Imagine a situation where someone says “The fridge at work is broken”. There are probably two assumptions you make when hearing this utterance. First, that there actually exists a fridge at the workplace of the speaker, and second, that there is exactly one fridge. Both of these assumptions are called presuppositions in the semantics/pragmatics literature and they are referred to as the presuppositions of existence and uniqueness of the definite determiner “the”.
Presuppositions are background assumptions that speakers of a conversation take to hold. They are usually triggered by a lexical item, the so-called presupposition trigger. In the example above, this would be the definite determiner “the”. Since we know that it can only be felicitously used with unique objects due to its presuppositions, we can draw conclusions about the number of fridges based on its use. Compare the example with the utterance “A fridge at work is broken.”, that is, with the same utterance containing the indefinite determiner “a”. The assumption about the existence of a fridge remains the same. However, there is no inference of the fridge being unique. Rather, one could deduce that there is actually more than one fridge at the workplace of the speaker. Similarly to the case of the definite determiner, we deduce this based on the fact that indefinite determiners are only felicitously used with non-unique objects. However, the status of this anti-uniqueness inference is more controversially discussed in the literature.Footnote 1 It has been argued that both uniqueness and anti-uniqueness inferences are part of the non-literal meaning component of sentences. However, open questions are whether they are equal in strength, and how and when these different inferences arise.
The question we address in this paper is whether listeners use inferences associated with definite and indefinite determiners to disambiguate utterance meaning as early as possible, even if the speaker does not always use these determiners felicitously. Much previous research has provided evidence that listeners may, often swiftly, adapt to the idiosyncrasy of the given speaker. This applies to many different aspects of the interpretation of language, including phonetics/phonology (Kleinschmidt & Jaeger, 2015; Roettger & Franke, 2019), syntax (Fine, Jaeger, Farmer & Qian, 2013; Jaeger & Snider, 2013), semantics (Yildirim, Degen, Tanenhaus, & Jaeger, 2016), and pragmatic factors (Grodner & Sedivy, 2011; Stranahan, 2018). However, to the best of our knowledge, there is so far no work investigating adaptation effects of presuppositional information for online processing. Moreover, there is a vast amount of literature on the processing of felicitous and infelicitous uses of presuppositions in different contexts (see Schwarz 2007; Schwarz & Tiemann, 2012; Tiemann et al., 2011; Tiemann, 2014; for a recent review, see Schwarz, 2016), but almost no experimental investigations of when and how the interpretation of utterances may be affected by information encoded in the presuppositions of certain expressions. The present study tries to fill these gaps. To this end, we will compare how listeners’ online interpretation of definite and indefinite determiners changes depending on how reliable the speaker is in using the determiner felicitously. To do so, we compare a group of participants encountering only felicitous uses of determiners with a group that also encounters infelicitous uses of determiners. In the following, we will introduce presuppositions and the triggering mechanism in more detail, focusing on determiners. This is followed by a discussion of earlier work suggesting that the process of presupposition evaluation is started immediately on the presupposition trigger. We report one experiment comprising two parts: in a production task, we test whether participants use the presupposition usually associated with the determiner to convey information. The subsequent mouse-tracking task addresses whether participants use determiners to disambiguate utterance meaning and if so, whether this is different for the definite and the indefinite determiner.
Presuppositions
Informally speaking, presuppositions are background assumptions that are shared by all interlocutors of a conversation. They are introduced by certain words, so-called presupposition triggers. One classical example of such a trigger is the definite determiner. It introduces the presupposition that there exists a unique individual with the property described by the noun it combines with. Technically speaking, these words introduce appropriateness conditions, that is, certain restrictions on what the context must look like for the sentence containing them to be felicitously uttered. The assumption is that if the presupposition of a trigger is not met in the context, uttering a sentence containing it is infelicitous. This is illustrated in (1). In (1-a), the presupposition of the definite determiner, that there is a unique apple, is fulfilled in the context. Thus, the sentence is felicitous. In (1-b), the presupposition of uniqueness is not fulfilled in the context and the sentence is infelicitous (or inappropriate).
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1.
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(a)
Context: There is an apple and a banana on the desk.
Please give me the apple.
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(b)
Context: There are three apples and a banana on the desk.
