Flora Schwartz
email: flora.schwartz@isc.cnrs.fr

Justine Epinat-Duclos

Ira Noveck

Jérôme Prado
email: jprado@isc.cnrs.fr

Dan Sperber

Christian Scheiber

Lewis Bott

Helene Villani

Sandrine

The neural development of pragmatic inference-making in natural discourse

Older interlocutors are more likely than younger ones to make pragmatic inferences, i.e., inferences that go beyond the linguistically encoded meaning of a sentence. Here we ask whether pragmatic development is associated with increased activity in brain structures associated with inference-making or in those associated with Theory-of-Mind. We employed a reading task that presents vignettes in one of two versions, one of which is expected to prompt more pragmatic processing. Both versions present a major premise containing three possibilities (e.g. Xavier is considering Thursday, Friday or Saturday for inviting his girlfriend out). In the Fully-Deductive (control) condition, the major premise is followed by two disjunction-elimination premises through two separate lines (one indicating that Saturday is not convenient and another saying that Thursday is not convenient); this is followed by a valid conclusion (e.g., "I'll reserve Friday"). In the Implicated-Premise condition, the first disjunction-elimination premise is followed by a second similar one that eliminates the same disjunction (e.g. both lines explain why Saturday is not convenient). In this condition, readers may pragmatically enrich the conclusion (i.e. "I'll reserve Friday" pragmatically implicates that Xavier is also eliminating Thursday from consideration). Reading times in Experiment 1 showed that processing the speaker's conclusion in the Implicated-Premise condition becomes increasingly more effort-demanding as readers reach adolescence. Experiment 2 showed that this developmental pattern is related to age-related increases of fMRI activity in fronto-parietal regions typically involved in inference-making processes. We found no evidence indicating age effects related to Theory of Mind areas.

Introduction

Pragmatics is concerned with the way a listener goes beyond what a speaker says in order to understand what the speaker means [START_REF] Grice | Studies in the Way of Words[END_REF]. It covers a wide range of readily perceptible phenomena, such as metaphor (John is a cheetah to describe a fast runner) and irony (that went well to describe a failed meeting) as well as more subtle cases such as commands (consider how Pick up the tall glass can indicate to the listener that there is a smaller glass in the speaker's frame of reference). Common to all these cases is the fact that the linguistically encoded meaning of the utterance serves as a basis for inferring what the speaker intended.

Developmental progressions have been crucial to investigating pragmatics. The most discussed example in the experimental pragmatic literature focuses on underinformative utterances such as Some swans are white, which can be enriched to mean Some but not all swans are white (for reviews, see [START_REF] Noveck | Experimental pragmatics: a Gricean turn in the study of language[END_REF]Papafragou, 2015). Consider the work from [START_REF] Pouscoulous | A developmental investigation of processing costs in implicature production[END_REF] who showed 9-year-old and adult participants toy animals that were placed in and around a set of four boxes; one observable fact was that there was a turtle in each of the boxes and nowhere else. When participants were asked to evaluate the sentence "Some turtles are in the boxes" as true or false, nine-year-olds were significantly more likely than adults to answer true. That is because children appear satisfied with the semantic reading of Some (Some and perhaps all) while adults are more likely to pragmatically enrich the utterance to Some but not all boxes have a turtle (also see [START_REF] Huang | Semantic meaning and pragmatic interpretation in fiveyear olds: Evidence from real time spoken language comprehension[END_REF][START_REF] Katsos | Crosslinguistic patterns in the acquisition of quantifiers[END_REF]. That pragmatic abilities become increasingly evident with age can be extended to a range of phenomena, including irony (Fillipova & Astington, 2010), metaphoric reference [START_REF] Noveck | When children are more logical than adults: Experimental investigations of scalar implicature[END_REF]Almor et al., 2007) and idioms [START_REF] Caillies | Children's understanding of idioms and theory of mind development[END_REF].

Given the plethora of studies that reveal a progressive emergence of pragmatic abilities among children, the question we ask here is a general one: what are the neural structures that subserve this development? We consider two possible neural systems in order to answer this question. One is derived by assuming that developmental changes arise due to generally improving inferential abilities as indicated by neuroimaging studies that point out how lateral frontoparietal regions known to support inference-making in adults [START_REF] Monti | Functional neuroanatomy of deductive inference: A language-independent distributed network[END_REF][START_REF] Van Overwalle | Social cognition and the brain: a meta-analysis[END_REF][START_REF] Prado | The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies[END_REF][START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF][START_REF] Vendetti | Evolutionary and Developmental Changes in the Lateral Frontoparietal Network: A Little Goes a Long Way for Higher-Level Cognition[END_REF]) mature from middle childhood to adolescence. For example, studies on analogical reasoning have demonstrated relatively late age differences in the bilateral rostrolateral prefrontal cortex (RLPFC), dorsolateral prefrontal cortex (DLPFC), and inferior parietal lobule (IPL) [START_REF] Crone | Neurocognitive development of relational reasoning[END_REF][START_REF] Wendelken | Increased selectivity over development in rostrolateral prefrontal cortex[END_REF], Dumontheil et al., 2010), areas that are thought to support relational integration [START_REF] Dumontheil | Development of abstract thinking during childhood and adolescence: The role of rostrolateral prefrontal cortex[END_REF] and working-memory demands [START_REF] Badre | Functional Magnetic Reasonance Imaging evidence for a hierarchical gradient in the Prefrontal cortex[END_REF] of inference-making. Age-related increases of activity between middle childhood and adolescence have also been found in the RLPFC and DLPFC when participants make deductive inferences such as All As are Bs and All Bs are Cs therefore All As are Cs [START_REF] Mathieu | Distributed neural representation of logical arguments in school-aged children[END_REF]. Finally, anatomical studies show structural changes (e.g., an increase in white matter density) in the lateral prefrontal cortex until adolescence (Barnea-Goraly et al., 2005;[START_REF] Westlye | Differentiating maturational and aging-related changes of the cerebral cortex by use of thickness and signal intensity[END_REF]. Overall, neuroimaging studies provide evidence for a relatively late functional and anatomical maturation of the lateral frontoparietal regions subserving inference-making. The maturation of this inference-making network may be a critical factor underlying the development of pragmatic skills in children and adolescents 1 .

