Prior empirical work in semantic development has produced an impressive finding showing that children can reliably detect a modal's relative force (e.g., that must is stronger sounding than may) by five-and-a-half years of age. We investigate the extent to which a representation of relative force can account for an understanding of epistemic modals when their logical meaning is considered (i.e., when modals are interpretable as expressions of necessary and possible conclusions). Experiment 1 presents a replication of Hirst & Weil's hidden-object task, which originally included the supremely forceful indicative is. Thirty-two five-year-olds were required to find a peanut hidden under one of two containers based on a pair of statements that contrasted is with has to, has to with might, or is with might. Half the children were entitled to search for the peanut upon hearing the two statements and half were required to indicate only where they would look. Results largely confirmed the influence of relative force in this paradigm. Both groups of children usually searched under the container associated with the stronger-sounding term. Experiment 2 employed a modified version of the hidden-object task in which contrasts presented one true and one false modal statement and 32 five-year-olds, 20 seven-year-olds, 16 nine-year-olds and 20 adults were asked to determine which of two modal statements was correct. Half the contrasts presented a relatively weaker-sounding modal term in the true statement and the other half presented equally forceful modal terms in the two statements. No age group systematically endorsed a false stronger-sounding modal statement over a true weaker-sounding one. The five-year-olds' rate of correct responding overall was above levels predicted by chance. Mature logical modal understanding was found among seven-year-olds who routinely endorsed a contrast's true modal statement. These findings suggest that deductive inference is an early semantic component of modal terms.
 
 

INTRODUCTION

 A modal term, such as must or may, conveys several distinct but related meanings. Pragmatically, a modal implies a level of speaker certainty or relative force. For example, the speaker who asserts must in (1a) sounds relatively more certain than the one who asserts may in (1b).
 
 

(1a) George must be in his room.

(1b) George may be in his room.
 
 

In conveying an inference, a modal implies that the speaker has reached a necessary or possible conclusion. For example, the speaker's use of must in (1a) indicates that, based presumably on a logical inference, George is necessarily in his room. Similarly, the deductive use of may in (1b) implies that George is possibly in his room. Modals have a deontic sense, as well, in which the speaker's assertion of must in (1a) indicates that George is obliged to be in his room and the modal may in (1b) indicates that George is permitted to be in his room.

It has become commonplace to categorize modal statements with respect to epistemic or deontic interpretations (Johnson-Laird, 1978). The epistemic aspect concerns the inferring of knowledge states and can be subdivided into a) a subjective kind which concerns the relative force that can be detected pragmatically by the listener and b) an objective kind which concerns logical conclusions inferred by the speaker (Lyons, 1977). The deontic aspect concerns social regulations (e.g., where must conveys obligation and may permission).

Although this brief introduction neatly classifies three kinds of modal meaning, our account is not intended to be exhaustive. Complete systematizations of modals (e.g., Palmer, 1965; Wells, 1979; Perkins, 1983) typically include ability-related uses, as in She can play golf, and would have to include relatively unusual categories, such as the supernatural modality (or wish) heard in May the best man win (Nicoloff, 1994). Moreover, systematizations make other finer distinctions. In the domain of deontic uses, for example, statements can be subdivided into those which focus on the constraint on an agent's action, as in I may play outside until tea-time, and into those acts that are performed in the uttering of the sentences, as in May I go out to play? (Wells, 1979). Our characterization of modal meaning, based on pragmatic, logical, and deontic interpretations, is intended to highlight the largely overlooked role for the logical meaning in the acquisition of modal terms.

Researchers have pursued the study of modal semantic development in two ways, one observational and the other experimental. We first focus on studies of naturalistic speech by Wells (1979) and Perkins (1983). Wells (1979) studied children whose ages ranged from 15 to 45 months; Perkins (1983) studied children whose ages ranged from six to twelve years. These studies yielded similar findings and provide much of the background for the work to date on modal terms. First, Wells (1979) found that children spontaneously produce modals before they are three years old. The modal can appears regularly in his sample by the time children are 30 months old (the criterion being that half the children at that age produce the word), followed by have got to, shall, and could at 36, 39, and 42 months respectively. Second, Wells's corpus showed that deontic modal expressions (I can [meaning may] play outside all afternoon) are primary and are later followed by inferential uses (That might be John [at the door]). Perkins largely confirmed these findings from older children. He found that 1) six-year-olds demonstrate command over an, albeit restricted, range of modals and that 2) there appears to be a developmental shift from deontic-related to inferential-related uses of modals. The latter conclusion is based on children's production of the modal can, the most frequently used modal in the sample. Permission-related uses of can (as opposed to expressions labelled as Ability, Circumstantial Possibilty, and Suggestion) were the main kind of modal expressions among six-year-olds and were the least used meaning among 8-year-olds, at which age Circumstantial Possibility emerged as, and remained, the primary contextual purpose for expressing can. That early deontic interactions form the basis of modal meaning has motivated much of the research in the area (Hirst and Weil, 1982; Stephany, 1986; Byrnes and Duff, 1989).