# Please give me the apple.
Whereas felicitous uses of the definite determiner require a unique discourse referent (i.e., the definite determiner presupposes uniqueness), the indefinite determiner is assumed to require there to be more than one referent in the context. As a result, its use becomes odd if it is known that the referent is unique, as in (2).
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2.
# A sun is shining.
It was thus suggested in the literature that the indefinite determiner presupposes anti-uniqueness (see Kratzer, 2005, or the discussion in Heim, 1991, 2011) in the same way the definite determiner presupposes uniqueness. Under this view, both definite and indefinite determiners come with their own restrictions on what are appropriate contexts. Henceforth, we will refer to this theory as the “presupposition theory” and assume that both inferences are equally robust and accessed quickly.
However, Heim (1991) noted that (3) can be uttered without it being certain that there is more than one 20-ft-long catfish: it suffices that the speaker is not sure that there is exactly one 20-ft-long catfish.
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3.
Robert caught a 20-ft-long catfish.
From such observations, Heim (1991) concluded that the inference associated with the indefinite determiner is weaker than the presupposition of the definite determiner. To capture this, she proposed to add another principle to the Gricean maxims of conversation, Maximize Presupposition, which says: Presuppose as much as possible! (see also Chemla, 2009; Percus, 2006; Sauerland, 2008; Schlenker, 2012, for more refined versions of Maximize Presupposition). This principle can account for the fact that using indefinite determiners is infelicitous when it is common ground that the referent is unique, as in (4-a). More specifically, it explains the oddness of (4-a) by means of pragmatic reasoning over presuppositional stronger alternatives (Heim, 1991; Percus, 2006; Sauerland, 2008; Schlenker, 2012). The sentence in (4-b) is an alternative since it only differs from its competitor regarding the presuppositions it introduces. It introduces more presuppositions that are true in the context (since we know people have one unique father) and is thus the presuppositionally stronger alternative. When a listener hears the presuppositionally weaker sentence (4-a), s/he assumes the speaker must believe the presupposition of the stronger alternative to be false. The reasoning behind this conclusion is based on two main assumptions: (1) that the speaker obeys the conversational maxims including Maximize Presupposition, and (2) that the speaker tries to be cooperative in doing so. The hearer thus assumes that if the speaker believed the presupposition of (4-b) to be true, s/he would have used this version, because it would be more informative on a presuppositional level. Since s/he did not, s/he must believe it to not hold. The belief that the victim does not have a unique father, however, is contrary to common knowledge and, therefore, leads to the oddness of (4-a).Footnote 2
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4.
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(a)
\(*\) A father of the victim arrived at the crime scene. (Heim, 1991)
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(b)
The father of the victim arrived at the crime scene.
In other words, anti-uniqueness is derived by (1) considering the (stronger) alternative with the definite determiner and (2) negating its presupposition. The inferences, which are the result of pragmatic reasoning based on Maximize Presupposition, are not presuppositions proper under this view. Henceforth, we will refer to them as anti-presuppositions (Percus, 2006). They are theoretically kept apart from presuppositions (and implicatures) and should be processed differently. As opposed to the assumptions of the “presupposition theory” introduced above, the anti-presupposition arising with the indefinite determiner has a weaker status than the presupposition of the (stronger) definite determiner; we will refer to this theory as the “anti-presupposition theory” in the following. Because the anti-uniqueness inference is derived by initially considering the (stronger) alternative of the definite determiner and subsequently negating it, processing of the indefinite determiner should thus be more complex than processing the definite determiner.
A third type of theory assumes that the indefinite determiner triggers an implicature due to its competition with other quantificational terms, for example, “every/all” or “another” (Chierchia, Fox, & Spector, 2012; Grønn & Sæbø, 2012). These quantificational terms form a lexical scale with the indefinite determiner (Horn, 1972). An implicature arises when the weaker item on such a scale is chosen, in this case the indefinite determiner. All items that are higher in the scale (items that trigger stronger alternatives) get negated: for example, the implicature of “A boy came” is that “Not all boys came”. This negation process requires the assumption of existence of other boys, and anti-uniqueness follows as a consequence. Contrary to the competition on a presuppositional level according to Maximize Presupposition, the competition between alternatives in this case arises on the level of assertion (“a” and “all” differ on the level of assertion, whereas “a” and “the” are alike on that level). Variants of this argue that anti-presuppositions are essentially implicatures in that they can be informative and follow from the same general mechanism (of exhaustification) (Magri, 2009; Schlenker, 2012; Singh, 2011). According to these theories, the definite and indefinite determiners are also asymmetric in the inferences they introduce: whereas the indefinite determiner should come with an implicature, which has shown to be processed even more rapidly (at least if certain conditions are met) than presuppositions (Bill, Romoli, & Schwarz, 2018; but see also Chemla, 2008), the definite determiner should come with a presupposition. We will refer to this theory as the “implicature theory”.
