth (1992) noted that while contrastive accent is necessary on a remnant, it is not actually required on the correlate, though it could be useful in locating the intended correlate.

Finally, and perhaps most crucially for present purposes, the antecedent and the elided clause stand in a scalar relationship. In particular, the negative antecedent (I can’t drink beer) seems to strongly imply or contextually entail the clause containing the ellipsis, also negated (I can’t drink vodka for (7a)), intuitively evoking a scalar relationship between beer and vodka (Fillmore et al. 1988; Toosarvandani 2010). Two kinds of scales are often discussed in the literature. The first are conventionalized or lexicalized scales, in which closed-class elements are logically ordered via semantic entailment or informativity. For example, lexical elements like cardinal numbers <one, two, three, …>, modals <can, must> and quantifiers <none, some, all> form conventionalized scales via entailment (Horn 1972; Hirschberg 1985). Such scales are thought to be context-independent, as they generalize to many occasions of use (e.g., Stiller, Goodman & Frank 2011). To take (7d) as an example: if you drink two beers, then, in all situations, you have also drunk one. Therefore, the (negated) proposition expressed in the antecedent clause (I can’t drink one beer) entails the (negation) of the ellipsis clause with the elided content (I can’t drink two beers).

The second kind of scales are sometimes known as ad hoc scales, which are highly dependent on context or the conversation at hand, and one must therefore know a great deal about the specific situation in addition to world knowledge and perhaps speaker intention to interpret them correctly (e.g., Hirschberg 1985). For example, (7a) can be understood as implicating that if I am unlikely or lack the capacity to drink beer, I therefore also am unlikely or lack the capacity to drink vodka, given its greater potency. Similarly, (7c) somehow implies that drinking beer is an easier or more expected activity than making wine, and so if I cannot perform the former, I therefore cannot perform the latter, even though drinking beer and making wine are logically unrelated events (a teetotaling oenologist might strike us as unusual, but certainly not as contradictory).

It is currently unclear whether one kind of scale might be more difficult to recover than the other. Conventionalized scales might be psychologically privileged, in that they could be accessible in more general contexts than ad hoc relations. Such a view would be compatible with Levinson’s (2000) neo-Gricean account, in which generalized conventional implicatures constitute interpretive defaults, and are consequently more readily accessible than particularized conventional implicatures. In other words, the unconstrained nature of ad hoc scalar relations would make them less accessible to comprehenders constructing interpretations in real time. Recent experiments do not shed much light on the matter, though they have shown that children (Papafragou & Tantalou 2004) and adults (Katsos & Bishop 2011) may treat these two kinds of scales in very different ways (for more discussion, see Katsos & Cummins 2012).

Example (8) illustrates that the (contextually) weaker element in focus-sensitive coordination must be located in the first conjunct; some may precede all (8a), but in many dialects the reverse is semantically incoherent, though seemingly grammatical (8b). Of course, this restriction does not carry over to other conjunctions, even those like but and although which make similar contributions to the discourse (8c).

The basic properties we assume for focus-sensitive coordination are summarized in (9).

We believe that these properties place a unique set of demands on the sentence processing system. As we shall see, they also allow us to formulate two potentially opposing hypotheses regarding the processing routines recruited to interpret ellipsis structures in real time. First, however, we articulate our assumptions regarding what basic information the processor needs in order to process focus-sensitive coordination generally.

1.2 Processing ellipsis and focus-sensitive coordination

As the literature on processing ellipsis structures is rapidly growing (e.g., Phillips & Parker 2014, for review), we will introduce only the bare essentials here. We assume that the processor must address three basic requirements (10) in order to resolve any remnant-based ellipsis, as discussed in Carlson & Harris (2017) for focus-sensitive coordination and Harris (2019) for sluicing ellipsis. Again, although we assume for concreteness that the structure of the ellipsis site is recovered from the context or from the antecedent site, this assumption is not required for the essentials of our account.

We use example (6) to illustrate the three tasks in more depth in (11). We assume that each process depends on the previous one. For instance, the parser must have established the basic syntactic category of the remnant (step 1) before it can locate a correlate of the appropriate type in the antecedent clause (step 2). Similarly, generating a structure for the elided clause (step 3) depends on having selected an appropriate correlate from the antecedent clause (step 2).³ Note that the parsing mechanisms needed for step 1 are standard, and are not processes unique to ellipsis.

Although focus-sensitive coordination has been studied far less than other kinds of ellipsis structures, there are a few recent results that bear on the processes outlined above. Regarding step 1, Harris (2016) found a small bias for VP remnants over DP/NP remnants in a variety of offline completion tasks when the fragment after let alone appeared without context (replicated in Harris & Carlson 2016, 2018). However, simply mentioning a salient DP object in preceding text weakened or overturned the bias. Further, VP and DP remnants did not show any categorical differences in online reading in eye tracking. He argued that these results were consistent with an ellipsis account over a simple coordination account, and that the processor constructs the clause containing the remnant upon encountering a focus-sensitive coordinator. In a follow up study, Harris & Carlson (2016) showed that the bias towards VP remnants could not be attributed to exposure in text alone, as English corpus searches showed a general mild preference for DP, not VP, remnants. Following Toosarvandani (2010), they proposed that the remnant-correlate pair is sensitive to an accessible Question Under Discussion, i.e., the question or topic that immediate conversation is meant to address, explicitly or implicitly (Roberts 1996, 2012).

With respect to step 2, Harris & Carlson (2016, 2018) found that the processing strategies used to pair the remnant, once parsed, with a correlate were similar to those used in other ellipsis structures. In particular, the processor appears to prefer the most local (or nearest) correlate of the appropriate syntactic type, a preference that prevails in sluicing and most likely reflects the tendency for English focus to appear late in a clause (for arguments from sluicing, see Carlson, Dickey et al. 2009). The preference for the most local correlate is exhibited not only across a variety of written and spoken corpora, but also very early in the online processing record. The general patterns are thus compatible with an ellipsis account in which the processor seeks to make the antecedent and the ellipsis clauses, especially the contrasted elements, parallel along syntactic, semantic, and prosodic dimensions (Carlson 2001; Dickey & Bunger 2011).

