Dynamics of semantic processing: The interpretation of bare quantifiers

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1 Dynamics of semantic processing: The interpretation of bare quantifiers Frank Wijnen 1* and Edith Kaan 2 to appear in Language and Cognitive Processes 1 Utrecht Institute of Linguistics OTS Utrecht University Trans JK Utrecht, The Netherlands 2 Program in Linguistics University of Florida 4131 Turlington Hall ~ Box Gainesville, FL , USA tel fax *corresponding author short title: Interpretation of bare quantifiers 1

2 Dynamics of Semantic Processing: The Interpretation of Bare Quantifiers Abstract A bare cardinal, such as four in the fragment Five ships sailed out. Four, can be interpreted in at least three ways: (1) as four of the five ships mentioned (a forward directional reading); (2) as four other ships (a parallel reading); or (3) as four different entities (a non-anaphoric reading). The first reading is preferred, although this preference can be influenced by various factors. In the present study, we investigated at which point during on-line processing bare cardinals are interpreted. Results from a completion task, a difficulty rating task and an on-line incremental acceptability judgment task suggest that there is an immediate preference to interpret bare cardinals as forward directional, leading to processing difficulty at the cardinal when it is not compatible with such an interpretation (as in Five ships sailed out. Six ). However when later information at the verb contradicts a forward directionality reading, revision into a parallel reading is almost effortless. 2

3 Acknowledgements Portions of the results reported were presented earlier at the 14th Annual CUNY Conference on Human Language Processing, University of Pennsylvania, Philadelphia (PA), March 2001, and the workshops From Sentence Processing to Discourse Interpretation: Crossing the Borders (Utrecht University, July 3, 2001), and Syntax and Beyond (Max Planck Institute of Cognitive Neuroscience, Leipzig, August 2003). EK was supported by McDonnell-Pew grant # ; FW by a fellowship of the Royal Netherlands Academy of Arts and Sciences (KNAW). We thank Carolien van den Hazelkamp for her help in running Experiment 3. 3

4 Dynamics of Semantic Processing: The Interpretation of Bare Quantifiers To date, the bulk of online studies of sentence processing have dealt with structure building. Syntactic ambiguity has proven to be a useful window onto the time course of parsing and the nature of (initial) attachment decisions. In this study, we go beyond structure building proper, and investigate sentential semantic processing, which has thus far received only scarce attention. We are interested in the decisions underlying the on-line construction of a semantic representation and, particularly, the time course of processing. In analogy to what has been done in research on syntactic processing, we use ambiguity as a tool. Our experiments make use of the ambiguity inherent to bare quantifiers, i.e., noun phrases in which the nominal head is unexpressed, and the determiner consists of a cardinal. Quantifiers, such as three, some, and every have a restrictor and a nuclear scope. In a sentence like (1a), the quantifier all has men as its restrictor, and laugh as its nuclear scope. The sentence expresses the following proposition For all x in the relevant domain, if it is true that x is a man, then x laughs. In current semantic analyses, we often see the denotation of a structure like this expressed in the form of a so-called tripartite structure (1b, cf. Diesing, 1990). 1. a. All men laugh. b. S operator restrictor nuclear scope all(x) men(x) laugh(x) 4

5 In cases like example 1, each of the components of the semantic representation is identified in the surface structure of the sentence. The situation changes in a nontrivial way when parts of the quantificational (tripartite) structure are not overtly given, as with five in example (2). 2. Ten protesting students marched by. Five were shouting insults. A perceiver needs to infer the restrictor of a bare cardinal in order to understand the sentence. For most people, it is most natural to assume that the restrictor of five is the set of students that marched by. A moment s reflection, however, helps in realizing that this is not the only permissable interpretation. The five unspecified entities could also be, for example, five other students who happened to disagree with those protesting. This ambiguity resembles the ambiguity that can arise from pronominal anaphora in particular contexts, such as in (3), where both he and him can refer to both John and Bill. In fact, we would argue that the bare cardinal construction is akin to such pronominal anaphors, as both appear to be interpreted by direct reference to a discourse model (cf. Hankamer & Sag, 1976). 3. John met Bill. He asked him a favor. A difference between pronouns and bare quantifiers is that in the case of bare quantifiers as in (2), the anaphor denotes a subset from a set defined in the preceding context, rather than an individual entity. Another difference is that a pronominal is an 5