Another possibility is that emerging pragmatic abilities are linked to a developing Theory of Mind (ToM) (Epley et al., 2004b;Dumontheil et al., 2010) because a critical 1 Even though we refer here to this set of lateral frontoparietal regions as an "inferencemaking network", it should be emphasized that we do not believe this network is specifically involved in inference-making. Rather, the network is more likely involved in domain-general processes involved in inference-making. feature of understanding a speaker's intended meaning is the attribution of mental states to others. Although ToM-related skills, such as perspective taking (understanding other's objectives and preferences) and the evaluation of false beliefs (i.e. distinguishing between what someone believes and reality), appear to develop relatively early in children [START_REF] Wellman | Meta-analysis of theory-of-mind development: the truth about false belief[END_REF]Baillergeon et al., 2010;[START_REF] Southgate | Action anticipation through attribution of false-belief by 2-year-olds[END_REF], there are also studies suggesting that ToM continues to develop well into adolescence (Dumontheil et al., 2010). For example, Dumontheil et al (2010) showed a late developmental improvement in the ability to take into account a speaker's perspective in an online communication game [START_REF] Keysar | Taking perspective in conversation: the role of mutual knowledge in comprehension[END_REF][START_REF] Keysar | Limits on theory of mind use in adults[END_REF]. This late development is also consistent with two neuroimaging studies indicating that several of the brain regions thought to be involved in ToM are not mature until late childhood [START_REF] Mills | Developmental changes in the structure of the social brain in late childhood and adolescence[END_REF][START_REF] Saxe | Brain regions for perceiving and reasoning about others in school-aged children[END_REF]. For example, [START_REF] Saxe | Brain regions for perceiving and reasoning about others in school-aged children[END_REF] found functional changes between 6 and 11 years of age in the temporo-parietal junction (TPJ), a core region supporting ToM [START_REF] Van Overwalle | Social cognition and the brain: a meta-analysis[END_REF]. Additionally, [START_REF] Mills | Developmental changes in the structure of the social brain in late childhood and adolescence[END_REF] showed an increase in gray matter volume among children between 7 and 10 years of age in the medial prefrontal cortex (mPFC), posterior superior temporal sulcus (pSTS), and TPJ, three core regions of ToM [START_REF] Van Overwalle | Social cognition and the brain: a meta-analysis[END_REF]. As far as pragmatic text comprehension tasks go, it has been demonstrated how brain regions associated with Theory of Mind are central to irony understanding in adults [START_REF] Spotorno | Neural evidence that utterance-processing entails mentalizing: The case of irony[END_REF]; given that the development of irony has been documented, it would make sense to suppose that children's weaknesses with respect to irony are due to a lack of maturity of ToM. It is thus very reasonable to hypothesize that the occurrence of pragmatic competence with age points specifically to maturing ToM regions.

Here we aim to test between these two hypotheses by identifying the brain regions supporting the development of pragmatic inference-making in children and adolescents. We adopted a text-comprehension task that our group has used recently with adults for the neural investigation of pragmatic inference-making [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF]. This paradigm presents a series of stories that include an utterance stated by a story character (1f below) that could be interpreted in one of two ways as a function of a small change in the preceding context. The first sort of interpretation is referred to as Fully-Deductive because the nature of a character's remark is, in effect, a conclusion drawn from two successive disjunction-elimination inferences, as exemplified in lines (1c) through (1e), that reduce three possibilities to one:

(1) (a) Xavier wants to surprise Claire by inviting her to a restaurant.

(b) He hesitates between these three days of the week:

(c) Thursday, Friday or Saturday.

(d) Claire cannot go on Saturday because she has a theatre course.

(e) Further, Thursday would not work because he is having dinner with his parents.

(f) He says: "I'll invite her for Friday."

(g) He hopes she will be available that day.

As this story (translated from French) exemplifies, it begins with an introduction setting up a context (in lines 1a and 1b) before presenting a disjunctive statement in which three possibilities are mentioned (in 1c). Two of these possibilities are then eliminated by the speaker (in 1d and 1e) such that its conclusion (in 1f), which logically follows, serves as a kind of verification.

The other sort of interpretation is referred to as an Implicated-Premise interpretation.

There, the story sets up the context in such a way that the line in (1f) is not conclusive; that is, only one possibility of three is eliminated. To arrive at this sort of interpretation, consider the above story in (1), but replace the word "Thursday" with "Saturday" in line (1e) so that it now reads as:

(1) (e') Further, Saturday would not work because he is having dinner with his parents.