What, then, is the processor to do when the clause containing the remnant and ellipsis is not parallel with the antecedent? Instances of sprouting discussed above represent an extreme case, in which the remnant lacks a constituent in the antecedent. As reviewed above, prior studies have found that sprouted correlates incur a processing cost during online comprehension, due either to an ellipsis-specific operation in which the ellipsis site is modified to include a variable corresponding to the correlate (Frazier & Clifton 1998), or else to a side effect of a bias against non-parallel antecedents (Dickey & Bunger 2011). Focus-sensitive coordination, however, raises an intriguing possibility regarding sprouting. In addition to finding a correlate for the remnant (step 2), the correlate and remnant must ultimately be put onto a contextually salient scale whose properties are inferred through context (step 3). Notably, in cases of focus-sensitive coordination, sprouted correlates could facilitate recovery of a contextually salient scale via an entailment relation between the antecedent and elided clause.

In example (12a), the processor presumably must pair the remnant chemistry with the overt correlate carpentry, and accommodate an appropriate scale, e.g., one which deems carpentry a less difficult subject than chemistry, creating an inference from not being able to study carpentry to not being able to study chemistry. Without an overt correlate (12b), however, the proposition obtained from the antecedent (that Michael is not able to study) necessarily entails the proposition obtained from the clause containing the remnant and the ellipsis (that Michael is not able to study chemistry).⁴

In sluicing ellipsis, however, the relationship between clauses is much different. In the case with sprouting (13b), no such entailment relationship holds between the antecedent clause (Michael studied something) and the clause corresponding to the ellipsis (what₁ he studied t₁). The relation is instead one of identity, in which the some aspect of the antecedent clause is unknown, unidentified, or unreported.

In the remainder of this paper, we explore two possibilities. On the one hand, it is in principle conceivable that the cost for sprouting is limited to sluicing and other types of ellipsis besides focus-sensitive coordination, in that, without a scalar relation between clauses, there would be no interpretive advantage for sprouting in these structures. That is, if ad hoc scales are costly to compute, then sprouting in focus-sensitive coordination, by virtue of providing an entailment relation between the clauses, might actually simplify the task of sentence processing. In particular, a ready-made scale might outweigh the general preference for parallelism, provided that such a scale makes the inference task easier, as in (14).

This possibility rests on the premise that ad hoc scales are costly to compute, at least compared to entailment relations. Although we have no direct evidence for or against the Scalar Advantage Principle, we considered it a very likely conceptual possibility. The principle was motivated in part by our intuition that interpreting sentences with lexicalized scales as in (7d) requires no special knowledge about discourse or the intentions of the speaker. In contrast, interpreting sentences like (7a) requires establishing a contextually salient relationship, and such relationships are, in principle, unbounded. Although our primary motivation for SAP is conceptual, we do not think it implausible in principle. For example, a branch of research in sentence processing and general cognition has concluded that processing resources are generally quite limited. As a consequence, some language processing tasks are shallow or incomplete (e.g., Ferreira et al. 2002; Sanford & Sturt 2002; Sanford & Graesser 2006, among many others). Assuming that conventionalized relations are more readily available than situation-specific or ad hoc relations, structures that do not require ad hoc scalar relationships might demand fewer processing resources. In other words, conventionalized relations might simply be less taxing to access, especially without sufficient discourse context. Of course, the validity of such a preference remains an empirical question.

On the other hand, it is possible that the processor always prefers a correlate that is maximally parallel to the remnant as a matter of course, regardless of the advantage to interpretation. We define parallelism as the presence of any of a number of similarities (morphological, prosodic, syntactic, semantic, etc.) between contrasting or conjoined phrases (Carlson 2002). On this view, we expect that parallelism between the correlate and remnant would facilitate processing focus-sensitive coordination (15), as in other cases of ellipsis processing (e.g., Carlson 2001; Carlson et al. 2009).

As noted earlier, initial studies of parallelism mainly concentrated on unelided conjoined elements instead of ellipsis. Frazier et al. (1984) showed that conjoined sentences were read faster when the clauses were more similar to each other in a range of ways, from active/passive voice to the animacy of an object DP. Mauner, Tanenhaus, & Carlson (1995) also found that matching active/passive voice eased the processing of VP Ellipsis sentences. Frazier, Munn & Clifton (2000) showed that semantically similar but syntactically unlike conjoined phrases (prepositional phrases or PPs with Adverb Phrases, for example) were processed more slowly than syntactically parallel conjoined phrases. Henstra (1996) found a bias for conjoined DPs to match in definiteness and presence of modifiers.

In various studies of ambiguous ellipsis sentences, Carlson (2001, 2002; also Carlson et al. 2009) found that the interpretation of these sentences responded to DP similarity in many features, such as definiteness, DP form (names vs. pronouns vs. definite or indefinite phrases), and gender, with a processing preference for pairing more similar correlates and remnants. The effects held true across ellipsis sentences with the conjunction and, such as gapping or VP Ellipsis, but also ones which did not, such as comparatives and bare remnant ellipsis. In all of these sentence types, remnant phrases (usually DPs) left behind by ellipsis contrasted with correlates within the unelided antecedent clause. Similarities between potential correlates and the remnant (and lack of similarity with other potential correlates) influenced the likelihood of an interpretation in which the similar phrases contrasted. In auditory experiments, contrastive (L+H*) accents on a potential correlate and remnant (and not on other possible correlates), creating what could be called prosodic parallelism, also increased matching interpretations, though they did not disambiguate the sentences by any means. There are some remaining issues regarding the role of contrast in processing ellipsis: for example, Rooth (1992) observes that accents or even focus on the first member of a contrastively focused pair of phrases is not necessary, though Carlson’s work shows that accent placement can clearly aid processing (see Harris & Carlson 2018 for additional discussion).