6 overt anaphor, while the anaphoric element in constructions such as (2) is not. It is a null nominal: five [ NP ]. We can ask whether the (non)overtness of the nominal restrictor ( five as opposed to five students ) makes a difference in the interpretational preference. Note that the same ambiguity arises both with overt and non-overt restrictors. Just as five in example (2), five students in (4) can either refer to five of the ten just mentioned, or five other students. Nonetheless, there appears to be a slight difference in preference, such that five students is more easily interpreted as not belonging to the set of ten protesters previously introduced, whereas five is preferably associated with this set. We will briefly return to this issue in the results section of Experiment Ten students marched by. Five students were shouting insults. Two main questions arise with respect to the processing of quantifier restrictor ambiguity. First, why do people prefer to take the antecedent of five in example (2) above to denote five elements out of the previously specified set, rather than five other students? An answer to a question like this should take the form of a model of comprehension enumerating the factors (syntactic, semantic, pragmatic, etc.) that co-determine interpretation, and spelling out their interactions in a principled way. The second question concerns the time course of processing. At what point during the processing of a structure like (2) does the processor assign an interpretation to the null anaphor? Two diametrically opposed hypotheses are conceivable. Either the processor defers interpretation until sufficient information has been perceived, in order to unerringly determine the intended meaning, or it attempts to fully process and inter- 6

7 pret the underspecified element as soon as it is presented. This opposition, as may be clear, is parallel to the opposition between determinism and non-determinism (incrementality) in structural parsing (Crocker, 1999; Mitchell, 1994), including the possibility that backtracking and repairing ( garden pathing ) occur under particular circumstances in the case of the non-deterministic processor. In this study we focus on the second issue (time course), assuming a model of quantifier interpretation along the lines proposed by Hendriks and De Hoop (2001). Their optimality semantics is framed in the Optimality Theory framework, proposed by Prince and Smolensky (1997; 2004); for applications to syntax, see, e.g. Keller and Alexopoulou (2001). Optimality semantics is a constraint satisfaction model, modeling the assignment of interpretations to linguistic expressions from the listener s point of view: the interpretation assigned to a given syntactic structure is the result of the application of a set of ranked constraints. These constraints are soft, that is, they can be violated in order to satisfy higher ranked constraints. The model proposed by Hendriks and De Hoop is especially geared to explaining the interpretation of underspecified linguistic expressions (ellipses, comparatives), which pose a challenge to strict compositionality. Below we will only discuss the constraints that are relevant for the interpretation of quantifier restrictors (for more details, see Hendriks & de Hoop, 2001). One general pragmatic constraint is Don t Overlook Anaphoric Possibilities (DOAP). It says that if a linguistic expression is ambiguous between anaphora and independent reference, the anaphoric reading is preferred. For our set relation examples, this predicts that a restrictor should be found in the preceding discourse context. Frazier (1999 p. 113) also suggests that there is a strong preference for reconstructing a covert restrictor from context, which, she argues, is related to conversational maxims and the 7

8 principle of relevance. DOAP can be satisfied in various ways. One is captured by the Forward directionality constraint: The topic range included by the domain of quantification of a determiner (set A) is reduced to the topic range induced by the intersection of the two argument sets of this determiner. (Hendriks & de Hoop, 2001 p. 19). For instance, in example (2), the forward-directional interpretation of five is that its restrictor is students that marched by, and hence, that the new (nuclear scope) information is predicated of this set, rather than of, say, a general set of students. Forward directionality is a structural property of discourse, contributing to its informativeness (see Van Kuppevelt, 1996). An anaphoric reading of an expression can also arise by means of Parallelism, a general constraint applying to various kinds of ellipsis and anaphora: As an antecedent of an anaphoric expression, choose a (logically, structurally, thematically) parallel element from the preceding clause[s] (Hendriks & de Hoop, 2001 p. 20). For instance, in sentence (2), the parallel interpretation would be one in which students, as the element structurally parallel to the zero noun phrase in the second sentence, is the restrictor of five. This results in a reading in which Five refers to five other students. We noticed that parallelism in this particular case is not the preferred option in constraint satisfaction terms: Forward Directionality outranks Parallelism. Finally, there is the constraint Avoid contradiction. This constraint is ranked above all others, which means that other constraints can be violated in order to prevent a semantic contradiction. For instance, in (5), the weaker constraint Parallelism must win out over Forward Directionality, since otherwise a contradiction would arise (since twelve cannot be a subset of ten). 8