There are limitations to the conclusions that one can draw from the observational studies however. One is that recorded modal uses may reflect the situations in which children tend to find themselves and not necessarily their progressive mastery of the studied terms. Early modal uses of can may appear mostly deontic (as opposed to inferential) because younger children are perhaps more likely to be in situations that bring up concerns for their safety or situations that require their subordination (as opposed to situations that engage their collegiality). Another limitation of the observational studies of semantic modal development is that they do not tell us the extent to which the rarely appearing terms reflect subjects' knowledge of their underlying concepts. It does not follow that the 8- to 12-year-olds in Perkins's study do not have an adult understanding of, say, the modal might because it rarely appears in their spontaneous productions. For example, in an investigation of modal comprehension Coates (1988) showed that 8- and 12-year-old children employ the modal might in an adult-like manner. Kucjaz and Maratsos (1975) made a similar point with respect to modal syntactic development and showed that a two and a half year old may very well have more competence than indicated by spontaneous production. Yet despite their limitations, the naturalistic findings have provided a valuable sketch of children's semantic modal development and sufficient grounds to test specific hypotheses.

Empirical research on modal semantic development has focussed primarily on the developing knowledge of the pragmatic meaning (Moore, Pure, & Furrow, 1990) and how it is presumably related to, or emerges from, a deontic understanding (Hirst & Weil, 1982; Byrnes & Duff, 1989). Although tests of comprehension have not supported the latter hypothesis (Hirst & Weil, 1982; Byrnes & Duff, 1989), research from this perspective has produced an impressive finding showing that children, from three years of age and onward, have an increasing ability to detect the relative force of epistemic modals (Hirst & Weil, 1982; Hofmann, 1986; Byrnes & Duff, 1989; Moore et al, 1990). For example, Hirst & Weil's seminal epistemic task (which is described below) shows that from the time children are five-and-a-half years old, they can detect that must sounds more forceful than should which, in turn, sounds more forceful than may. Developmental patterns reveal that children first make gross, and then finer, distinctions based on the relative certainty conveyed by the modal terms. The investigations also reveal that children make significant progress between the ages of three and four. In similar studies that have been influential in establishing the theory of mind approach, Moore and colleagues (Moore, Bryant, & Furrow, 1989; Moore & Davidge, 1989; Moore & Furrow, 1991) have shown that children develop a comparable pragmatic ability with mental verbs where, e.g., know expresses relatively greater speaker-certainty than think. Empirical efforts have thus led to a robust effect: children fine tune their understanding of modals (and mental verbs) through the pragmatic detection of relative force.

 In contrast, the child's appreciation of the logical implications of modal terms has received relatively little attention, particularly in the empirical approach. Besides being of interest in its own right, the semantic development of modals' logical meaning can provide insight into children's understanding of notions related to necessity and possibility, a topic of much interest to cognitive developmentalists (e.g., Pieraut-Lebonniec, 1980; Byrnes & Overton, 1986; Horobin & Acredolo, 1989). Modals used to express logical inference determine that a conclusion is necessary, not necessary, possible, or impossible; must, need not, may, and cannot can be used to express these four kinds of modal conclusions, respectively. Central to such modal understanding is the reliance on background information that leads to the appropriate inferences. For example, for one to understand (1a) in its logical sense, one presupposes that the speaker has surveyed evidence (perhaps that George is playing a piano that is in his room). Modal reasoning is ubiquitous because one is often required to draw conclusions by way of evidence, i.e., without the benefit of direct observation. By focusing on the logical component, our goal is to provide for a more complete account of children's developing knowledge of modal terms.

 Given that no prior work has directly investigated the logical dimension in semantic modal development, we propose two ways in which the logical meaning of epistemic modals might be acquired and test between them. First, one can postulate that the logical meaning of epistemic modals is acquired with the onset of (or is perhaps directly derivable from) an understanding of the pragmatically-driven, deontically-derived understanding of relative force. Byrnes & Duff (1989) have suggested such a proposal by implying that the relatively precocious ability to understand the pragmatic sense of epistemic modals ought to be taken as equivalent to a logical understanding and argued (p. 387) that their findings contradict Pieraut-LeBonniec's (1980) claim that comprehension of possibility and necessity is only apparent around the ages of nine or ten.

Alternatively, one can postulate that an appreciation of the logical component in modal development is independent of relative force understanding. This approach would argue that for the logical component to be understood, there would have to be an appreciation of rules of inference that cannot be drawn from hierarchical structures like relative force alone (see Jackendoff [1994] for a discussion of the inference-rule component in concept development). According to this proposal, the pragmatic ability to detect relative force is by no means an indication of logical understanding.

 The two proposals lead to different predictions. If a mature appreciation of relative force is influential in logical understanding then there should be some indications of that influence in tests of children's understanding of logical modals. Also, relatively young children (five-year-olds) would be expected to show a mature appreciation of the logical meaning of modals. Alternatively, if an understanding of logical comprehension is independent of other meanings then relative force judgements would have no bearing on children's responses in tests that employ modals to express a logical inference. If this second proposal is correct, then the developmental course of understanding epistemic modals' logical meaning would appear to be unlike the one for relative force understanding. In the present work, we sought to determine the extent to which relative force can account for epistemic modal semantic development. Below we critically review Hirst & Weil's (1982) seminal study, which provides the paradigm for the experiments that follow.

According to the relative force hypothesis, the following four statements convey decreasing levels of speaker certainty:
 
 

(2a) The peanut is under the box.

 (2b) The peanut must be under the box.

 (2c) The peanut should be under the box.

 (2d) The peanut may be under the box.
 