We take parallelism to be an extra-grammatical factor that affects processing of ellipsis structure and conjoined structures, rather than a grammatical constraint. The most extreme nonparallel condition is one in which a remnant lacks a correlate entirely, as in sprouting examples of sluicing or focus-sensitive coordination structures, which are nonetheless entirely grammatical structures. We take these cases as a testing ground for comparing the predictions of the Scalar Advantage Principle and the Parallel Contrast Principle.

When it comes to sprouting in focus-sensitive coordination, the two principles make the opposite predictions. The Scalar Advantage Principle predicts an advantage for sprouting, and the Parallel Contrast Principle predicts a penalty for sprouting. There is already some evidence for the Parallel Contrast Principle for focus-sensitive coordination. Carlson & Harris (2017) considered cases of “zero-adjective contrast” in which the remnant DP contained an adjective like red without a corresponding adjective in the correlate (16). In a search of the Corpus of Contemporary American English (COCA; Davies 2008), zero-adjective contrast was found to be extremely rare in text (less than 1% of 1644 cases of much less ellipsis).

A series of auditory and written questionnaires confirmed that zero-adjective contrast was dispreferred compared to examples with parallel DPs in naturalness rating tasks, and was avoided in sentence completion. Finally, in a self-paced reading study with items like (17), they observed a penalty immediately on DP remnants (an easy one) when the correlate lacked a corresponding adjective contrast (complex), but a penalty on VP remnants (burn one) when there was an adjective in the correlate. The result was interpreted as providing evidence against the Scalar Advantage Principle, as there was a clear cost for computing zero-adjective contrast, and the second result as an indication that the processor anticipates upcoming contrast, in which case the salient contrast evoked by complex would have initially misled the processor.

Despite the existing evidence that zero-adjective contrasts are costly to compute, the following set of experiments follows up on a number of remaining questions and concerns. First, we are cautious about analogizing the addition of an adjective to the remnant too closely with the established case of sprouting in sluicing. Where the analogy breaks down is that the remnant DP does in fact have a correlate DP in the antecedent clause in such cases, but the correlate simply lacks the expected sub-contrast within it. Thus, the processor might not need to posit a variable at logical form so much as readjust the kinds of scales or comparisons it can accommodate. Second, Carlson & Harris’ (2017) main focus was more on the distribution of remnants after the much less coordinator, and less on the online processing profile associated with computing zero-adjective contrast in focus-sensitive coordination. The present study utilizes eye tracking while reading in order to gain a more fine-grained picture of processing focus-sensitive coordination structures during natural reading, which allows us to identify possible tradeoffs when initially encountering the remnant and later measures associated with interpretation. Finally, the structure we are studying permits an additional test of correlate-remnant semantic mismatch, which forms a kind of intermediate case between parallel correlate-remnant pairs and sprouting. It also affords us the opportunity to determine how much subjects attended to the semantic and pragmatic compatibility between the correlate and the remnant.

We present three norming studies and two eye tracking studies below, each of which contain items based on the following pattern (18). The first three conditions have PP (prepositional phrase) remnants, whereas the last three conditions have VP remnants (18d–f), which both served as a statistical control and prohibited participants from anticipating a PP remnant. The first sentence (18a) illustrates PP sprouting, in which a PP remnant completely lacks a corresponding PP correlate (the No Matrix PP condition). The second sentence (18b) contains an overt PP correlate that matches the remnant along syntactic and pragmatic dimensions (both indicate time; the Compatible PP condition). The third (18c) provides a case of moderate correlate-remnant mismatch (the Incompatible PP condition). While the correlate is of the same syntactic type, a PP, it doesn’t permit comparison along a comparable scale (the remnant is about time while the supposed correlate is about location). Bold formatting was added here and elsewhere for clarity of exposition, but did not appear in the experiment.

The second eye tracking study explores whether the effects of PP sprouting are mitigated in supporting contexts, comparing the effect of sprouting cases like (18a) over controls (18b) with and without contexts introducing the PP remnant. In all, the results support the Parallel Contrast Principle, in that readers rely heavily on the form of the antecedent clause to identify suitable correlates, and that this process persists even in contexts supporting the PP remnant.

2.1 Experiment 1A: Completion study

2.1.3 Results and discussion

Both authors annotated the responses according to which element in the matrix clause the completion contrasted with, regardless of the syntactic category of the completion. For example, both Sunday and on Sunday completions were treated as contrasting with the matrix PP on Saturday. PP contrast completions were syntactically realized as such DPs 48% of the time. Completions coded as DP contrasts had to contrast with a different DP in the initial clause, such as the subject or object. A few cases of initial disagreement were resolved through discussion between authors.

Two effects are clearly observable from Table 1; see also the left panel of Figure 1. First, when there was a PP in the matrix clause, participants supplied vastly more PP completions (~80%). The strong preference for PP completions in such cases suggests that the PP constituents provided salient contrasts for the much less coordinator. Of course, in this study the compatible/incompatible distinction for PPs was meaningless because there was no remnant PP provided. Instead, the two conditions just illustrate that both PPs in the matrix clause were appropriate possible correlates when participants could write in their own remnant.

Table 1

Experiment 1A: Completion norming study. Percentage of completions supplied by subjects by grammatical category.

	Completion contrast
Matrix	PP	DP	VP
No Matrix PP	4%	40%	56%
Compatible PP	78%	8%	14%
Incompatible PP	81%	9%	10%

Figure 1

Experiments 1A–B. Norming studies. Left panel: Results from the sentence completion study. Right panel: Results from the naturalness rating study presented as centered z-scores.