9 5. Ten protesting students marched by. Twelve were shouting insults. The reverse condition, in which e.g. Forward Directionality is saved by violating Avoid Contradiction, does not occur. Example (6) can never be interpreted to mean that three students did and did not attend the meeting, as Forward Directionality would prescribe. 6. Four students attended the meeting. Three did not. As pointed out above, the focus of this study is not the factors that determine interpretation, but the real time process that underlies it. As a working hypothesis, we assume that semantic processing shares a distinguishing feature with parsing, viz. that it makes immediate, defeasible commitments. This is what Frazier (1999) calls the strong immediacy principle for interpretation. Processing studies of quantifiers Direct empirical evidence on the time course of quantifier interpretation is scarce: Kurtzman & MacDonald (1993) and Villalta (2003) primarily deal with scope ambiguities in sentences with two quantifiers. Kurtzman & MacDonald tested sentences such as Every kid climbed a tree and A kid climbed every tree, in which every can have wide or narrow scope. These sentences were followed by a continuation sentence that was compatible with either the wide or narrow scope reading. Judgment data on these continuations indicate that various factors determine whether the quantifier was assigned narrow or wide scope. However since the data were based on end-of-sentence judgments, these 9

10 experiment do not yield much information concerning the dynamics of quantifier interpretation. An interesting claim regarding the time course of quantifier interpretation is made by Villalta (2003). On the basis of research on scope ambiguities in how many questions, Villalta proposes a model in which the semantic processor prefers to avoid reanalysis (an instantiation of economy), and hence, in the case of ambiguity, the first quantifier is not assigned a referent until the second is encountered. Self-paced reading time data are argued to be in line with this model. In a different line of research, Sanford, Moxey & Paterson (1994) observed that quantifiers differ from each other with respect to which set they make salient. On the one hand, so-called positive quantifiers make the reference set salient, i.e., the set denoted by the quantified phrase. Negative quantifiers, on the other hand, increase the salience of the complement of the reference set (i.e., the complement set). This has an immediate online effect, as demonstrated in eye-tracking experiments, suggesting that quantifiers are interpreted immediately, although other interpretations of these data cannot be excluded. One study that is most closely related to the one reported here is Frazier, Clifton, Rayner, Deevy, Koh & Bader (2003). A series of experiments was conducted, using discourses like the one in (7), in various languages. 7. Five ships appeared at the horizon Three ships sank. Frazier et al. demonstrated that readers clearly prefer a reading in which the quantified 10

11 noun phrase in the second sentence refers to a subset of entities from the set introduced in the first sentence (a Forward Directionality reading, in our terminology). In addition, the off-line results suggest that this preference is modulated by the structural position of the quantified phrase, viz. inside or outside the verb phrase. Eye tracking experiments showed that the Forward Directionality preference emerges online, such that it modulates the processing time of a subsequent text segment that either is compatible or incompatible with the preferred reading. However in this study, the crucial regions were not well-balanced across conditions. In addition, the critical quantifier could sometimes be compatible with both forward directionality and a parallel reading. The present study In the present study, we used discourses in which the crucial element is a bare cardinal, i.e., a number word without a following noun. The experimental paradigm is illustrated in (8). 8. a. Forward Directional It turned out that five ships did not survive the hurricane. The coast guard reported this morning that four had capsized during the night in the towering waves. b. Late Parallel It turned out that five ships survived the hurricane. The coast guard reported this morning that four had capsized during the night in the towering waves. 11