In sum, three different approaches are available to explain the effects of uniqueness and anti-uniqueness resulting from the definite and the indefinite determiner. (1) According to the “presupposition theory”, both determiners carry their own presuppositions proper and thus processing the two determiners should be equally difficult. (2) According to the “anti-presupposition theory” based on Maximize Presupposition, the anti-uniqueness inference of the indefinite determiner is derived indirectly from negating the uniqueness presupposition of the definite determiner. Thus, processing indefinite determiners should be more difficult than processing a definite determiner. (3) According to the “implicature theory”, the indefinite determiner comes with an implicature instead of an (anti-)presupposition. In this case, one may expect the indefinite determiner to be more easily processed than the definite determiner.
Previous investigations of processing determiners
Experimental investigations of presuppositions have increased in recent years (for a recent review, see Schwarz, 2016). Here, we focus on studies dealing with (1) the early processing of presuppositions/inferences triggered by determiners, (2) differences between felicitous and infelicitous uses of determiners, and (3) potential differences between definite and indefinite determiner.
In a self-paced reading study, Altmann and Steedman (1988) investigated the syntactic consequences of a definite noun phrase having its presuppositions met or not met by the context. The data revealed early processing of the presupposition, before the end of the sentence. More precisely, participants were presented with test sentences in two different contexts. Context 1 introduced two candidates for a potential referent (a safe with a new lock and a safe with an old lock, see (5)), while Context 2 introduced exactly one candidate for a potential referent (see (6)).
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5.
Context 1: A burglar broke into a bank carrying some dynamite. He planned to blow open a safe. Once inside he saw that there was a safe with a new lock and a safe with an old lock.
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6.
Context 2: A burglar broke into a bank carrying some dynamite. He planned to blow open a safe. Once inside he saw that there was a safe with a new lock and a strongbox with an old lock.
In the test sentence in (7), the prepositional phrase “with the new lock” modifies the noun phrase “safe”. As a result, the uniqueness presupposition is met in both contexts for this test sentence. This is not the case for the test sentence in (8), whose presupposition is only satisfied by Context 2.
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7.
The burglar/blew open/the safe/with the new lock/and made of/with the loot.
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8.
The burglar/blew open/the safe/with the dynamite/and made of/with the loot.
Reading times differed in the disambiguation region (i.e., on the prepositional phrase “with the new lock” or “with the dynamite”). Test sentences with an unmet uniqueness presupposition as in (8) were read slower than test sentences as in (7). Thus, the authors conclude that people experience processing difficulties at an early point in time, when the uniqueness presupposition of the definite determiner is not met. However, no evidence for processing difficulties on the presupposition trigger itself was reported. We believe that the relatively late effects are most likely due to the experimental design. In particular, the content of the presuppositions was only known on the prepositional phrase, because only then it was clear which referent was considered unique in the context. In sum, the results suggest that a presupposition is processed as soon as it is fully known. A more detailed analysis of syntactic ambiguity resolution strategies was done by Spivey, Grosjean, and Knoblich (1995) who provide further evidence for an immediate influence of pragmatics and logically specific biases in syntactic ambiguity resolution.
Tiemann et al. (2011) reported three self-paced reading studies and acceptability ratings on presupposition processing as induced by different triggers (German “wieder”: English “again”; “auch”: “also”; “aufhören”: “stop”; “wissen”: “know”, and definites in the shape of possessive noun phrases). In their first experiment, which is important for the current paper, they focus on the processing of the trigger itself. Participants were presented with a context (as in (9)) and the authors compared test sentences including a presupposition trigger (as in (10)) with sentences including a neutral word that does not trigger a presupposition (as in (11)), and with semantically unacceptable sentences (as in (12)).