Second, in cases where there was no PP in the matrix clause, participants completed sentence fragments largely with either VP (56%) or DP (40%) completions,⁵ replicating the general VP bias found for let alone coordinators in other completion experiments (Harris 2016; Harris & Carlson 2016, 2018). Crucially, when there was no PP in the matrix clause, i.e., the PP Sprouting condition in upcoming experiments, only 4% of the responses were PP completions. The observed bias against PP completions without a matrix PP to serve as a correlate is therefore most compatible with the Parallel Contrast Principle, in which comprehenders prefer correlate-remnant pairs that are parallel in form.

To determine how similar completions to experimental items were to patterns observed in text and speech, we annotated 1670 relevant examples of the much less structure in COCA (Davies 2008). Of those, 234 examples (14% of the total) had PP remnants. Most of the PP remnants (146, or 62% of PP remnant examples) used the same preposition as a contrasting phrase in the antecedent clause, and so only the DP within the remnant was truly contrastive. An additional 83 examples (35% of PP remnant examples) had PPs with prepositions that did not match the preposition of a first-clause PP, as illustrated in (20). In 19 of those cases, the remnant PP was not on the same dimension as any PP in the first clause; in 8 of the 19, there was no PP at all in the first clause (21), and so true sprouting of a PP occurred in 3% (8 of 234) of the relevant cases, a rate that is on par with the 4% observed in the completion experiment.

(20)	There are few national markets to simplify the distribution of water within nations, much less across national borders. (Not sprouting: PPs contrasting on location)

(21)	There ought not to be violent crimes, much less in a church during the glorious fading days of August? (PP sprouting: no PP in antecedent)

Overall, the results from the corpus and completion studies show that PP sprouting is avoided in production. We now examine whether sprouting a PP remnant is penalized when provided directly to a comprehender.

2.2 Experiment 1B: Naturalness ratings study

2.3 Experiment 1C: Eye tracking study

2.3.3 Results

We report significant results for several standard eye tracking measures: first pass time, the sum of fixation durations from first entering a region until exiting to the left or right; go past time, the duration from first entering a region to first exiting to the right; second pass time, the time spent re-reading a region after having gone past the region previously; and total time, the sum of all fixations in a region at any point in reading. We also report the percentage of regressions out of a region.

All statistical models were given the same deviation coding and random effects structures as the naturalness ratings experiment. Following standard practice, models of continuous measures used the Gaussian distribution, whereas models of binomial data were modeled as logistic linear regressions. Prior to analysis, outliers from first fixation and first pass distributions were censored using winsorsation, so that the scores below the 5^th percentile and above the 95^th percentile are replaced with the score at the 5^th and 95^th percentile, respectively (Dixon 1960; Tukey 1962). Outliers in go past and total time measures were identified visually and removed, resulting in less than 1% data loss per measure. As mentioned, remnant length was included as a predictor in models of the remnant region. Several models were created for each measure and region, increasing the complexity of the fixed effects factors by adding in trial position (the sequence in the overall experiment) as an additive and then interactive predictor. In the case of go past times, trial position was approximated in terms of first and second halves of the experiment, which resulted in a better model fit. We report the best fitting model defined as the one with the significantly lowest AIC (Akaike 1974) or, in the case of equivalent models, the one with the fewest fixed effect parameters.

Only the remnant and the region following are reported for first fixation, first pass, go past times, and regressions out; see Table 4. All regions are reported for regressions in, second pass re-reading, and total times; see Table 5. The linear mixed effects models are presented in Tables 6 and 7. Results are presented in terms of three theoretically significant effects: a PP advantage, a PP Sprouting penalty, and an interaction between remnant type and sprouting. All significant effects are reported.

Table 4

Experiment 1C: Eye tracking Means and standard errors for first fixation durations, first pass times, go past times, regressions out on the Remnant and Spill over regions.

Contrast	Remnant	Region		Region
		Remnant	Spill over	Remnant	Spill over
		First fixation durations		First pass times
No Matrix PP	PP Remnant	216 (4)	226 (4)	424 (12)	226 (4)
	VP Remnant	216 (4)	229 (4)	476 (17)	229 (4)
Compatible PP	PP Remnant	222 (4)	228 (3)	426 (13)	228 (3)
	VP Remnant	219 (4)	225 (4)	480 (16)	225 (4)
Incompatible PP	PP Remnant	223 (4)	227 (4)	438 (13)	227 (4)
	VP Remnant	232 (5)	226 (4)	502 (15)	226 (4)
		Go past times		Regressions out
No Matrix PP	PP Remnant	584 (23)	620 (26)	20% (3)	4% (1)
	VP Remnant	592 (25)	572 (25)	14% (2)	4% (1)
Compatible PP	PP Remnant	488 (18)	558 (24)	9% (2)	1% (1)
	VP Remnant	607 (25)	567 (24)	17% (3)	3% (1)
Incompatible PP	PP Remnant	558 (24)	593 (25)	17% (3)	4% (1)
	VP Remnant	623 (25)	565 (24)	14% (2)	3% (1)

Table 5

Experiment 1C: Eye tracking. Means and standard errors for regressions in, second pass, and total times for all regions.