 

The statement in (2a) uses the indicative is, but is assumed to be more forceful than the strongest modal must. In the original hidden-object task (Hirst & Weil, 1982), young subjects are presented two of these statements about two different containers (e.g., one puppet would say The peanut must be under the box and the other would say The peanut may be under the cup) and are then allowed to search under the container of choice. Note that the subsequent search means that children actually receive feedback because the peanut is always placed in the container associated with the stronger term. When presented each of the six possible contrasts, Hirst and Weil (1982) reported that five-and-a-half-year-old children systematically found peanuts by following the stronger-sounding statement. Four-year-olds' performance was expert if one excludes statements with the modal should, as expressed in (2c).

 Generally, the hidden object paradigm tells us little about children's ability to, and inclination to, understand epistemic modal statements logically. In fact, both statements in any of the paradigm's contrasts can be true and both can be false because there is no background evidence with which to make truth evaluations. One feature in Hirst & Weil's original paradigm that perhaps reveals children's effort to rely on background, and thus on an objective form of, information is that children were allowed to search for the hidden peanut after each trial. It is plausible that the children benefited from the feedback because their searches promptly demonstrated that task success requires the application of a relative-force rule in which is > must > should > may. If this is so, relative force may not be as intrinsic to children's decision-making behaviour as first thought. It is conceivable then that more random responding would result in the absence of feedback (where a given peanut's actual hiding place is withheld). Moore et al. (1990) replicate certain portions of Hirst & Weil's findings (by contrasting the terms must and might) without feedback (i.e., children did not search for hidden peanuts until the end of the experimental session), but Moore et al. also did not include a control group to determine whether their modification had any effect on performance.

Moreover, follow-up studies have typically focused on modal-modal contrasts (Moore et al., 1990; Byrnes & Duff, 1989) and have largely ignored the indicative/modal contrasts. Although Hirst & Weil present findings showing that children consistently find the indicative is to be more forceful than the other terms, we consider it worthwhile to attempt a replication of this finding because in a modal reasoning context the use of is would be slightly peculiar (in the absence of an observable object). If children bring considerations of modal reasoning to the hidden-object task, responses may reveal that the mention of an indicative is potentially confusing.

We conducted two experiments. In Experiment 1, we attempted to replicate Hirst & Weil's original findings. Five-year-olds were assigned to one of two conditions -- feedback and no-feedback -- as a hidden-object task systematically contrasted statements containing is, has to, and might. If an understanding of modals requires something other than relative force then the lack of feedback was expected to lead to more random responding. We then reconstructed the hidden-object paradigm so that provided evidence allowed subjects to evaluate epistemic modal statements, which were true or false. In Experiment 2, children and adults were presented a) one true modal statement and one false modal statement and asked to determine which is correct. Three pairs of contrasts included a true modal statement that is relatively weaker-sounding than its false contrast. If relative force determines responses, it was expected that subjects in the revised hidden-object paradigm would be more likely to endorse the stronger-sounding (albeit false) statements.

Hirst & Weil's paradigm was adopted with five minor modifications. First, following Byrnes & Duff (1989), the more colloquial expressions has to and might were used instead of must and may. Second, our sentence formulations were presented as There [is/has to be/might be] a peanut under the [box/cup]. Byrnes and Duff employed It [has to be/might be...]) and both Hirst & Weil and Moore et al. began their sentences with The peanut). Our formulation allowed for maximally equivalent modal expressions across the two experiments conducted. Third, subjects were assigned to one of two conditions: feedback and no-feedback. In the feedback condition, children were allowed to check their chosen container upon hearing the two statements; in the no-feedback condition, children indicated which was their container of choice, but they were not entitled to check its contents until the session was completed. Feedback was varied to test for possible effects due to learning. Fourth, children were presented with three contrasts (all possible combinations of is, has to, and might) and given four trials with each. Hirst & Weil presented two trials with each of six contrasts (because they had included the modal should in their tasks). Fifth, only five-year-olds were included because prior studies reveal that even four-year-olds have a system that differentiates between the three terms in the study.

 If Hirst & Weil's findings are replicable, one should find that children indicate that is is a more powerful cue than has to, and has to a more powerful cue than might. If type of feedback is critical, then children in the feedback condition should yield more successful searches than those in the no-feedback condition.

 METHOD

Subjects

 Thirty two five-year-old native English speakers participated. Their mean age was 5;5 and they ranged in age from 5;3 to 5;7. Subjects were recruited from the Twin Cities (Minneapolis-St. Paul) metropolitan area of Minnesota.

Materials

 Seventeen pairs of overturned cups and boxes were arranged, left to right, in pairs of 5, 6, and 6. A peanut was hidden under one container of each pair. As per Hirst & Weil (1982), the first five were for practice trials.

Design and Procedure

 Children were randomly assigned to one of two conditions. Children were presented a set of twelve test trials, four each of the three possible contrasts between is, has to and might. That is, the three kinds of statements were:
 
 

There is a peanut under the cup (or box).

 There has to be a peanut under the cup (or box).

 There might be a peanut under the cup (or box).
 
 

Peanuts were evenly distributed among the cups and boxes and children were informed first about the cup. Four random orders were prepared; thus, in each condition, four children were assigned to each of four orders.