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9.
Context: Tina ist mit einer guten Freundin shoppen.
Tina is shopping with a good friend.
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10.
Sie kauft wieder rote Handschuhe.
She buys red gloves again.
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11.
Sie kauft heute rote Handschuhe.
She buys red gloves today.
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12.
*Sie kauft freundlich rote Handschuhe.
She buys red gloves friendly.
Sentences with the neutral word were rated best, followed by sentences including the presupposition trigger and unacceptable sentences. Second, and most importantly, reading time data revealed that—for the position of the presupposition trigger—sentences with a trigger induced the longest reading times, followed by sentences with a neutral word, while unacceptable sentences were read fastest (see also Schneider, Bade, & Janczyk, 2020). This pattern suggests that a presupposition trigger immediately demands more attention, because it alerts the reader to consider the preceding context. Furthermore, in their third experiment, they investigated whether a presuppositional sentence in a neutral context (neither making the presupposition explicitly true nor false) evokes longer reading times than in a falsifying or verifying context. The data revealed early effects on the trigger, which also suggest that processing of the presupposition begins immediately upon encountering the trigger.
Unfortunately, reading times were not analyzed for individual presupposition triggers, as there were not enough items for each trigger to allow for strong conclusions. It is thus unclear whether the same pattern holds for all triggers or not.
There is further evidence for an immediate processing of presupposition triggers from electrophysiological studies. For example, van Berkum, Brown, and Hagoort (1999) and van Berkum, Brown, Hagoort, and Zwitserlood (2003) used event related potentials (ERPs) to investigate the interplay of referential and structural factors during sentence processing in discourse. To do so, the authors used referentially ambiguous noun phrases. In these studies, participants were presented with a discourse as in (13) and (14). A corresponding test sentence was, for example, “David told the girl that had been on the phone to hang up.” In discourse (13), uniqueness of the noun phrase “the girl” in the test sentence was granted, because the discourse introduces only one salient girl. In contrast, this is not the case in the other discourse (14), where both girls are equally salient. As a result, the uniqueness presupposition is not fulfilled up to the disambiguating relative clause (“...that had been on the phone...”).
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13.
David had told the boy and the girl to clean up their room before lunchtime. But the boy had stayed in bed all morning and the girl had been on the phone all the time.
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14.
David had told the two girls to clean up their room before lunchtime. But one of the girls had stayed in bed all morning and the other girl had been on the phone all the time.
The definite noun phrases evoked early ERP effects already on the noun, when the uniqueness presupposition was not met. Thus, referential ambiguity appears to be detected very early during sentence processing. Contrary to Altmann and Steedman (1988), evaluation of the presupposition was not delayed until to the relative clause, but instead participants considered the presupposition against the context as early as they heard or read the noun. This may come as a surprise given that participants knew that there were also sentences where the presupposition failure was resolved by the following relative clause, similar to the participants in Altmann and Steedman (1988) becoming aware that the following prepositional phrase was important for evaluating the presupposition. The difference might be due to the different syntactic status of relative clauses and prepositional phrases. Taken together, the studies of van Berkum et al. (1999, 2003) support the idea of early processing of presuppositions triggered by the definite determiner. Participants realize that there might be presupposition failure of a definite noun phrase immediately on the noun itself.
Evidence for immediate presupposition processing also comes from Kirsten et al. (2014) who investigated the processing of definite and indefinite determiners in an ERP study. Two types of contexts (see (15)) introduced either a single referent (e.g., one polar bear) or multiple referents (e.g., some polar bears). Test sentences were alike except for the determiner used (“the/a”) and were either presented in a matching condition where the context sentence introduced the noun phrase with an indefinite determiner “ein/e” (Engl.: “a”) or in a mismatching condition where it contained a quantifier such as “einige” (Engl.: “some”) or “viele” (Engl.: “many”).
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15.
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(a)
Antje war gestern im Zoo in Düsseldorf und besuchte einen /einige Eisbären im Bärengehege.
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(b)
Antje visited the Düsseldorf zoo yesterday and saw a/some polar bear/s in the bear enclosure.
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16.