12 c. Early Parallel It turned out that three ships survived the hurricane. The coast guard reported this morning that four had capsized during the night in the towering waves. In all three conditions, the second sentence contained a bare quantifier (four). In the Forward Directional condition (8a), this quantifier can plausibly refer to a set of entities mentioned in the first sentence five ships. In the Late Parallel condition (8b), the verb in the second sentence (capsized) is only compatible with the interpretation of four as referring to a set of different ships, i.e., ships that were not among the ones that survived the hurricane. In the Early Parallel condition (8c), the number word used in the first sentence is smaller than in the second. The quantifier in the second sentence can therefore not refer back to the set mentioned earlier, but must refer to a set of other ships. If there indeed is a preference for a forward directional interpretation of bare quantifiers and if online interpretation is immediate and complete, one could expect the following pattern of results. First, in the Late parallel condition (8b), readers will immediately interpret four as referring to the set of ships mentioned earlier, in accordance with Forward Directionality. Consequentially, they will experience difficulty at the verb downstream, capsized, which signals that the forward directional reading is incorrect and a parallel reading needs to be constructed. Second, in the Early Parallel condition (8c), forward directionality is counteracted right at the bare cardinal itself, and an immediate revision toward parallelism will ensue, leading to an increased difficulty at and immediately after the quantifier. The Forward Directionality condition (8a) serves as a control. 12

13 Three experiments (in Dutch) were conducted. The first was a sentence completion study with the primary aim to verify whether materials like (8) in fact yield a forward directionality preference. To this end, participants were presented with twosentence discourses like the one exemplified in (8), in which the second sentence was cut off after the quantifier in subject position ( four in the example). The second experiment was an offline difficulty rating study. Given a preference for forward directionality and the assumption of immediate full interpretation, it was expected that the critical sentence in items like (8b) and (8c) would be judged to be more difficult than items like (8a), because the b- and c-versions entail a revision of the initial interpretation. Experiment three, finally, comprised a continuous acceptability judgment task. The critical sentences of discourses like (8) were presented in a phrase-by-phrase moving window paradigm, and participants were asked to judge at each new segment whether the sentence up to that point was still interpretively acceptable. This task yields two dependent variables: rejection rates and decision times per segment. We expected that if a particular segment was incompatible with the preferred Forward Directionality interpretation participants would either reject it, or would spend more time processing on this or subsequent segments. Experiment 1: sentence completion Participants Twenty-four native speakers of Dutch (four men), all of them students at Utrecht University, took part in the experiment. Their ages ranged from 18 to 36 years. All were naïve as to the purpose of the experiment. 13

14 Materials Twenty-four 2-sentence texts in Dutch were constructed, each in three versions, as exemplified in (8). The crucial (bare) quantifier was the subject of a subordinate clause in the second sentence. We used subordination in order to create a distance spanning several words between the end of the first sentence and the crucial quantifier. This was done to prevent spill-over or wrap-up effects from impinging on the processing of the bare cardinal in the on-line study (Experiment 3). The items that were used in the questionnaire study were presented only up to and including the bare cardinal in the second sentence. Inspecting example (8) above will make clear that this resulted in a materials set in which two thirds of the critical sentences had a bare cardinal smaller than the cardinality of the small restrictor defined by the introductory sentence. These items differed with regard to the verb phrase used in the introductory sentence (cf. 8a and 8b). In the remaining one third of the stimuli, the cardinal in the first sentence was smaller than the crucial one in the second sentence (cf. 8c). A list of the materials used in this and the next experiments can be found in the appendix. The experimental items were distributed across three lists, such that only one version of every item was present on each list. The experimental items were interspersed with 48 filler items, all consisting of 2-sentence discourses, of which the second sentence contained anaphoric and non-anaphoric quantified expressions of various types, and which were also cut off directly after these quantifiers. The order of presentation was determined by quasi-randomization, with the restriction that no more than two experimental items were presented in direct succession. Each list had its own random 14