Contrast	Remnant	Regressions in
		Subject	PP region	Much less	Remnant	Spill over	Final
No Matrix PP	PP Remnant	17% (3)	—	23% (3)	6% (2)	30% (3)	—
	VP Remnant	17% (3)	—	15% (3)	4% (1)	31% (3)	—
Compatible PP	PP Remnant	26% (3)	8% (2)	11% (2)	4% (1)	29% (3)	—
	VP Remnant	24% (3)	6% (2)	18% (3)	5% (2)	31% (3)	—
Incompatible PP	PP Remnant	23% (3)	8% (2)	18% (3)	8% (2)	32% (3)	—
	VP Remnant	26% (3)	12% (2)	17% (3)	5% (2)	24% (3)	—
		Second pass times
No Matrix PP	PP Remnant	113 (20)	—	88 (11)	60 (12)	133 (18)	—
	VP Remnant	87 (14)	—	63 (10)	41 (9)	113 (15)	—
Compatible PP	PP Remnant	167 (28)	45 (9)	44 (9)	39 (9)	120 (16)	—
	VP Remnant	150 (22)	46 (8)	55 (8)	45 (10)	113 (14)	—
Incompatible PP	PP Remnant	162 (27)	57 (11)	60 (9)	49 (10)	130 (16)	—
	VP Remnant	133 (21)	67 (11)	55 (8)	58 (11)	102 (16)	—
		Total times
No Matrix PP	PP Remnant	1305 (37)	—	402 (16)	568 (22)	710 (28)	609 (25)
	VP Remnant	1243 (38)	—	381 (14)	586 (22)	649 (26)	649 (25)
Compatible PP	PP Remnant	1320 (38)	529 (21)	364 (13)	501 (21)	654 (26)	625 (25)
	VP Remnant	1296 (40)	549 (23)	380 (13)	595 (25)	658 (26)	620 (24)
Incompatible PP	PP Remnant	1351 (41)	513 (22)	364 (12)	549 (20)	680 (26)	620 (25)
	VP Remnant	1314 (39)	523 (21)	365 (13)	629 (25)	637 (25)	585 (21)

Table 6

Experiment 1C: Eye tracking. Linear mixed effects regression models for the remnant and spill over regions for first fixation durations, first pass times, go past times, and percentage of regressions out.

Region	Parameters	First fixation durations			First pass times
		Estimate	Std. Error	t-value	Estimate	Std. Error	t-value
Remnant	(Intercept)	248.64	11.15	22.3*	111.38	29.13	3.82*
	PP Remnant	–1.62	2.26	–0.72	–23.26	4.60	–5.06*
	Incompatible PP	7.15	3.19	2.24*	12.96	6.47	2.00*
	No Matrix PP	–6.23	3.19	–1.95+	–6.60	6.48	–1.02
	Length	–1.25	0.60	–2.10*	20.44	1.51	13.54*
	PP Remnant × Incompatible PP	–4.52	3.19	–1.42	–5.49	6.48	–0.85
	PP Remnant × No Matrix PP	1.72	3.20	0.54	2.85	6.48	0.44
Spill over	(Intercept)	231.96	5.09	45.57*	231.96	5.09	45.57*
	PP Remnant	–0.19	1.98	–0.09	–0.19	1.98	–0.09
	Incompatible PP	0.20	2.80	0.07	0.20	2.80	0.07
	No Matrix PP	0.16	2.80	0.06	0.16	2.80	0.06
	PP Remnant × Incompatible PP	1.25	2.81	0.45	1.25	2.81	0.45
	PP Remnant × No Matrix PP	–3.04	2.81	–1.08	–3.04	2.81	–1.08
	Parameters	Go past times			Regressions out
		Estimate	Std. Error	t–value	Estimate	Std. Error	Wald Z
Remnant	(Intercept)	178.52	48.52	3.68*	–1.02	0.43	–2.35*
	PP Remnant	–24.27	8.22	–2.95*	0.06	0.12	0.50
	Incompatible PP	16.06	11.57	1.39	0.16	0.12	1.38
	No Matrix PP	12.17	11.59	1.05	–0.01	0.09	–0.07
	Length	23.44	2.58	9.09*	–0.06	0.02	–2.58*
	PP Remnant × Incompatible PP	–0.88	11.58	–0.08	0.13	0.12	1.11
Spill over	PP Remnant × No Matrix PP	27.65	11.60	2.38*	0.25	0.12	2.16*
	(Intercept)	572.57	40.87	14.01*	–3.61	0.29	–12.33*
	PP Remnant	6.29	7.81	0.81	0.10	0.24	0.43
	Incompatible PP	0.38	11.03	0.03	0.29	0.23	1.25
	No Matrix PP	12.53	11.03	1.14	–0.03	0.17	–0.17
	PP Remnant × Incompatible PP	2.07	11.07	0.19	0.33	0.24	1.36
	PP Remnant × No Matrix PP	9.69	11.05	0.88	0.01	0.23	0.03

Table 7

Experiment 1C: Eye tracking. Linear mixed effect regression models for regressions in and total times.