Each child was seated in front of a table and told that for each pair of containers, there was a peanut hidden under one of them. As in Hirst & Weil (1982), practice trials were comprised of children hearing puppets contrast statements such as The peanut will be under the box and The peanut will not be under the cup. Children in the feedback condition looked under their chosen container after each trial. Children in the no-feedback condition indicated their choice by placing a penny atop their chosen container and were allowed to see how successful they were after the practice session. The children had little trouble with the training. In the infrequent event that a child chose a container that did not cover the peanut, the experimenter asked the child to close her eyes (to make it seem that the peanut was being rehidden) and, upon reopening them, was presented the same contrast which had failed to lead the child to discovery the previous time. Training concluded when a child found all five of the hidden peanuts.

 In the experimental portion of the experiment, children heard the puppets present two statements as in the practice trials, but the sentences were presented as There (is/has to be/might be) a peanut under the (box/cup). Each contrast -- is/has to, has to/might, is/might -- was presented four times. Presentation was balanced so that each term in a contrast twice appeared first and twice appeared last. In the feedback condition, children verified their choices after declaring where they believed they would find the peanut; in the no-feedback condition, children placed a penny atop their chosen container to indicate where they thought one could find the hidden peanut and, after the experimental session, the experimenter lifted each of the child's chosen containers in a game-like manner.
 
 

RESULTS

A child's response was considered successful when it was in accord with the the relative force hypothesis (where is > has to > might). A child heard each contrast a total of four times. Our main concerns were to determine that expectations of the relative force hypothesis were verified and to test whether type of feedback had any effect. Table 1 shows the rates at which subjects followed the more forceful cue and how subjects across the two feedback groups responded.
 
 

TABLE 1 Percentage of trials in which five-year-old children choose containers associated with a stronger relative force (where is > has to > might). N=32

 ---------------------------------------------------------------------------------------------------------
 

Note. Each cell reflects subjects' performance on two trials with each contrast. A sentence was presented as There (is/has to be/might be) a peanut under the (cup /box). * p < .01, when based on chance predictions.

Table 1 shows that subjects chose the container associated with the stronger-sounding term in the contrasts is/might and has to/might on 84% and 71% of the trials, respectively. These are equivalent to means of 3.4 and 2.8 (out of four chances), respectively. Responses favouring the indicative is in the is/might contrast were significantly higher than those predicted by chance, t(31)=8.93, p < .001, as were responses favouring has to in the has to/might contrast t(31) = 5.13, p < .001. Subjects chose the container associated with is over has to on 58% of the trials (which is equivalent to 2.3 successful searches out of four chances); this did not differ significantly from predictions based on chance, t(31)=1.62, p=.12, n.s. However, post-hoc t-tests showed that the is/might contrast yielded significantly more successful searches than the has to/might contrast, t(31) =2.96, p < .01, indicating illocutionary superiourity of is over has to. This last result partly accounted for the significant effect for Contrast in the ANOVA.

 Table 1 also shows how subjects performed as a function of within-contrast order, e.g., how rates of successful searches were affected when the is/has to contrast first presented the indicative is and when the contrast first presented has to. Analyses of presentation order (stronger-first vs. stronger-last) revealed that the children showed a significant preference to follow the cue from a contrast's latter statement in both the is/has to and is/might conditions. When is was presented first and has to second, children endorsed is on 44% of the trials; when has to was presented first and is second, children endorsed is on 72% of the trials, t(31)=3.24, p < .01. Likewise, the five-year-olds endorsed is over might less readily when is was presented first (successful searches on 78% of the trials) rather than second (91%), t(31)= 2.10, p < .05. In contrast, children's preference for has to over might remained consistent regardless of presentation order. When has to was presented first, children chose has to over might on 69% of the trials and when has to was presented second, children endorsed has to on 73% of the trials. Thus, order effects were apparent only when is was part of a contrast.

Discussion

 Our findings with is, has to, and might, largely support expectations from the relative force hypothesis. The results reveal highly consistent effects, even among the subjects who were not entitled to get feedback about their decision. Children valued the puppets' statements above all else and, as found in the earlier studies, they appreciated the subtle distinctions that were drawn for them.

Our findings concerning two of the three studied contrasts are in line with results from previous studies. Performance in response to the is/might contrast in this experiment (successful searches on 84% of the trials) was highly comparable to the kind of performance Hirst & Weil reported with an is/may contrast (one can calculate that 88% of their five-year-old subjects endorsed is). Likewise, performance in response to the has to/might contrast (success on 71% of the trials here) was comparable to others in the literature. Hirst & Weil's tables reveal that 72% of their five-year-olds made successful searches on must/may contrasts. Byrnes & Duff reported that 78% of their five-year-old subjects made successful searches on a has to/might contrast and, Moore et al., judging from a graph, showed that around 85% of their five-year-old subjects made successful searches on a must/might contrast.

Although children showed 1) a tendency to prefer is over has to in a direct contrast and 2) that they were more likely to endorse the cue from is in the is/might contrast than has to in the hasto/might contrast, the children's preference for is over has to was not significantly different from predictions based on chance. This varies somewhat from the comparable manipulation in Hirst and Weil's study (whose 5-year-olds were successful on 75% of the trials that presented an is/must contrast). One might expect that Hirst and Weil's result to be more in line with one's intiuitions because a factual statement ought to seem more forceful than a statement that points to an inference. However, as we argue below, it should not be surprising to find this impression modifiable. Below, we consider three hypotheses that could explain our novel result.