In other words, Implicated-Premise stories provide two justifications for eliminating just one possibility before presenting the story-character's utterance. Now, Xavier's conclusion in (1f)

--that Friday is a good day for the invitation --still makes sense, but can be understood in one of two ways: A participant could process (1f) without a deep reading, i.e. by simply accepting the speaker's utterance without giving further thought to the speaker's reasoning. In this way, the linguistically encoded reading is in effect good enough for processing its meaning. The other way to process (1f) is to note that the conclusion puts the reader in a position to infer that Xavier is eliminating Thursday, or must have a reason to eliminate Thursday, even though he never said so explicitly. This is a pragmatic inference on the part of the reader, whose effort to understand the utterance is part of an attempt to access the speaker's intention.

Note that this is not an obligatory inference on a par with a deductive one. Our prior study [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF] showed that adults take longer to read the critical line (1f) when it is a potential source for an Implicated premise (in the context of a line like [1e']) than they do when it is part of a Fully-Deductive conclusion (in the context of a line like [1e]).

In turning to our current developmental study, the goal is twofold.

Materials

Participants were presented with two sorts of short stories containing a disjunctionelimination argument similar to the scenarios in (1) as described in the Introduction (see Table 1). All stories were composed of 7 sentences each, with a mean length of 376 characters per sentence (standard deviation [sd]=28.5), and had the same structure: Sentence through (e) represented the main premises of the argument. Specifically, sentence (b) always pointed out that there were three possibilities that could account for an event (e.g., going out on one of three days of the week). Sentence (c) enumerated these possibilities (e.g., "Thursday, Friday or Saturday") and sentence (d) ruled out one of these possibilities (e.g.,

"not on Saturday"). The key manipulation was in sentence (e). In half of the stories (i.e.,

Fully-Deductive stories), sentence (e) ruled out a second possibility out of the three (e.g., "not on Thursday"). In the other half of the stories (i.e., Implicated-Premise stories), sentence (e)

gave another reason for eliminating the possibility that had been already ruled out in sentence (d) (i.e., confirming "not on Saturday"). Sentence (f) presented the story character's critical remark (e.g., "it will be on Friday"). Therefore, in Fully-Deductive stories, the utterance necessarily follows from the premises and is confirmatory. In Implicated-Premise stories, participants read the protagonist's conclusion and are in a position to draw a further inference that would justify the conclusion. Sentence (g) was the wrap-up sentence. In general, only one word differed between Fully-Deductive and Implicated-Premise stories (in sentence (e)).

Seventeen different story frameworks were created. Each framework involved a different situation and different characters. Each participant read either the Fully-Deductive or the Implicated-Premise version of a framework.

Twelve stories were randomly chosen for each participant and these were evenly divided between Fully-Deductive and Implicated-Premise stories. Two-thirds of Fully-Deductive and Implicated-Premise stories were followed by a yes/no comprehension question (e.g., "In your opinion, does Xavier plan to invite his girlfriend?", see Table 1). This question was designed to verify that participants were paying attention to the content in the stories.

One-third of Fully-Deductive and Implicated-Premise stories were followed by a question that required participants to judge whether the conclusion made by the character was justified (e.g., "In your opinion, is Xavier justified to think that he should invite Claire on Friday?", see Table 1). The justification question provides an off-line measure to determine whether participants detect the difference between the two types of story.

Experimental procedures

The experiment was programmed with MATLAB while using the Psychophysics Toolbox [START_REF] Brainard | The psychophysics toolbox[END_REF]. Stories were presented line by line on a computer screen.

Participants were instructed to read at their own pace and to press the space bar to read the next sentence. Each story started with a red fixation cross, which appeared on the left side of the screen. The cross remained red for 3 seconds, orange for 1 second and green for 1 second.

Each line of the story was then displayed in a left-justified manner half-way up the screen.

Each sentence remained on the screen until the participant pressed a key, or after 12 seconds if no key was pressed. A black screen was displayed for a half-second between each sentence.

After the disappearance of the last line, a white fixation cross appeared on the left of the screen for 2 seconds. The question then appeared at the center of the screen. Participants had a 12 second window to answer the question. The trial ended with the participant's response or after the allotted time if no response was provided. Each story was directly followed by a period of visual fixation (ranging from 2 to 4 seconds). All stories were presented in a randomized order.

Analyses

Statistical analyses were conducted using the lme4 package implemented in R (Bates, Maechler & Bolker, 2012). Log-transformed reading times were analyzed using a linear mixed model, while responses to comprehension and justification questions were analyzed using logistic mixed models. All full models included in their fixed effects an intercept, a main effect of Story version (i.e., Fully-Deductive versus Implicated-Premise), a main effect of Age, and an interaction between Story version and Age. The categorical factor Story version was deviation coded as -0.5 for Fully-Deductive stories and 0.5 for Implicated-Premise stories. Age was entered as a continuous variable by coding third-graders, fifthgraders, seventh-graders, ninth-graders and adults as 8.5, 10.5, 12.5, 14.5 and 25 years (respectively)2 . The continuous variable Age was then mean-centered. All models also had maximal random effects structure, with by-subject random intercept and slope for Story version, as well as by-story random intercepts and slopes for Story version, Age, and their interaction. Main effects and interactions were tested using likelihood ratio tests between mixed effect models differing only in the presence or absence of fixed effects of interest. The dataset and R scripts are available at Mendeley Data: http://dx.doi.org/10.17632/fd7t5h3grb.2.

Results and discussion

The linear mixed model with reading time of the conclusion (i.e., sentence (f)) as dependent variable revealed a significant main effect of Age (β=-0.02, SE=0.004, The adults' data here are consistent with those from our previous study [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], where we found longer reading times for the conclusions in Implicated-Premise stories as well as lower acceptance rates for the justification questions when compared to the Fully-Deductive stories. Here we extend these results by reporting a developmental divergence in a)

χ
conclusion-reading times that become significant among adults and in; b) accepting the justification question that begins to emerge at around 9 th grade. Importantly, this developmental trend emerged without negatively affecting the participants' overall comprehension of stories (which increased with age).