Region	Parameters	Regressions in				Total times
		Estimate	Std. Error	Wald Z	Estimate	Std. Error	t-value
Subject	(Intercept)	–1.54	0.18	–8.69*	1308.8	62.71	20.87*
	PP Remnant	–0.01	0.07	–0.14	17.44	11.89	1.47
	Incompatible PP	0.15	0.10	1.49	26.15	16.82	1.55
	No Matrix PP	–0.34	0.11	–3.12*	–27.45	16.79	–1.64
	PP Remnant × Incompatible PP	–0.09	0.10	–0.82	3.35	16.84	0.20
	PP Remnant × No Matrix PP	0.01	0.11	0.11	3.19	16.80	0.19
PP Region	(Intercept)	–2.48	0.62	–4.00*	98.32	42.97	2.29*
	PP Remnant	–0.10	0.14	–0.72	–5.80	8.58	–0.68
	Incompatible PP	–0.19	0.14	–1.37	7.47	8.69	0.86
	Length	–0.02	0.04	–0.59	28.21	2.50	11.28*
	PP Remnant × Incompatible PP	0.18	0.14	1.34	4.04	8.57	0.47
Much less	(Intercept)	–1.89	0.17	–11.4*	374.67	13.54	27.68*
	PP Remnant	0.06	0.11	0.52	1.20	4.86	0.25
	Incompatible PP	0.14	0.11	1.21	–11.02	6.88	–1.60
	No Matrix PP	0.02	0.08	0.25	14.47	6.87	2.11*
	PP Remnant × Incompatible PP	0.02	0.11	0.15	1.43	6.88	0.21
	PP Remnant × No Matrix PP	0.28	0.11	2.50*	9.95	6.88	1.45
Remnant	(Intercept)	–3.09	0.21	–14.82*	116.00	46.98	2.47*
	PP Remnant	0.10	0.13	0.77	–24.73	7.41	–3.34*
	Incompatible PP	0.22	0.18	1.24	17.21	10.43	1.65
	No Matrix PP	–0.12	0.20	–0.60	6.43	10.43	0.62
	Length	—	—	—	26.98	2.42	11.14*
	PP Remnant × Incompatible PP	0.13	0.18	0.75	–8.75	10.44	–0.84
	PP Remnant × No Matrix PP	0.15	0.19	0.79	23.38	10.44	2.24*
Spill over	(Intercept)	–1.10	0.23	–4.85*	664.8	47.28	14.06*
	PP Remnant	0.06	0.07	0.79	13.37	7.91	1.69
	Incompatible PP	–0.09	0.10	–0.88	–5.93	11.19	–0.53
	No Matrix PP	0.06	0.10	0.59	12.03	11.18	1.08
	PP Remnant × Incompatible PP	0.19	0.10	1.92+	2.20	11.21	0.20
	PP Remnant × No Matrix PP	–0.06	0.10	–0.62	12.33	11.19	1.10
Final	(Intercept)	—	—	—	612.5	35.75	17.13*
	PP Remnant	—	—	—	0.63	7.47	0.08
	Incompatible PP	—	—	—	–12.27	10.55	–1.16
	No Matrix PP	—	—	—	12.50	10.55	1.18
	PP Remnant × Incompatible PP	—	—	—	12.54	10.57	1.19
	PP Remnant × No Matrix PP	—	—	—	–17.11	10.56	–1.62

2.3.3.1 PP advantage

Compatible with the results from the norming studies, an advantage for PP remnants over VP remnants appeared on the remnant region for first pass (a 57 ms advantage), go past (a 64 ms advantage), and total times (also 64 ms advantage); see the top left panel of Figure 2. We propose that PP remnants were faster in these measures because the matrix PP presents a highly salient constituent to contrast with the remnant as implied by the completion norming study. Given the early, and persistent, advantage for PP remnants, the processor might have initially anticipated a PP remnant upon encountering the much less coordinator. We take the PP advantage as the statistical reference level against which to compare the case of Sprouting and Incompatible PPs.

Figure 2

Experiment 1C. Top left panel: PP Remnant advantage on the remnant region for first pass, go past, and total time measures. Remaining panels: Interaction between Remnant type and Matrix clause structure showing that the advantage for PP remnants is reduced or overturned in No Matrix PP conditions.

2.3.3.2 PP Sprouting penalty

Crucially, the predicted exception to the advantage for PP remnants occurred when there was no PP in the matrix clause for the remnant to contrast with, i.e., just in the case of PP Sprouting, shown in Figure 2. The advantage for PP remnants was either eliminated (as in go past and total times) or else reversed (manifesting in increased regressions out of a region) when a PP remnant had to be paired with a correlate sprouted from the matrix clause. Although there was a PP advantage in go past times on the remnant region: a 119 ms advantage for Compatible PP remnants and a 65 ms advantage for Incompatible PP remnants, the pattern reversed in No Matrix PP conditions in an 8 ms PP penalty, t = 2.38. Similarly, in total times on the remnant region, a 94 ms advantage for Compatible PP remnants and an 80 ms advantage for Incompatible PP remnants was reversed in an 18 ms penalty for PP remnants compared to VP remnants in the No Matrix PP condition, t = 2.24. In keeping with the predicted penalty for Sprouting, the percentage of regressions out of the remnant was modulated by the presence of a matrix PP: although regressions increased when the remnant was a VP in Compatible PP conditions by 8%, there was a 6% increase in regressions on PP remnants in the No Matrix PP condition, z = 2.16, p < 0.05.

2.3.3.3 Incompatible PP penalty

A model with the first and second halves of the experiment included as an interactive predictor provided a better fit of the go past data on the remnant than other models computed. In this model, the interaction between Remnant type and the Incompatible PP condition was significantly reduced in the second half (13 ms penalty for Incompatible PP remnants over VP remnants) compared to the first half of the experiment (a 73 ms penalty for Incompatible conditions), t = –2.66, suggesting that participants might have either begun broadening the contextual dimensions along which the contrasts were to be compared, or else adopted a different reading strategy, allowing them to progress through the sentences more quickly. There were no other indications of processing costs associated with Incompatible PPs.

3.1 Experiment 2A: Completion study with context

3.2 Experiment 2B: PP sprouting in context

3.2.3 Results

The data cleaning and analysis procedure from Experiment 1C were used in the present experiment, except that conditions were sum coded so that Supporting context and the Matrix PP conditions were treated as the statistical reference levels. Means and standard errors are reported in Tables 8 and 9. The effects are presented in terms of three theoretically significant effects: the effects of context, PP Sprouting, and their interaction. Reading behavior on the context sentence was not examined. As before, only the remnant and the immediately following spill over region are reported for first fixation durations, first pass times, go past times, and regressions out; see Table 8 for means and Table 10 for statistical models. All regions are reported for measures involving re-reading of a region, regressions in, second pass, and total times; see Table 9 for means and Tables 11–12 for statistical models. All significant effects are reported.

Table 8

Experiment 2B: Eye tracking in context. Means and standard errors for first fixation durations, first pass times, go past times, regressions out.