Our primary hypothesis concerning the near equivocality of the is/has to contrast involves the interaction of two factors. One factor is that the use of has to is a rather compelling cue in a scenario where the discussed object is unseen. A statement expressed with a modal such as has to implies that the speaker is aware of something so compelling that it makes the implicit logical inference seem about as powerful as seeing the discussed object directly. The other factor is that -- in the absence of a direct observation -- a reference to an object with is, although supremely forceful, may seem pragmatically peculiar enough to lend some doubt to the speaker's accuracy. Further, we hypothesize that this interaction results in a standoff with respect to relative force and encourages children to follow the latter cue (perhaps because of limitations in memory). We believe that the potentially confusing use of is leads to the order effects associated with the is/might contrast as well, but in that case might does not present itself to be a very compelling alternative. In short, we argue that when the peanut is not directly observable (as in a modal reasoning scenario), a statement with the expression has to, used to allude to evidence, may well provide a cue powerful enough to be on par with the potentially confusing is.

To illustrate this hypothesis, imagine being informed that our friend George was holding five coins and that two slipped out. Given that none of the coins were visible from the start, would it not be more appropriate to say George must be holding three coins than George is holding three coins? Using the modal must alerts the listener to the fact that the conclusion is based on a compelling, relevant inference and not on an observation (Dan Sperber, personal communication). This conversational-pragmatic explanation can be directly linked to the hidden-object task where the discussed object is always out of view at the time of the puppets' utterances.

A second possible hypothesis concerning the potential ascendancy of has to is that there are many contexts in which has to actually entails is. In any domain in which theories produce necessary conclusions that anticipate subsequent discoveries (e.g., scientific or forensic endeavours), one could find instances where a necessary proposition entails observable facts. Consider Darwin who -- upon seeing a Madagascan orchid having a foot-long (30 cm) neck -- logically concluded that in Madagascar, there must exist a moth with proboscides capable of extending 10 or 11 inches (25-28 cm). He had never seen such a moth, yet he made the modal conclusion based on his theory of evolution (and was roundly ridiculed). Forty years later, such a moth was discovered (Milner, 1993). Other domains (e.g., language learning) provide similar scenarios that lead to perhaps less exotic discoveries. We do not think that it is mistaken to suppose that children anticipate discoveries concerning quotidien (and linguistic) events the way Darwin did about evolutionary phenomena and that this theory-driven expectancy becomes part of one's meaning for must and its equivalents. That must(p) should entail is(p) corresponds with principles of modal logic (Lyons, 1977; Kartunnen, 1972). Although we do not assume, as Braine & Rumain (1983) and Perkins (1983) have discussed elsewhere, that children routinely employ logical principles that follow from Leibnizian possible world semantics, modal logic does describe why such an entailment is supportable.

Another possible explanation of our novel finding is that (perhaps due to dialect) the experimenters de-emphasized is and stressed has to in the is/has to contrast, making has to appear stronger when it appeared second. We do not think that this explanation is likely for the following two reasons. First, this explanation would have to be extended to the other two contrasts and there is no indication that it can be. If one accepts that consistent de-emphases and stresses led to the failure to find a preference for is over has to, the same explanation would have to be extended to the is/might contrast and, in that case, we find order effects but none that offset the superiour force that is attributed to is over might. Our finding for the is/might contrast (successful searches on 84% of the trials) nearly matched Hirst & Weil's for the is/may contrast (success on 88%). Similarly, if consistent de-emphases and stresses led to our finding for is and has to, semantic neighbours according to the relative force account, then consistent de-emphases and stresses would presumably be operating between has to and might as well. In that contrast, we did not find order effects and, again, we found results comparable to others in the literature. Second, the two experimenters rehearsed the presentation so that all phrases were articulated evenly and naturally throughout a session and without undue stress on the critical experimental words, on the word "peanut," or on the containers. It seems to us that it would require consistent and exagerrated de-emphases and stresses to offset the semantics of the investigated terms in this task.

We maintain that our findings -- the approaching equivocality found in the is/has to contrast and the order effect associated with contrasts including is -- are reliable. That has to can appear, at times, as forceful as is is important because one might expect some appreciation for the implicit logical meaning of modals among five year olds and the potential ascendancy of has to would support this expectation. The reported order effect is revealing as well in that it shows that children are sensitive to the appropriateness of utterances with respect to their conversational contexts. As described above, there are many situations in which a proposition with has to (or its equivalents) is more compelling than an equivalent proposition substituted with an indicative. Further experimentation in which one can vary formulations and contexts would resolve what underlies findings with indicative/modal contrasts and would provide for a relevant scientific discussion.

To summarize, the first experiment demonstrated that children extracted no additional objective information by checking their container of choice after each trial; subjects' responses apparently depended on the statements themselves and not the feedback. Generally, the children gave the impression that making their choices was relatively easy. One subject said, "all I did was listen to the puppet who sounded more important." However, when is was part of any contrast, we found order effects. We understand this to mean that children take note of the experimenter's choice of words and that many determine that the use of is is peculiar in the presented context. Finally, we propose that this pragmatic peculiarity plays a role in leading subjects to consider has to a good competitor of is. Although relative force provides a very useful guide for responding on the hidden object task, one can see that five-year-olds do not only follow an is > has to > might hierarchy in their responses. The results suggest that, to some extent, children consider the appropriateness of a statement in relation to the provided context.

In this Experiment, two modal statements were again contrasted, but were presented in a context that determines that only one was logically correct. For example, subjects were presented might/has to contrasts where might correctly described a deducible conclusion and has to did not. Experiment 2 included a broader age-range of subjects in order to determine whether there is a growing competence in this modified hidden-box paradigm. We present the modified hidden-object task below.