We can think of at least 3 possible explanations for this developmental trend, which we now consider one at a time. First, the effect might result from the detection of an infelicity earlier in the story. That is, older participants (as compared to younger ones) may find the 5 th sentence (sentence (e)) of Implicated-Premise stories infelicitous, because it might repeat some information that was already mentioned in the 4 th sentence. This might have downstream consequences on reading times of the conclusion and explain why there is increasing divergence between Implicated-Premise conclusion-reading times and Fully-Deductive conclusion reading-times with age. It is important to note that all of our stories were written with the utmost care so as to minimize such infelicity in sentence (e). That is, the information that was repeated in sentence (e) was always accompanied by further justification. For example, consider these consecutive statements (lines (c) through (e), translated from French) from our "what night to go out story", "what form of transportation shall he use story" and the "what language are they speaking story":

(2) (c) Thursday, Friday or Saturday.

(d) Claire cannot (go out) on Saturday because she has a theatre course.

(e) Besides, Saturday is not convenient because she is going out with her parents.

(3) (c) By train, by motorcycle, or by car.

(d) His motorcycle isn't working because it broke down yesterday.

(e) Besides, he never uses his motorcycle to go on vacation. (e) She adds after: "I am sure it is not Portuguese."

As one can see, each story presents participants with two reasons to eliminate one option. This arguably occurs in everyday life and is not infelicitous per se. Nonetheless, we acknowledge that this repetition might contribute to the difference observed between Implicated-Premise and Fully-Deductive stories.

A second explanation for the observed effect is that, in a way similar to cloze probability effects [START_REF] Kutas | Brain potentials during reading reflect word expectancy and semantic associtation[END_REF][START_REF] Coulson | Conceptual integration and metaphor: an event-related potential study[END_REF], premises in Fully-Deductive stories may allow sophisticated readers to know which alternative is going to be mentioned in the conclusion. In contrast, premises in Implicated-Premise stories may not allow such a prediction. In other words, the most sophisticated readers may be surprised when reading the conclusion in the Implicated-premise condition because they are not expecting it.

We acknowledge that surprise may come into play with age and that it becomes part of the process in arriving at an alternative reading. Note that this explanation would put the effect squarely in the realm of pragmatics and not as an example of sentence-level processing. To put it in Gricean terms (1989), one could argue that our more sophisticated participants recognize that a maxim (of Relevance) has been violated and that this generates further implicatures in order to maintain the Cooperative Principle. Regardless, a participant would be put in the position to consider what happened to the remaining possibility. The question is whether readers are more likely to pursue that consideration with age.

A third explanation, which we proposed in our previous adult study [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], is that conclusions in Implicated-Premise stories are more likely than those in the Fully-Deductive condition to encourage further pragmatic inference-making and particularly among more sophisticated participants. That is, sophisticated readers may make an effort to understand the utterance as part of an attempt to access the speaker's intention. The present experiment is therefore consistent with the idea that pragmatic inference-making emerges over the course of development [START_REF] Huang | Semantic meaning and pragmatic interpretation in fiveyear olds: Evidence from real time spoken language comprehension[END_REF][START_REF] Katsos | Crosslinguistic patterns in the acquisition of quantifiers[END_REF][START_REF] Pouscoulous | A developmental investigation of processing costs in implicature production[END_REF]. If correct, this explanation would raise an intriguing question: which abilities would be responsible for the emergence of such pragmatic inference-making in this task? On the one hand, it may be attributed to the development of inference-making mechanisms over the course of childhood and adolescence. On the other hand, increasingly sophisticated pragmatic abilities may depend upon a more acute ability to attribute mental states to others (i.e., ToM). The goal of Experiment 2 was to test between these hypotheses using fMRI.

Experiment 2

The goal of Experiment 2 was to determine the structural source that accounts for the emerging developmental effect. We employed the paradigm from Experiment 1 as we used fMRI to measure developmental changes among children between the ages of 8 and 15. We also relied on the extant literature to draw conclusions about the role that different brain networks (i.e., inference-making versus ToM) may play in this reading task. 6) had no diagnosis of dyslexia and a reading score higher than a standardized score of 70 on the Alouette test [START_REF] Lefavrais | Test de l'Alouette[END_REF]). Overall, ten participants were excluded from further analysis for one of the following reasons: performance below or close to 50% on the comprehension questions (n=3), excessive head motion during the imaging session (n=2), poor brain coverage (n=1), technical issues during image acquisition (n=3), or an excessive delay between the imaging session and the completion of the standardized tests (n=1). Thus, the analyses included 18 subjects (9 females), aged from 8.35 to 14.71 (mean=11.61, sd=1.89).

Material and Methods

Participants

Parents gave their written informed consent and children gave their assent to participate in the experiment. Families were paid 80 euros for their participation. The experiment was approved by the local ethics committee (CPP Lyon Sud-Est II).

Materials

Fully-Deductive and Implicated-Premise stories were similar to those used in Experiment 1 (see Table 1). However, to maximize signal-to-noise ratio for the fMRI data, 6 additional stories were presented to participants for each story version. That is, there were 24 stories with a disjunctive argument in this experiment (12 Fully-Deductive and 12 Implicated-Premise stories). Following [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], 12 filler stories were also included to help disguise the goal of the experiment in the scanner (see Table 1). Filler stories did not contain disjunctive arguments.