Context	Matrix PP	Remnant	Spill over	Remnant	Spill over
		First fixation		First pass
Supporting	Matrix PP	216 (5)	228 (5)	340 (14)	465 (21)
	No Matrix PP	217 (4)	228 (5)	352 (14)	433 (18)
Neutral	Matrix PP	222 (5)	229 (5)	346 (13)	438 (17)
	No Matrix PP	218 (5)	231 (5)	381 (15)	475 (19)
		Go past		Regressions out
Supporting	Matrix PP	415 (21)	531 (31)	12% (3)	6% (2)
	No Matrix PP	433 (22)	480 (26)	16% (3)	5% (2)
Neutral	Matrix PP	433 (20)	506 (31)	15% (3)	3% (1)
	No Matrix PP	487 (25)	563 (33)	18% (3)	8% (2)

Table 9

Experiment 2B: Eye tracking in context. Means and standard errors for regressions in, second pass times, total times.

Context	Matrix PP	Subject	PP region	Much less	Remnant	Spill over	Final
		Regressions in
Supporting	Matrix PP	13% (3)	11% (3)	15% (3)	1% (1)	34% (4)	—
Supporting	No Matrix PP	11% (3)	—	19% (4)	6% (2)	34% (4)	—
Neutral	Matrix PP	18% (3)	8% (2)	17% (3)	2% (1)	32% (4)	—
Neutral	No Matrix PP	13% (3)	—	20% (4)	5% (2)	29% (4)	—
		Second pass times
Supporting	Matrix PP	110 (31)	50 (12)	41 (11)	17 (6)	124 (19)	—
Supporting	No Matrix PP	96 (27)	—	62 (15)	53 (14)	126 (17)	—
Neutral	Matrix PP	118 (22)	41 (10)	52 (10)	35 (10)	107 (17)	—
Neutral	No Matrix PP	123 (27)	—	77 (15)	49 (13)	110 (20)	—
		Total times
Supporting	Matrix PP	1149 (47)	456 (21)	368 (17)	385 (19)	607 (32)	498 (26)
Supporting	No Matrix PP	1095 (45)	—	351 (20)	439 (22)	567 (28)	484 (31)
Neutral	Matrix PP	1102 (51)	459 (21)	353 (15)	431 (21)	544 (25)	488 (24)
Neutral	No Matrix PP	1106 (48)	—	371 (22)	496 (31)	634 (36)	541 (34)

Table 10

Experiment 2B: Eye tracking in context. Linear mixed effects models for first fixation durations, first pass times, go past, and regressions out.

Parameters	First fixation durations				First pass times
	Estimate	Std. Error	t-value	Estimate	Std. Error	t-value
(Intercept)	218.02	3.52	62.01*	349.77	19.19	18.23*
Neutral	–2.41	2.25	–1.07	–10.53	5.53	–1.91+
No Matrix PP	–0.35	2.24	–0.16	11.61	5.52	2.10*
Neutral × No Matrix PP	1.78	2.27	0.78	–1.28	5.60	–0.23
(Intercept)	228.98	4.14	55.33*	433.06	26.88	16.11*
Neutral	–1.56	2.22	–0.70	–2.90	7.10	–0.41
No Matrix PP	1.17	2.23	0.53	5.36	7.15	0.75
Neutral × No Matrix PP	0.18	2.25	0.08+	–11.81	7.19	–1.64
	Go past			Regressions out
	Estimate	Std. Error	t–value	Estimate	Std. Error	Wald Z
(Intercept)	438.32	21.46	20.43*	–2.02	0.22	–9.04*
Neutral	18.22	10.43	1.75+	0.10	0.14	0.75
No Matrix PP	15.85	10.41	1.52	0.12	0.14	0.90
Neutral × No Matrix PP	7.35	10.50	0.70	–0.02	0.14	–0.13
(Intercept)	505.45	33.58	15.05*	–3.81	0.55	–6.89*
Neutral	12.13	13.55	0.90	–0.10	0.24	–0.42
No Matrix PP	5.49	13.63	0.40	0.27	0.24	1.11
Neutral × No Matrix PP	21.54	13.68	1.57	0.35	0.24	1.46

Table 11

Experiment 2B: Eye tracking in context. Linear mixed effects regression models for regressions in and total times.

Region	Parameter	Regressions in			Total times
		Estimate	Std. Error	Wald Z	Estimate	Std. Error	t-value
Subject	(Intercept)	–2.08	0.21	–9.83*	1116.33	69.34	16.10*
	Neutral	0.15	0.14	1.11	4.02	18.94	0.21
	No Matrix PP	–0.18	0.14	–1.30	10.01	18.88	0.53
	Neutral × No Matrix PP	–0.07	0.14	–0.48	9.02	19.09	0.47
Matrix PP	(Intercept)	–2.24	0.22	–10.42*	450.21	23.86	18.87*
	Neutral	–0.14	0.22	–0.63	3.12	14.05	0.22
Much less	(Intercept)	–1.83	0.23	–7.85*	357.01	13.51	26.42
	Neutral	0.06	0.13	0.44	3.30	8.96	0.37
	No Matrix PP	0.15	0.13	1.11	3.47	8.93	0.39
	Neutral × No Matrix PP	–0.03	0.13	–0.20	7.00	8.99	0.78
Remnant	(Intercept)	–3.61	0.40	–9.10*	433.17	25.34	17.09*
	Neutral	0.20	0.32	0.61	26.41	11.06	2.39*
	No Matrix PP	0.74	0.32	2.31*	29.41	11.04	2.66*
	Neutral × No Matrix PP	–0.3	0.32	–0.92	–1.00	11.13	–0.09
Spill over	(Intercept)	–0.81	0.15	–5.41*	571.77	39.06	14.64*
	Neutral	–0.09	0.10	–0.86	–2.91	12.74	–0.23
	PP Sprouting	–0.05	0.10	–0.49	15.12	12.74	1.19
	Neutral × No Matrix PP	–0.04	0.10	–0.34	22.91	12.83	1.79+
Final	(Intercept)	—	—	—	492.66	36.16	13.62*
	Neutral	—	—	—	14.97	12.09	1.24
	No Matrix PP	—	—	—	13.01	12.10	1.08
	Neutral × No Matrix PP	—	—	—	12.05	12.2	0.99

Table 12

Experiment 2B: Eye tracking in context. By-subjects and by-items ANOVAs for second pass times.