Consider three boxes. One is open and has a toy parrot and a toy bear in it (the Parrot+Bear Box), the second is open and has only a parrot (the Parrot-only Box), and the third stays covered (Box C). Subjects are told that Box C has the same content as either the Parrot+Bear Box or the Parrot-only Box. It follows that There has to be a parrot in Box C and that There might be a bear. Furthermore, one can come up with two other true modal statements concerning the contents of Box C: There does not have to be a bear and There might be a parrot. This last statement violates conversational principles in that it is minimally informative to say only that there might be, when in fact there has to be, a parrot. We thus left out this statement from the contrasts. Four false modal statements concerning Box C can be articulated with this presentation: There cannot be a parrot, There cannot be a bear, There has to be a bear and There does not have to be a parrot.

FIG 1. A representation of the experimental paradigm as presented to subjects in Experiment 2. Each of the eight statements end with "in the box" and refer to Box C which remains covered.

 
 

\

True Statements	False Statements
1. There has to be a parrot	5. There has to be a bear
(Necessarily parrot).	(Necesssarily bear).
2. There might be a bear	6. There cannot be a bear
(Possibly bear).	(not-Possibly bear).
3. There does not have to be a bear	7. There does not have to be a parrot
(not-Necessarily bear).	(not-Necessarily parrot).
4. There might be a parrot	8. There cannot be a parrot
(Possibly parrot).	(not-Possibly parrot).

In this forced-choice paradigm, subjects heard each of two puppets articulate a modal statement. One puppet expressed a true modal statement and one a false modal statement -- subjects were required to say which puppet was right. Subjects heard six contrasting pairs of statements that had either a) the weaker-sounding of two modals in a true statement (e.g. There might be a bear vs. There has to be a bear), or b) two equally forceful modals (e.g., There has to be a bear vs. There has to be a parrot). The latter group included one contrast whose statements present opposites (There has to be a parrot vs. There cannot be a parrot [cf. Byrnes & Duff, 1989]). Sixteen contrasts between true and false modal statements are possible; six were chosen to test whether the relative force hypothesis can be extended to judgments concerning logical epistemic modals. If children were to rely on the relative force of modals, they were expected to agree with the more certain-sounding puppet. If contrasted statements are equivalently forceful, the relative force hypothesis would be expected to lead to chance responding. If subjects have an appreciation for the logical meaning of epistemic modals, they were expected to focus on validity contrasts and to ignore relative force contrasts.
 
 

METHOD
 
 

Subjects

 Thirty-two five-year-olds, 20 seven-year-olds, 16 nine-year-olds and 20 adult native English speakers participated. The children's mean ages (range) were 5;5 (5;1 - 5;11), 7;5 (7;1 - 8;0), and 9;4 (9;0 -9;5). Subjects were recruited from the Twin Cities area. Adults participated to fulfill requirements for the Introductory Psychology course at the University of Minnesota.

Materials

 Two open boxes and one closed box were presented. One open box contained a parrot and another contained a parrot and a bear. Subjects were told that the closed box had the same contents as one of the two closed boxes (see Procedure). Subjects heard six true/false contrasts: (1) There might be a bear/There has to be a bear, (2) There might be a bear/There cannot be a bear, (3) There does not have to be a bear/There cannot be a bear, (4) There has to be a parrot/There has to be a bear, (5) There does not have to be a bear/There does not have to be a parrot, (6) There has to be a parrot/There cannot be a parrot. Contrasts 1 - 3 compared a true, weaker-sounding modal statement to a false stronger-sounding modal statement. Contrasts 4 and 5 each employed the same modal terms, but only one in each contrast is true. The two statements in Contrast 6 were equally forceful, but the true statement was affirmative and the false one negative. Wherever possible, a contrast used the same animal to maximize uniformity.

Design and Procedure

Two random orders of contrast pairs were prepared. Contrast pairs were prepared to meet the following criteria: 1) truthful statements were divided evenly, as first or second, among the contrasts and 2) the presentation order of each contrast was further inverted for half of the five-year-olds (piloting showed no effects for order among seven-year-olds).

 Training was designed to be similar to that of Experiment 1. It began by introducing two puppets, Pat and Wylbur, and by saying that the two puppets were friends who always disagree. Children were told that when one puppet was right, the other was wrong. For example, in reference to the white Experimental room, Pat said "the wall is red" and Wylbur said "the wall is white." Children are then asked, "Who is right?" The same technique concerning a feature of the room was used to provide a situation in which Pat was right.

Subjects were then shown four boxes. Two boxes were open: one box contained a horse and a fish (Horse+Fish Box) and the other contained just a horse (Horse-only Box). The two other boxes were covered but were identical to the Horse+Fish Box and the Horse-only box. Subjects were shown the two open boxes and asked to tell the experimenter what they saw. Subjects were then shown one of the covered boxes (chosen at random) and heard the Experimenter say, "A friend of mine gave me this box and said 'all I know is that whatever is inside this box looks like what's inside this Box (Experimenter pointed to the Horse+Fish Box) or what's inside this Box (Experimenter pointed to the Horse-only Box).'" Subjects were then instructed to peek inside the box, but to not say what they saw (they saw either a horse alone or a horse and a fish).