Experimental procedures

The task and stimulus timing were identical to those in Experiment 1. However, in addition to being read on the screen, each line was spoken over headphones too. Periods of visual fixation between stories constituted the baseline. The fMRI session was split into 6 runs that contained 6 stories each (2 Fully-Deductive stories, 2 Implicated-Premise stories, and 2 filler stories). Stories were presented in a pseudo-randomized order, so that two stories of the same type were not following each other within a run. Behavioral responses during scanning were recorded using MR-compatible keypads placed below each hand. Stimuli were generated using Presentation software (Neurobehavioral Systems, Albany, CA) and displayed on a computer screen that was viewed by the participants through a mirror attached to the head coil.

Several days before the fMRI session, participants were invited to the lab to complete the psychometric tests (i.e., IQ, AQ and Alouette reading test) and to practice the task in a mock fMRI scanner. During that practice session, children were presented with 12 filler stories (whose content differed from the filler stories used in the main experiment).

Imaging acquisition

Functional and anatomical images were acquired with a Philips 3T Achieva scanner (Philips Medical systems, Best, Netherlands). A high-resolution anatomical scan was collected for each participant (Field of view=240x240 mm, 512x512 matrix, TR=1278 ms, TE=3.047 ms, flip angle=8°, slice thickness=0.9 mm, number of slices=188). Functional sequences were collected with a gradient-echo, echo-planar sequence (TR=2200 ms, TE=30 ms, flip angle=90°). Twenty-six axial slices were acquired per volume (slice thickness=3.5 mm, Field of view=220 mm, 128x128 matrix).

fMRI preprocessing

Images were analyzed with SPM8 (Statistical Parametric Map 8, Welcome Department of Cognitive Neurology, London, UK). The first 6 volumes of each run were not acquired to allow for T1 equilibration effects. Functional images were corrected for slice acquisition delays and realigned to the first image of the first run to correct for head movements. Volumes with excessive head motion were further identified using the ArtRepair software [START_REF] Mazaika | Methods and Software for fMRI Analysis of Clinical Subjects[END_REF]. Specifically, following the criteria used in our previous studies [START_REF] Demir | The differential role of verbal and spatial working memory in the neural basis of arithmetic[END_REF][START_REF] Kissine | Pragmatics as metacognitive control[END_REF]2016;[START_REF] Mathieu | Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children[END_REF], volumes showing rapid scan-toscan movement greater than 1.5 mm were substituted by the interpolation of the 2 nearest non-repaired volumes. Runs with more than 10% of repaired volumes were excluded from the analysis (based on this cut-off, one run was discarded for 4 participants and 2 runs were discarded for 2 participants). Realigned images were spatially smoothed with a Gaussian filter prior application of the ArtRepair algorithms. Because voxels were anisotropic, this filter was also anisotropic (4 × 4 × 8 mm full-width at half maximum). Finally, in line with our previous studies on children within the same age range [START_REF] Prado | Developmental dissociation in the neural responses to simple multiplication and subtraction problems[END_REF][START_REF] Schwartz | The neural development of conditional reasoning in children: Different mechanisms for assessing the logical validity and likelihood of conclusions[END_REF], all individual brains were normalized into the standard adult MNI space.

Statistical analyses of fMRI data were performed according to the GLM. Following [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], brain activity elicited by the conclusion of each story was modeled by a block encompassing the last two sentences (i.e., sentences (f) and (g)). The onset of this block was time-locked to the beginning of sentence (f) and the offset was time-locked to the beginning of the question. Sentences (a) to (e) were modeled as events of no interest with an onset time-locked to the beginning of sentence (a) and an offset time-locked to the beginning of sentence (f). The question was modeled as an event of no interest. For each subject and for each run, this model was applied to the three types of stories (Fully-Deductive, Implicated-Premise and filler stories). Time series were high-pass filtered (1/128 Hertz) and serial correlations were corrected for first-order (AR1) autocorrelations.

fMRI analyses

Following [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], fMRI data were analyzed using a Region of Interest (ROI) approach. Specifically, we aimed to measure activity in brain networks involved in inference-making and ToM. Several studies have identified the RLPFC, DLPFC and IPL as critical regions for inference-making in children and adults [START_REF] Crone | Neurocognitive development of relational reasoning[END_REF][START_REF] Wendelken | Increased selectivity over development in rostrolateral prefrontal cortex[END_REF][START_REF] Mathieu | Distributed neural representation of logical arguments in school-aged children[END_REF][START_REF] Vendetti | Evolutionary and Developmental Changes in the Lateral Frontoparietal Network: A Little Goes a Long Way for Higher-Level Cognition[END_REF]. Therefore, we defined bilateral ROIs in each of these regions based on coordinates from our previous study on adult participants that employed the same task [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF]. To define ROIs involved in ToM, we turned to a meta-analysis of neuroimaging studies on ToM (Van Owervalle, 2009). ToM ROIs were located in the bilateral TPJ, the mPFC and the PC (Table 2). In line with [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF], all ROIs were 6-mm radius spheres and were defined using the SPM toolbox Marsbar. The fMRI signal (beta weight) was averaged for each subject and story version (Fully-Deductive and Implicated-Premise) across all voxels within a given ROI. Beta weights from the bilateral RLPFC, bilateral DLPFC and bilateral IPL were then averaged to reflect activity in the inference-making network (see Fig. 2). Similarly, beta weights from the bilateral TPJ, mPFC and PC were averaged to reflect activity in the ToM network.