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(a)
Antje beobachtete, dass der/ein Eisbär sehr aggressiv war.
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(b)
Antje noticed that the/a polar bear was very aggressive.
The data revealed that participants recognized mismatching conditions already when reading the determiner. For both determiners, the mismatching effect became visible through an N400 and a P600 effect after onset of the noun.Footnote 3 Thus, the results support the idea of immediate processing of presuppositions, already starting on the trigger.
There is further evidence that information encoded in determiners is exploited to guide behavior. Dahan, Swingley, Tanenhaus, and Magnuson (2000) focused on gender information encoded in the determiner (in the French language) in an eye-tracking study and demonstrated that gender-marked determiners immediately directed the listeners’ eyes towards the object that matched the gender. This supports the idea of immediate processing of determiners and the use of information encoded in therein.
Further support for early processing of determiners comes from a visual-world eye-tracking study using a picture selection task (Bade & Schwarz, 2019a). In one critical condition, sentences like “A/The shirt in Benjamin’s closet is blue” were presented auditorily and paired with three different pictures, all of which showed a boy with a closet. On one of the pictures, the closet contained three shirts, one of which was blue (non-unique condition). On another picture, only one blue shirt was depicted (unique condition), and no shirts were depicted on a third (distractor) picture. Participants were asked to choose the picture they thought was corresponding to the sentence, and indeed they looked at the respective target picture (picture with a single shirt for the definite determiner, and picture with multiple shirts for the indefinite determiner) very early on upon hearing the noun. This suggests that the (anti-)uniqueness information encoded in the determiners was used rapidly for interpretation. In addition, differences between both determiners were observed. Inferences based on the use of the indefinite determiner were drawn to a much lesser degree than those evoked by the use of the definite determiner, as demonstrated by fewer target choices for the indefinite than for the definite determiner. Further differences between the determiners were observed in eye-tracking patterns for the cases where the target was chosen. Overall, these results are in line with the “anti-presupposition theory”, which predicts differences in processing patterns associated with the anti-uniqueness inference and the uniqueness presupposition.
Finally, mouse-tracking data from Schneider et al. (2019) also support this view. In two experiments, participants were asked to judge the appropriateness of sentences like “Of these, Jan received the/a banana.” in contexts showing that Jan’s mother bought three pieces of fruit (e.g., one banana and two pears, or two bananas and one pear). Participants made their judgment by moving the mouse cursor into response boxes located in the top right and left corners of the computer screen. The indefinite determiner was associated with more difficulty in processing (reflected in longer movement times and a larger area under the curve). Most importantly, the data of Schneider et al. (2019) also revealed an initial deviation into the direction of the non-target response (i.e., the competitor) for the indefinite determiner. This was predicted by the “anti-presupposition theory” exploiting Maximize Presupposition (Heim, 1991), which suggests that participants first consider the uniqueness presupposition of the definite alternative when encountering an indefinite determiner.
In sum, there is evidence for early processing of presuppositions introduced by definite determiners, as demonstrated by effects observed on the trigger and briefly thereafter, when the content of the presupposition is known. Furthermore, additional processing costs were observed when the presupposition is not met by the context. This effect may, however, be modulated by additional cognitive load (see Clifton, 2013). Finally, the available evidence suggests processing differences between determiners.
Overall, the existing experimental literature on presuppositions focused on the processing costs associated with presuppositions of different triggers in different contexts. One question that this research concentrated on was whether presuppositions are more difficult to process in contexts in which their use is infelicitous (i.e., when the presupposition was not verified). Another focus was on the question, when these effects occur. With the exception of Bade and Schwarz (2019a, b) previous research did not address the issue of whether early information about uniqueness and anti-uniqueness encoded in determiners is used to make predictions about a sentence’s meaning. A weakness of the few studies that addressed how inferences associated with definite or indefinite determiners affect interpretation (Bade & Schwarz, 2019a) is that it was unclear from the task used in the experiment whether the information encoded by the determiner would be relevant for the choice. In general, it was unclear for the participants what was hinging on their choice of picture. Another weakness of many experiments on definiteness in general is that it only became apparent on the noun whether uniqueness or anti-uniqueness was satisfied, because more than one referent to which the definite or indefinite noun phrase could refer was provided in the context.