15 order. Procedure The lists were compiled into 10-page stapled booklets, with an instruction on the first page and 9 pages of items (8 items per page). The instruction stated that the participants were to complete the second sentence without much contemplation, in a way that they felt was most natural, and furthermore that they were required to go through the list in one run, without retracing or correcting previously completed sentences. Results and discussion The sentence completions were assigned to one of the following four categories: forward directional responses (ex. 9); parallel responses (ex. 10); non-anaphoric responses (ex. 11); ambiguous and null responses. 9. Bij een busongeluk in Spanje waren twintig mensen betrokken. De ANWB liet weten dat er tien // mensen omgekomen waren. (participant nr. 3) Twenty people were involved in a bus accident in Spain. The tourist office reported that ten // people had died. 10. Uit de brief bleek dat drie leerlingen het examen hadden gehaald. De rector meldde daarbij dat er vier // leerlingen gezakt waren. (participant nr. 1) The letter stated that three students passed the exam. The principal reported that four // had failed. 11. In de halve finale van de Grand Prix haalden zeven coureurs de eindstreep niet. De talloze toeschouwers zagen hoe er drie // auto s total loss waren na afloop. 15

16 (participant nr. 6) Seven drivers did not make to the finish in the semi-finals of the Grand Prix. The innumerable spectators saw how three // cars were totaled at the end. Table 1 gives an overview of the results. The distribution of response types was affected by Condition, as indicated by a χ 2 value of (df = 4, p < 0.001) for the full 3 (condition) by 4 (response type) contingency table. Overall, parallel responses occurred most often (41.5%). This type of response was most often observed in the Early Parallel condition (8c). This was expected since the cardinal (quantifier) in the second sentence was larger than in the first. In the two conditions in which the first cardinal was larger than the second, forward directional responses predominated (40.4%) although not as strongly as expected on the assumption that Forward Directionality is the default. In particular, condition (8b) yielded more parallel responses than condition (8a), despite the fact that in both conditions the first cardinal was larger than the second. Conversely, forward directional continuations were less numerous in condition (8b) (32.3%) than in condition (8a) (48.4%). The χ 2 value for the 2 (conditions 8a, b) by 2 (parallel/forward directional response) contingency table is 19.8, which was significant at the.001 level. (Insert TABLE 1 about here) The items used here were constructed with the second experiment in mind. The Late and Early Parallel items (cf. 8b and 8c above) were designed to track the perceiver s reaction to information contradicting the forward directional interpretation of 16

17 the bare quantifier. The Forward Directional items (8a), by contrast, while keeping the second sentence constant (for methodological reasons), were not intended to engender such a contradiction. As a result of these desiderata, the first sentences of the Forward Directional items contained a verb phrase that was different from that in the Late and Early Parallel items. The observed difference in percentages of parallel responses between on the one hand Forward Directional items, and, on the other, Late and Early Parallel items might be ascribed to this difference. It is unclear, however, why the different verb phrases yield these different response patterns. One factor might be the ability of the verb phrase to evoke a contrast, and, hence, a set of contrasting entities. This might facilitate a parallel interpretation of the bare cardinal. However, our attempts to objectify this quality have not been successful. In the Introduction, we briefly touched upon the difference between bare cardinal and full noun phrase anaphors with respect to quantifier interpretation. We therefore investigated the frequencies of full NP and bare cardinal continuations in our data. A total of 573 classifiable responses was collected (3 were ambiguous). In 278 of these (48.5%), no overt noun was supplied. In 104 cases (18.2%), the relevant noun given in the first sentence was repeated, and 191 responses (33.3%) contained a different (new) noun. We cross-classified these data against type of response (forward-directional, parallel, and non-anaphoric). Unsurprisingly, the vast majority of responses classified as non-anaphoric contained new nouns (96.4%). Most pertinent to the overt/non-overt issue are the forward directional and parallel continuations. Table 2 supplies the frequencies of continuations with new nouns, repeated nouns and elided nouns. When a forward directional response was given, null nouns occurred 2.7 times as often as overt nouns (repeated and new). For the parallel responses the ratio was 1.4 (χ 2 = 8.61, df = 2, p = 17