It is important to acknowledge that the sample size in Experiment 2 (n=18) was smaller than in Experiment 1 (n=132). Because there is no previous fMRI study on the development of pragmatic abilities in children, effect size estimates were not available to inform sample size. This raises the possibility that Experiment 2 may be underpowered and that the chance of discovering true effects is relatively low [START_REF] Button | Power failure: why small sample size undermines the reliability of neuroscience[END_REF]. Therefore, rather than using frequentist statistics as in Experiment 1, we turned to Bayesian analyses to analyze the experiment and assess its sensitivity [START_REF] Morey | The philosophy of Bayes factors and the quantification of statistical evidence[END_REF][START_REF] Lee | Bayesian Cognitive Modeling: A Practical Course[END_REF]. Specifically, we applied the Sequential Bayes Factors (SBF) procedure to estimate the strength of evidence for age-related changes of activity (H1) versus no age-related changes of activity (H0) as a function of increased sample size, both in the inference-making and the ToM network [START_REF] Rouder | Optional stopping: No problem for Bayesians[END_REF][START_REF] Schönbrodt | Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences[END_REF]. In the SBF procedure, a Bayes factor (i.e., BF10) is repeatedly calculated as sample size increases, until there is enough evidence for either H1 or H0. Because BF10 will always converge either towards 0 (if H0 is true) or towards infinity (if H1 is true), data collection may be stopped when enough evidence is gathered. As suggested by [START_REF] Jeffreys | The Theory of Probability, 1st/3rd Edn[END_REF], a BF10 > 3 indicates "substantial evidence" for H1 versus H0 (i.e., "substantial" indicating evidence starting to be worth taking note of; [START_REF] Lee | Bayesian Cognitive Modeling: A Practical Course[END_REF]. Conversely, a BF10< 1/3 indicates substantial evidence for H0 versus H1. Therefore, 3< BF10< 1/3 indicates data sensitivity for distinguishing between H1 and H0 and has been used as a stopping rule for data collection in previous studies (e.g., [START_REF] Martin | Perceiving time differences when you should not: Applying the El Greco fallacy to hypnotic time distortions[END_REF]. All analyses were performed with JASP (https://jasp-stats.org). Beta maps for all participants and conditions are available at NeuroVault, along with ROI masks:

Results and discussion fMRI data

We first focused on conclusions of Implicated-Premise stories and used Bayesian

Pearson correlations to estimate the strength of evidence for age-related change (H1) versus no age-related change (H0) of activity in those stories. In the inference-making network, there was substantial evidence for H1 versus H0 (BF10 = 5.40), with activity being positively correlated with age (r = 0.58) (see Fig. 3A,left). The SBF procedure indicated that substantial level of evidence was obtained with about 12 participants (see Fig. 3A,right). In the ToM network, however, there was substantial evidence for H0 versus H1 (r = -0.10, BF10 = 0.31) (see Fig. 3B,left). This level of evidence was obtained with about 13 participants (see Fig. 3B, right). Therefore, there was evidence for a positive relationship between age and activity associated with conclusions of Implicated-Premise stories in the inference-making network, but not in the ToM network.

and age in the inference-making and in the ToM network (correlation between age and difference in activity between inference-making and ToM network for Fully-Deductive conclusions: r = 0.27, BF10 = 0.50) (see Fig 5). Evidence for main-effects and other lowerorder interactions is shown on Table 3. For the sake of completeness, frequentist analyses are described the Supporting information.

Behavioral data

Even though this was not the main goal of Experiment 2, we also analyzed behavioral responses in the scanner to evaluate whether patterns were similar to those obtained in Experiment 1. First, log-transformed reading times of the conclusion (i.e., sentence (f)) were analyzed in a Bayesian ANOVA with default prior scales. The ANOVA included the withinsubject factor Story version (Fully-Deductive versus Implicated-Premise) and the betweensubject factor Age. BMA indicated anecdotal evidence for main effects of Story version (BF10 = 2.31) and Age (BF10 = 1.31). There was also anecdotal evidence for the Story version×Age interaction (BF10 = 1.11). That is, even though a visual examination of conclusion reading times as a function of age and story version suggests an age-related increase in the cost of reading conclusions of Implicated-Premise stories when compared to Fully-Deductive ones (see Fig. 6A), there was only marginal evidence for this pattern with the sample size of Experiment 2. Consistent with an increasing body of literature, this might suggest that neural measures can be more sensitive than behavioral measures in tracking a developmental phenomenon [START_REF] Gabrieli | Prediction as a humanitarian and pragmatic contribution from human cognitive neuroscience[END_REF]. Frequentist statistics for reading times of conclusions in Experiment 2 are described in the Supporting information.

Second, responses to justification questions were analyzed using a similar Bayesian ANOVA with default prior scales. BMA indicated extreme evidence for a main effect of condition (BF10> 100). That is, participants were much less likely to accept conclusions in Implicit-Premise stories than in Fully-Deductive stories (24% versus 81%). There was anecdotal evidence for a main effect of Age (BF10 = 0.65) and for a Story version × Age interaction (BF10 = 2.06). Unlike in Experiment 1, a visual examination of responses to justification questions as a function of age and story version indicates no age-related decrease in Implicated-Premise stories (see Fig. 6B). That is, unlike in Experiment 1, most young participants responded in an adult-like way to the justification questions of the two main kinds of stories. We can see three explanations for this result. One is that young children, who choose to devote several hours of their time to standardized tests and fMRI scanning, may be more motivated than children carrying out a reading task in school. As a result, they may pay more attention to the difference between the two types of stories. Another possible explanation is that the presence of filler stories in the fMRI experiment (as well as the greater number of trials) allows children to better appreciate the difference between the two main conditions. A last explanation is that Experiment 2 presented the lines of text both visually and aurally. In any case, an examination of developmental changes in reading times for Implicated-Premise conclusions (as compared to Fully-Deductive ones) points to a pattern that is largely similar to that observed in Experiment 1. So, while future work could address children's superior performance with the off-line justification questions here, indications are that our paradigm is indeed capturing pragmatic inference-making development in the scanner.