The experiment reported in the present paper extends the still small empirical basis for answering the following question: Is interpretation driven by presuppositional information encoded in determiners? An advantage of the present study over previous ones is that disambiguation was possible on the determiner itself, and not only on the noun. This makes it possible to identify immediate effects of the number information encoded in the determiner. Another advantage of the study presented here is that participants were directly addressed by the speaker. The assumption was that hearers would use all available cues given that they had to do a task for the speaker. Moreover, participants were informed that the speaker shared the same knowledge. As opposed to previous studies, participants thus had an incentive to draw the relevant inferences, and were informed of the epistemic state of hearer and speaker they needed to assume.
Experiment
In this section, we will first provide a forecast of the experimental approach followed by a brief introduction into mouse-tracking, the method we used to answer our main questions. We will then lay out the hypotheses in more detail.
The entire experiment comprises two parts. The first part is a forced choice production task where participants are asked to produce a sentence which appropriately describes a given situation. This task has several purposes: First, we aim at showing that participants are aware of the uniqueness presupposition of the definite determiner, and therefore use it predominantly in situations where the described item is unique. Second, we aim at testing whether participants systematically use the indefinite determiner when the object they want to refer to is non-unique. Finally, the data from the production task will be used to screen participants regarding whether they have a sufficient command of the correct usage conditions of both determiners in sentence production. We will exclude participants who commit more than 20% errors, that is, who do not use determiners in the intended way or make errors with the color or object choice (these participants will be replaced with new participants).
The second part is a mouse-tracking experiment with the aim to test whether listeners can rapidly integrate potential cues about uniqueness or anti-uniqueness in a context to achieve early predictive disambiguation, even before hearing the lexically disambiguating referent noun.
Mouse-tracking
Mouse-tracking has become a common method in cognitive psychology, since recent studies revealed that motion trajectories can reflect underlying cognitive processes. In fact, simple hand movements offer a continuous stream of motor output and provide real-time read-outs of ongoing cognitive processes. Spivey et al. (2005) were among the first who used mouse-tracking to answer language-related questions. Participants were instructed to start a trial via moving the mouse into a start box (in the lower center of the screen) and then follow the instructions of an auditory stimulus sentence (e.g., “Click on the candle!”) while watching a picture with items in the upper left and upper right corners of the screen. In one condition, the depicted words were similar in their initial phonemes (e.g., “candle” vs. “candy”), while in the other condition they were not (e.g., “candle” vs. “summer”). The trajectories of the movements towards the correct upper corner showed an attraction of the distractor word, when both words shared the initial phonemes. Thus, during processing of the target word, competing phonological representations appear active and influence the exact way the hand moves. Similar approaches have since been applied to, for example, social cognitive questions (Freeman, Dale, & Farmer, 2011), conflict tasks (Scherbaum, Dshemuchadse, Fischer, & Goschke, 2010), the effects of irrelevant stimulus variation on action execution (Janczyk, Pfister, & Kunde, 2013), or the influence of actions consequences on action execution (Pfister, Janczyk, Wirth, Dignath, & Kunde, 2014). Furthermore, mouse-tracking has also been used in sentence verification tasks to study conversational implicatures (Sauerland, Tamura, Koizumi, & Tomlinson, 2015; Tomlinson, Bailey, & Bott, 2013), predictive disambiguation based on early intonational cues (Roettger & Stöber, 2017; Roettger & Franke, 2019), and sentence negation (Dale & Duran, 2011).
Several parameters are usually extracted from the trajectories for further statistical testing. We here focus on the following parameters (see Fig. 1 for an illustration): (1) area under the curve (AUC) is the geometric area between the observed mouse-trajectory and an idealized straight line and becomes larger, the more the trajectory deviates from the straight line. According to Freeman and Ambady (2010), AUC provides a general measure of processing difficulty (Farmer, Cargill, & Spivey, 2007; Freeman, Ambady, Rule, & Johnson, 2008; Spivey, 2008). (2) Movement time (MT) is the time from stimulus onset until reaching the target box. (3) Turn towards target (TTT) is defined as the point in time when participants finally make their decision and turn towards the target without any subsequent reversals (Roettger & Franke, 2019).