 At this point, the first puppet would say "There is a fish inside the box" while the second puppet would say "There is no fish inside the box." The child was asked to say which puppet was right. If the child had peeked in the Horse+Fish Box, she would be expected to say that the first puppet was right; if the child had peeked inside the Horse-only Box, she would be expected to say that the second puppet was right. The same procedure was carried out on the other, closed box: the child peeked inside and one puppet said "There is a fish inside the box" and the other puppet said "There is no fish inside the box." In the rare event that an error was made, the subject was shown why it was incorrect. For example, if a child agreed with the puppet who said "There is no fish inside the box" when she had seen the interior of the covered Horse+Fish Box, the formerly-closed (Horse+Fish) box was opened and children were reminded of the two presented statements. Errors, which were very rare here, were pointed out only after both of the first two questions were presented.

Before the third and last contrast of the training session was presented, a child was asked to close her eyes as the Experimenter placed, at random, one of the closed boxes in front of the child. The child was told that to reply next time, the child did not need to open the box. The child then heard one puppet say "There is a horse inside the box," while the other said, "There is no horse inside the box." If a child said something like "I don't know, I have to look," the child was told "We know that this (covered) box can look like this box (the open Horse+Fish Box) or this box (the open Horse-only Box)." Typically, children answered correctly by agreeing with the puppet who said "There is a horse inside the box." If there were errors at this point in the training, the procedure was carried out again. Subjects who were seven years old or older had no difficulty at all with the training. Five-year-olds occassionally required more than one turn with this last training statement (such a subject would indicate that the only way to answer was to look inside the covered box before making a judgement).

Experimental trials concerned larger and differently colored boxes. One box contained a Parrot and a Bear (hereafter referred to as the Parrot+Bear Box) and the other contained just a Parrot (the Parrot-only Box). As in the training session, children were shown a box that was covered (Box C). They were again told that "a friend of mine gave me this box and said 'all I know is that whatever is inside this box looks like this Box (Experimenter pointed to the Parrot+Bear Box) or this Box (Experimenter pointed to the Parrot-only Box).'" However, unlike in the training session, this was the only covered box children encountered and they were told that they would not be able to look inside of it until the "game" was over.

 RESULTS

 Table 2 shows the rate at which subjects responded correctly to each of the six contrasts and indicates which response rates were significantly different from those predicted by chance. To investigate subjects' overall performance with the contrasts, a 4 (Age groups: 5-, 7-, and 9-year-olds and adults) X 6 (Contrasts) ANOVA was carried out with the contrast factor treated as a within-subjects variable. The Age effect was significant, F (3, 83) = 38.90, p < .001. Post-hoc Scheffé tests revealed that five-, seven- and nine-year-olds differed from one another with respect to rates of correct responses and that nine-year-olds were indistinguishable from adults. The effect of Contrasts was not significant and the Age X Contrast interaction was not significant. Similar results were found when a 4 (Age) X 2 (Contrast Types: weaker-but-true vs. equally forceful modals) ANOVA was computed with Contrast Types treated as a within subjects variable and where each contrast type had a maximum score of 3.
 
 

Note. Each of the statements began with the word "There" and ends with "in the box." The first modal statement in each presented pair in the Table is the correct one. * p < .05, ** p < .01, when based on chance predictons.

Seven-year-olds chose correctly at a very high rate overall (83%) and well above levels predicted by chance t(19)= 7.96, p < .01. The only contrast that did not reach levels of significance when compared to chance was the contrast has to be a parrot vs. has to be a bear, and seven-year-olds chose the correct puppet at relatively high rates (70%). It would be a fair assessment to say that seven-year-olds were the first to demonstrate mastery over the logical modal meaning as expressed in this Experiment. However, only the nine-year-olds chose correctly overall at a rate (98%) that resembled adults' rate of success (100%).

DISCUSSION

 In this experiment, we did not find evidence that children, even five-year-olds, rely on a modal-strength continuum when agreeing with any particular puppet. Instead, children considered a statement's truth value regardless of the modal's apparent forcefulness. Five-year-olds endorsed with some regularity one true weaker-sounding statement over a false stronger-sounding statement and with systematicity the true statement in one pair of equally-forceful modal contrasts. Seven-year-olds systematically agreed with the puppet who provided the truthful statement in five of the six contrasts (and approached significance on the sixth). Nine-year-olds and adults consistently preferred to agree with the truthful puppet in all six contrasts. Overall, these findings reveal that the role of relative force becomes muted when a situation requires a logical interpretation of epistemic modals.

Two possibilities might explain the significant findings with the five-year-olds. One is that the presence of negatives may have affected responses. Five-year-olds were more likely to endorse the correct puppet in those contrasts that pitted a correct, affirmative statement against an incorrect, negative statement. Although the probability is small that these two contrasts would have been the only ones to lead to high rates of correct responses among five-year-olds, it would be beneficial to systematically vary negatives as a factor in future research. The other possibility is that necessary conclusions were more salient than possible conclusions. That is, any contrast that concerned the parrot (which was necessarily in the covered box) may be easier to deduce than a statement concerning the bear (which was possibly in the box). This would explain why five-year-olds showed little difficulty in answering correctly when both statements in a contrast concerned a necessary conclusion (i.e., about the parrot) and showed evidence of having at least some difficulty with the others. The remaining five contrasts included at least one statement about a possible conclusion (i.e., about the bear).