General Discussion

In Experiment 1, we found that the reading time of conclusions in the Implicated-Premise stories (as compared to Fully-Deductive stories) significantly increased with age.

Given that pragmatic abilities are well known to develop from childhood to adolescence (e.g. [START_REF] Huang | Semantic meaning and pragmatic interpretation in fiveyear olds: Evidence from real time spoken language comprehension[END_REF][START_REF] Katsos | Crosslinguistic patterns in the acquisition of quantifiers[END_REF][START_REF] Pouscoulous | A developmental investigation of processing costs in implicature production[END_REF], this effect may be due to the fact that a conclusion in the Implicated-Premise condition can be considered as a source for an enriching pragmatic inference. In Experiment 2, we used fMRI to investigate the neural bases of this developmental trend in children from 8 to 15. We began with two competing hypotheses. One was that the emergence of pragmatic inference-making would be linked to areas known for other sorts of inference-making; the other was that the emergence of pragmatic inference-making would be linked to the development of ToM structures. We found evidence for age-related increases of activity in fronto-parietal regions associated with inference-making, but not in regions associated with ToM.

Pragmatic processing of conclusions in Implicated-Premise stories increases with age

At the behavioral level (Experiment 1), our results indicate that the reading time of conclusions in Implicated-Premise stories --as compared to Fully-Deductive stories -becomes increasingly distinctive between middle childhood and adulthood. This can be seen in two ways. First, our oldest participants took significantly longer to read the conclusions in Implicated-Premise stories as opposed to the conclusions in Fully-Deductive ones. Second, the acceptance rates of justification questions (asking whether the protagonist was justified to draw the conclusion) dropped progressively with age and significantly so for the Implicated-Premise stories when compared to the Fully-Deductive ones. Interestingly, Experiment 1's younger participants' rates of assenting to the justification questions are comparable across the Fully-Deductive and Implicated-Premise stories. The results among the older participants are consistent with our previous adult study [START_REF] Prado | Neural interaction between logical reasoning and pragmatic processing in narrative discourse[END_REF]. Overall, indications are that, with age, reading conclusions in the Implicated-Premise condition requires extra-processing as compared to conclusions in the Fully-Deductive condition.

Increased pragmatic processing of conclusions in Implicated-Premise stories is associated with increased activity in the inference-making network

We now turn to our main question (what develops with the more demanding pragmatic task?) by considering participants' neural activity associated with processing conclusions in Implicated-Premise and Fully-Deductive stories (Experiment 2). Using Bayesian analyses, we found substantial evidence for a lack of age-related increase of activity in the ToM network, both for conclusions of Implicated-Premise and Fully-Deductive stories. That is, changes of activity in the ToM network are unlikely to account for the developmental trend observed in Experiment 1. In the inference-making network, however, we found evidence for age-related increases of activity that were specific to Implicated-Premise conclusions and to that network.

That is, these changes were (i) not observed for Fully-Deductive conclusions and (ii) larger in the inference-making than in the ToM network. The inference-making network, which includes the RLPFC, DLPFC and IPL, has been consistently identified in various studies of conditional reasoning [START_REF] Monti | Functional neuroanatomy of deductive inference: A language-independent distributed network[END_REF][START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF], disjunctive reasoning [START_REF] Reverberi | Neural basis of generation of conclusion in elementary deduction[END_REF], categorical reasoning [START_REF] Goel | Functional neuroanatomy of three-term relational reasoning[END_REF][START_REF] Prado | Fractionating the neural substrates of transitive reasoning: Task-dependent contributions of spatial and verbal representations[END_REF], transitive reasoning [START_REF] Fangmeier | FMRI evidence for a threestage model of deductive reasoning[END_REF][START_REF] Prado | Spatial associations in relational reasoning: evidencefor a SNARC-like effect[END_REF]2013), matrix reasoning [START_REF] Crone | Neurocognitive development of relational reasoning[END_REF] and analogical reasoning [START_REF] Wendelken | Brain is to thought as stomach is to?? '': investigating the role of rostrolateral prefrontal cortex in relational reasoning[END_REF]. It has been argued that the different regions composing this system may be involved in different aspects of inference-making. For example, whereas the IPL and the DLPFC might be involved in the representation and maintenance of information (e.g., premises) in working memory [START_REF] Badre | Functional Magnetic Reasonance Imaging evidence for a hierarchical gradient in the Prefrontal cortex[END_REF], the RLPFC might support relational integration and play a critical role in integrating premises of arguments in order to produce or evaluate conclusions [START_REF] Bunge | Left, but not right, rostrolateral prefrontal cortex meets a stringent test of the relational integration hypothesis[END_REF][START_REF] Prado | Fractionating the neural substrates of transitive reasoning: Task-dependent contributions of spatial and verbal representations[END_REF][START_REF] Vendetti | Evolutionary and Developmental Changes in the Lateral Frontoparietal Network: A Little Goes a Long Way for Higher-Level Cognition[END_REF]. Overall, the hypothesized developmental emergence of pragmatic inference-making in our task is more likely associated with the maturation of the inference-making network than with greater engagement of the ToM network.