In the experiment proper, participants were asked to hand a named object from a shelf to the speaker. One or two items of the named object type were present on the shelf. In addition, one or two entities of a different object type (the competitor) were present. Stimulus sentences either contained the definite or the indefinite determiner. In “early disambiguation” conditions, participants could, in principle, know which object will be referred to already upon hearing the determiner. In contrast, in “late disambiguation” conditions, this is only possible after the target object has been named. Conceivably, however, early disambiguation makes sense only if a listener knows by experience that sentences with definite and indefinite determiners are used in a felicitous way. Thus, one group of participants only encountered felicitous sentences (the reliable group), a second group was presented with infelicitous sentences as well (the unreliable group).
An advantage of using German stimuli is that we can make sure that the definite description could not be plural, as the definite determiner is marked for grammatical gender. As the plural determiner for all three genders is form-identical with the singular feminine determiner, we only used masculine and neuter nouns in our experiment, which makes the definite determiner unambiguously singular. This is not the case in English, where “the” could still be followed by plural nouns, which would make the sentence completely acceptable in non-unique scenarios. The presupposition of definite determiners is that there is a unique maximal element, which is trivially fulfilled for the extension of any plural noun (as there always must be a unique maximum) (cf. Heim, 2011). Only in combination with the singular does the definite noun phrase presuppose uniqueness of an atomic individual with the described property. It is thus possible to predict on the (singular marked) definite determiner that the reference will fail if there are only non-unique referents in German, but not in English, where plural/singular marking only becomes obvious on the noun. The general expectation is thus that participants in our experiment could use the information of number encoded in the determiner right away and make the according choices rapidly.
Hypotheses
The first question we ask is whether people utilize the relevant meaning components of a determiner (uniqueness and anti-uniqueness) to form expectations about the likely referent, even before this referent is lexically given (and thus disambiguated). This is supported by previous experiments showing that presupposition processing starts on the trigger itself (e.g., Tiemann et al., 2011; van Berkum et al., 1999, 2003). Thus, for the “reliable group”, we hypothesize that conditions with unequal amounts of different objects on the shelf (i.e., the early disambiguation conditions) allow faster decisions already upon encountering the determiner in comparison with those conditions with equal amounts of different objects on the shelf (i.e., the late disambiguation conditions; Hypothesis 1).
A second question is whether there are processing differences between the definite and the indefinite determiner. The three theories introduced in Sect. “Presuppositions” allow three different predictions: (1) according to the “presupposition theory”, both determiners come with their own presuppositions. In this case, the prediction would be that both the uniqueness and the anti-uniqueness presupposition are accessed equally fast and cause comparable processing difficulties. Thus, no differences are expected in this case (Hypothesis 2a). (2) According to the “anti-presupposition theory”, processing the indefinite determiner requires an initial consideration of the uniqueness presupposition of the definite determiner and its subsequent negation. This predicts more processing difficulties for the indefinite than for the definite determiner (Hypothesis 2b; see also Schneider et al., 2019). (3) Finally, the “implicature theory” assumes that the indefinite determiner activates a different type of competition, namely on the level of assertion. This would make the associated inference an implicature, which is processed more rapidly than a presupposition. Accordingly, less processing difficulties are predicted for the indefinite than for the definite determiner (Hypothesis 2c; see also Bill et al., 2018).
A final question is whether the potential early effects of information about uniqueness and anti-uniqueness (as suggested in Hypothesis 1) are affected by occasionally infelicitous uses of the determiner.
The theories spelled out above make different predictions regarding how processing of either determiner is influenced by occasional infelicitous uses. According to the anti-presupposition theory, the definite determiner comes with a lexically stored presupposition whereas the indefinite determiner’s inference is the result of pragmatic reasoning. As a consequence, the definite determiner should be less affected by infelicitous uses than the indefinite determiner given the assumption that lexical information is generally harder to overwrite. Following the presupposition theory, both determiners come with lexically encoded information regarding number. Therefore, they should be equally affected by infelicitous uses. Finally, in the case of the implicature theory, the indefinite determiner should be more affected than the definite determiner. This is because implicatures are highly context-dependent expressions, easily affected by speaker reliability (Bott & Noveck, 2004), as opposed to lexical presuppositions.Footnote 4 These hypotheses will be referred to as Hypothesis 3.