18 .013). Excluding the responses where new nouns were supplied, the distributional difference between the forward directional and parallel responses was marginally significant (χ 2 = 3.5, df = 1, p =.061). These data agree with the intuition that bare cardinals are more easily associated with a forward directional interpretation than full nominals. (insert TABLE 2 about here) Summarizing, the data from the completion study suggest that there is a preference for forward directional interpretation of bare cardinals, but that this preference is apparently easily modulated by other factors. Experiment 2: difficulty rating In order to see whether the interpretational preference attested in Experiment 1 also affected perceived difficulty, we conducted a difficulty rating using the full versions of the sentences. Participants Forty-three volunteers, drawn from the same population as in Experiment 1, took part in the experiment (age 18 to 44 years; 7 male). None of them had participated in Experiment 1. Materials A set of 24 two-sentence items was constructed, similar to the materials used in Ex- 18

19 periment 1, except that the continuation sentences were complete (see (8)). For each item, three versions were constructed. In the (a) version (Forward Directional), the bare cardinal in the subordinate subject position of the second sentence, as well as the predicate were compatible with a forward directional interpretation. In the (b) version (Late Parallel), the bare cardinal in the second sentence allowed a forward directional interpretation, but the predicate was incompatible with this, so that eventually a parallel interpretation of the bare quantifier was the only option. In the (c) version (Early Parallel), the cardinality of the second sentence cardinal disallowed forward directionality, and the predicate forced a parallel reading. The experimental items were distributed across three lists, in such a way that each list contained all conditions, but only one version of each item was present on each list (Latin square). The experimental items were interspersed with 48 filler items, all of which contained anaphoric and non-anaphoric quantified expressions of various types. The order of presentation for all items was determined by quasi-randomization, with the restriction that no more than two experimental items were to be presented in direct succession. Each list had its own order. Procedure The lists were assembled into 10-page stapled booklets, 8 items per page. The second sentence of an item was printed immediately below the first. Below each item, a scale was printed, containing five integers (1 through 5) separated by dashes. The Dutch word makkelijk easy appeared to the left of the leftmost digit ( 1 ), and the word moeilijk hard directly to the right of the rightmost digit ( 5 ). The first page contained instructions. Participants were asked to mark the subjective difficulty of each item by circling 19

20 one of the digits 1 though 5 on the scale directly below it, and not to look back at previously marked items. Results and Discussion Forward directional items were rated to be easiest (2.06, sd = 0.91), followed by late parallel items (2.12, sd = 0.94), which in their turn were easier than early parallel items (2.27, sd = 0.99). The effect of condition was significant in a one-way repeated measures ANOVA (F 1 (2,41) = 5.25, p =.009; F 2 (2,22) = 4.20, p = 0.028). A planned comparison analysis indicated a linear trend in the data (F 1 (1,42) = 10.51, p =.002; F 2 (1,23) = 8.38, p =.008). Post hoc t-tests supported this: There was a significant difference between the Early Parallel and Late Parallel conditions (t 1 (42) = -2.03, p = 0.048; t 2 (23) = -2.39, p = 0.026). The difference in difficulty between the Early Parallel and Forward Directional conditions was reliable as well (t 1 (42) = 3.24, p = 0.002; t 2 (23) = 2.89, p = 0.008). The difference between Late Parallel and Forward Directional conditions did not reach significance, however (t = by participants; t = by items). These results confirm our expectations. Discourses that enforced a parallel reading of the bare cardinal, both early and late, were more difficult than discourses that were fully compatible with a forward directional interpretation. However, unexpectedly, the late parallel condition was easier than the early parallel condition. In order to further clarify these findings, we return to the results of Experiment 1. Recall that in Experiment 1 the (a) items, which correspond to the Forward Directional items in the present difficulty rating study, predominantly produced forward directional continuations. The low difficulty scores obtained for this condition thus match the completion data. The (b) items in the completion study (corresponding to the Late Parallel items in this experi- 20

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