If one considers the second possibility, the developmental patterns here correspond well with those found in psychological investigations. Prior work in cognitive development demonstrates that three to five year old children can detect when a scenario prompts a necessary conclusion (e.g., Fabricius, Sophian, & Wellman, 1987). Although prior work also reveals that four-year-olds have the primitive ability to detect when a scenario provides multiple possibilities (Sophian & Somerville, 1988), children are usually much older (about nine years old) before they understand when a particular conclusion is simply possible. That is, when presented with an outcome that could have arrived from two or more possible sources (e.g., imagine being asked to determine from which of two similar boxes an object came from and where the appropriate response is "can't tell"), children tend to adopt one of the potential sources as the true one and answer definitively (Pieraut-Lebonniec, 1980; Byrnes & Overton, 1986; Horobin & Acredolo, 1989). This tendency is referred to as premature closure (Acredolo & Horobin, 1987) and is relevant to the paradigm of Experiment 2 because some of the provided modal statements like There cannot be a bear can lead to "right" responses if children adopt the Parrot-only Box as the only representation of the covered box. To demonstrate a thorough appreciation of possibility, reasoners need conserve all the provided background knowledge and its diverse consequences (which is no small task). In this experiment, the apparent precocity of the seven-year-olds is most likely due to the fact that the modal statements obviate the need to produce responses of the sort "can't tell" and minimize cognitive effort. The fact that children as young as seven years old were able to appreciate possibility notions here lowers previous estimates and confirms speculations made by Braine & Rumain (1983).

 In sum, the results from Experiment 2 reveal that when subjects are required to evaluate modal statements based on evidence, the relative force of modals does not exert its influence. Success depends on the ability to determine which of two modal statements is logically correct in the face of background information. This is precisely what underlies an appreciation of logical modals and what distinguishes it from a pragmatic understanding. Five-year-olds show signs of having a primitive understanding of logical modals and seven-year-olds show that they have a relatively mature ability to understand the logical meaning of modals.

GENERAL DISCUSSION

 Two experiments aimed to investigate the influences of relative force and logical meaning in children's understanding of epistemic modals. In the test of relative force in Experiment 1, five-year-olds' performance generally revealed that they appreciate distinctions in relative force among the terms is, has to, and might. Even when feedback was withheld, children's preference to follow the more certain-sounding puppet was unaffected, thus highlighting that utterances are of primary importance in the hidden-object task and that post-hoc discoveries fail to alter subjects' judgments in subsequent trials. However, there were indications that relative force is not the only factor to consider in epistemic modal development: there were order effects in contrasts containing the indicative is and the is/has to contrast did not reliably prompt subjects to find the hidden object. An appreciation of the logical meaning of epistemic modals, or at least an awareness of what is contextually appropriate for their use, is consistent with these findings. Thus, factors aside from relative force have some, albeit a small, influence in hidden object tasks of this sort.

When we modified the task to investigate children's understanding of logical modals, we found that the influence of relative force was muted. In Experiment 2, three out of six contrasts pitted false, strong-sounding to true, relatively weak-sounding modal statements. Children did not show any systematic tendency to endorse the puppet who stated the stronger-sounding statement in the modified task. In the face of evidence, even five-year-olds demonstrated that they do not consider relative force at the expense of logical considerations. Seven-year-olds demonstrated near adult-like command by consistently endorsing the logically correct of two epistemic modal statements. Nine-year-olds' assessments resembled those of adults. Coates (1988) observed that a linguistically competent five-year-old still does not have an adult's system of modals; a cultivation of the logical component may well be critical to progress with modals. At the very least, it can be argued that logical understanding is a constraint on modal acquisition according to the criteria discussed by Shatz & Wilcox (1991).

The logical analysis of epistemic modal terms promotes a role for inference in the development of word meaning. Jackendoff (1994) considers a word's interaction with inference rules primary in the development of word meaning. Rules of inference in word learning are of central importance in the mental logic approach as well (Braine, 1990; Braine & O'Brien, 1991), which proposes that there is a logic that is universal among people. For example, Braine (1990: p.149) notes that in so far as fundamental inferences are tied to the meanings of sentential connectives like if, or, etc., a theory of the acquisition of inferences is tantamount to a theory of the learning of the meanings of these words. The present investigation potentially expands the scope of mental logic to modals and it directs attention to the interdigitation of logical and pragmatic principles in children's acquisition of word meanings. In a context in which a speaker is one's only source of information, a child focusses mostly on a modal's relative forcefulness for direction (and potential misdirection); when modal statements are recognized as following from evidence, relative force becomes secondary as children view the modal with respect to its logical requirements.

What distinguishes an understanding of has to from might? It is not merely a difference in speaker certainty, but a logical understanding as well. A modal conclusion with has to indicates that a scenario provides a conclusion that necessarily follows from a line of reasoning; might indicates that a conclusion under consideration follows from a line of reasoning as well, but that other inferences are available that provide alternative, or perhaps contradictory, conclusions. Theoretically, it is not obvious how these logic-based meanings are derivable from indications based on relative force and empirically, our findings question such a proposal.

Although signs of an adult-like appreciation of logical modals may not appear until children are seven years old, with the acceptance that some outcomes are only possible, building blocks for a logical appreciation of modals are present earlier. Children as young as five years of age can determine that an epistemic modal is appropriate for modal reasoning scenarios and they are inclined to give correct logical evaluations. Such findings strongly suggest that logical inference is a primary component of modal meaning and, moreover, that logical inference is indispensable for providing a complete account of modal semantic development.

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