Region	Effect	By-subjects		By-items
		F-value	p-value	F-value	p-value
Subject	Context	0.73	0.40	0.44	0.52
	Matrix PP	0.22	0.64	0.00	0.98
	Context × Matrix PP	0.00	0.96	0.02	0.88
Matrix PP	Context	0.17	0.68	0.18	0.67
Much less	Context	0.05	0.83	1.16	0.30
	Matrix PP	2.21	0.14	2.75	0.11
	Context × Matrix PP	1.35	0.25	0.06	0.80
Remnant	Context	0.03	0.86	0.28	0.61
	Matrix PP	4.49	<0.05	4.35	<0.05
	Context × Matrix PP	2.54	0.12	0.93	0.35
Spill over	Context	1.16	0.29	0.37	0.55
	Matrix PP	0.15	0.70	0.22	0.65
	Context × Matrix PP	0.09	0.77	0.14	0.71

3.2.3.1 Context effects

There was a marginal 18 ms penalty for Neutral contexts in first pass times on the remnant, t = 1.83, p = 0.06. First pass times are sometimes divided into trials where the reader has elected to regress back in text from those where she has elected to move forward, as they may represent distinct processing strategies when progressing through text (Altmann, Garnham & Dennis 1992; Rayner & Sereno 1994). Upon reaching a difficult portion of text, the reader may decide to return to previous regions, perhaps to resolve an ambiguity or to stall for more time (e.g., Mitchell et al. 2008). An alternative strategy in such cases is to continue to move forward, perhaps in hopes of finding useful information later in the sentence. Once trials with first pass regressions out of the remnant region were eliminated (leaving 34% of the observations from the total first pass data), there was a 44 ms cost for Neutral contexts, t = 2.69, which was moderated by an interaction, described in 3.2.3.3 below. A 51 ms penalty for Neutral contexts in total times, t = 2.39, was also observed. The cost for Neutral contexts indicates that subjects were attuned to the preceding sentence at the point of the remnant and that the Supporting contexts did successfully support the target sentences; see the left panel of Figure 3.

Figure 3

Experiment 2B. Left panel: Elongated reading times for Neutral compared to Supporting contexts in first pass and total time measures in the remnant region. Right panel: Reading time penalty for PP Sprouting conditions in first pass, second pass, and total time measures on the remnant.

3.2.3.2 PP sprouting cost

As in the previous experiment, sprouting in the No Matrix PP conditions was found to be costly immediately on the remnant region, regardless of preceding context, as shown in the right panel of Figure 3. In first pass times, readers spent 24 ms longer in No Matrix PP conditions, t = 2.10, indicating an early cost for PP sprouting. However, the cost for sprouting manifested primarily in measures of re-reading. Readers spent nearly twice as long in second pass re-reading measures on the remnant in the No Matrix PP condition (M = 51, SE = 10) compared to the Matrix PP (M = 26, SE = 6) condition in by-subjects ANOVAs, but not in by-items analyses. Further, PP Sprouting (M = 464, SE = 19) conditions elicited longer total reading times on the remnant compared to PP Matrix (M = 413, SE = 14) conditions, t = 2.66. Finally, readers made more regressions into the remnant region in the No Matrix PP condition (M = 6%, SE = 1) compared to the PP Matrix (M = 2%, SE = 1) condition, z = 2.73. The results indicate that readers encountered immediate and sustained difficulty when they were presented with a PP remnant but no corresponding correlate, forcing them to sprout a PP.

3.2.3.3 PP sprouting in context

While not central to the main hypotheses, we expected that Supporting contexts would facilitate recovery from any difficulty due to sprouting a PP argument. No interactions were observed in first fixation or first pass times. However, first pass times in which regressions out were eliminated indeed showed an interaction , in which Supporting contexts reduced reading times on the remnant in No Matrix PP conditions by 128 ms (p’s < 0.05 in by-subject and by-items t-tests), but had no effect on Matrix PP controls, as shown in the left panel in Figure 4. No interaction was observed for first pass times followed by regressions out of the remnant, where there was only a general facilitation for Supporting contexts ; see the right panel in Figure 4. The differential facilitation for PP Sprouting in Supporting contexts was therefore observed only when the reader made a forward progression through the sentence, a pattern which is perhaps related to how eager readers were to integrate the preceding context into the sentence on a particular trial.

Figure 4

Experiment 2B. Regression contingent analyses of first pass times on the remnant shown as centered z-scores. Left panel: First pass times in trials with regressions out of the remnant region showed a differential effect of context on No Matrix PP conditions, but no effect on Matrix PP conditions. Right panel: First pass times in trials without regressions out of the remnant region showed an advantage for Supporting contexts.

Other measures showed weak evidence in favor of a reduced PP sprouting penalty in Supporting contexts. Although not the best fitting model, an interaction consistent with a PP sprouting penalty was observed in go past times on the post remnant spill over region once trial order was included as an interactive predictor; there was a 57 ms cost for the No Matrix PP condition in the Neutral contexts, but a 51 ms advantage for PP Sprouting in Supporting contexts $[\widehat{\beta }=66.36,SE=29.67,t=2.24]$ , along with a trend indicating that the interaction reduced over the course of the experiment, t = –1.69. Finally, there was a non-significant trend for an interaction between Sprouting and Context for total times in the spill over region: While there was a 90 ms cost for PP sprouting in Neutral contexts, there was a 40 ms benefit for PP sprouting in Supporting contexts, t = 1.79.