Relevance of our findings to the literature on the neural bases of pragmatic processing

We believe that the current findings speak to recent neuroimaging findings on scalar inferences (which, as pointed out earlier, concerns the way an underinformative utterance such as Some x are y can be enriched to mean Some but not all x are y), arguably the most investigated pragmatic inference in the cognitive sciences. A recent line of neuroimaging work (Shetreet et al. 2014a(Shetreet et al. , 2014b;;[START_REF] Shetreet | Linguistic inability or poor performance: dissociating scalar implicature generation and mismatch in the developing brain[END_REF], which includes a developmental study, presents data supporting the claim that the main site responsible for scalar inference-making ought to be found in language areas (viz. left Inferior Frontal Gyrus); this claim stems from a theoretical approach that treats scalar inferences as linguistic in nature [START_REF] Chierchia | Scalar implicatures, polarity phenomena, and the syntax/pragmatics interface[END_REF]). Yet, this region is not part of the inference-making network in which we found agerelated increases of activity in our task. Given the current state of the literature on inferencemaking (which covers logical, linguistic, and pragmatic inference), we briefly consider two reasons to question the role of linguistic mechanisms from the left Inferior Frontal Gyrus in pragmatic inference-making. First, the part of the left IFG that was found activated in Shetreet et al. in 2014 (i.e., Brodmann Area [BA] 47) does not subserve linguistic functioning exclusively. For example, [START_REF] Monti | The boundaries of language and thought in deductive inference[END_REF] showed -through the juxtaposition of two very similar tasks that aimed to determine the neural underpinnings of logical inference-making and of linguistic inference-making -that BA47 is implicated in both linguistic inferencing and logical inferencing. This suggests that activity in BA47 does not necessarily point to linguistic computations only. Second, it is interesting to note that Shetreet et al.'s most discerning isolating case (one which compares an underinformative Some statement to their task's two other Some statements) points to BA10, i.e., a region of the RLPFC that is part of the inference-making network in the present task. Thus, a stronger claim for the literature, which encompasses Shetreet et al.'s data, is arguably that regions of the inference-making network as defined here -including the RLPFC -plays a key role in pragmatic inferencemaking.

Limitations

We consider two potential limitations to our work. First, we did not find any evidence for a developmental increase of activity associated with Implicated-Premise stories in the ToM network. Based on that observation and on evidence that activity increased in the inference-making network, we concluded that the development of pragmatic inferencemaking in our task was more likely due to the maturation of the inference-making than the ToM network. However, it is important to note that all children in the present study were older than 8. Thus, it remains possible that developmental changes of activity in ToM regions Second, performing cross-sectional fMRI experiments is challenging and the final sample size of Experiment 2 (n=18) is limited, especially when compared to that of Experiment 1 (n=132). It is therefore possible that Experiment 2 is not sensitive enough to detect true effects. To assess the sensitivity of our fMRI analyses, Experiment 2 was analyzed using Bayesian rather than frequentist statistics [START_REF] Morey | The philosophy of Bayes factors and the quantification of statistical evidence[END_REF][START_REF] Lee | Bayesian Cognitive Modeling: A Practical Course[END_REF]. That is, we reported the strength of evidence for H1 (there is an age-related change of activity) versus H0 (there is no age-related change of activity) in all analyses, thereby allowing readers to quantify evidence for the effects observed. We also used the Sequential Bayes Factors (SBF) procedure to indicate the number of participants required to reach substantial evidence for H1 versus H0 (and vice versa) [START_REF] Rouder | Optional stopping: No problem for Bayesians[END_REF][START_REF] Schönbrodt | Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences[END_REF]. Although we found substantial evidence for most of the critical effects with our sample size), we acknowledge that this sample size remains small. Thus, these fMRI results should be seen as providing the groundwork for future studies that might investigate the development of pragmatic inference-making in fMRI studies with larger sample sizes.

Conclusion

In sum, we investigated the neural development of pragmatic inference-making in natural discourse. While using ecologically valid texts that reflect natural discourse, our behavioral study is in keeping with the idea that pragmatic inferencing may increase with age through adolescence. At the neural level, we did not find evidence for age-related changes of activity in the ToM network. Instead, we found evidence indicating that activity in the inference-making network significantly increased from childhood through adolescence. Thus, the hypothesized development of pragmatic inference-making in our task is more likely supported by a functional maturation of inference-making brain structures rather than a maturation of ToM areas. Table 1. Two examples of disjunctive stories and a filler story used in the experiments (translated from French).

Notes. Filler stories were presented only in Experiment 2 and were always followed by a comprehension question. Otherwise, two thirds of the Fully-Deductive and Implicated-Premise stories were followed by a comprehension question and one third by a justification question (see text).

Disjunctive story 1 a. Xavier wants to surprise Claire by inviting her to a restaurant.

b. He hesitates between these three days of the week: c. Thursday, Friday or Saturday.

d. Claire cannot go on Saturday because she has a theatre course. Fully-Deductive cond: e. Moreover, Thursday would not work because he is having dinner with his parents. Implicated-Premise cond: e'. Moreover, Saturday would not work because he is having dinner with his parents. f. He says: "I'll invite her for Friday."

g. He hopes she will be available that day. Comprehension question:

In your opinion, does Xavier plan to invite his girlfriend? Justification question:

In your opinion, is Xavier justified to think that he should invite Claire on Friday?

Disjunctive story 2 a. Michael wants to start playing a musical instrument.

b. He hesitates between these three instruments:

c. The drums, the piano and the guitar.

d. His dad does not want him to play (take classes in) drums because it is too noisy. Fully-Deductive cond: e. Further, he cannot play (take classes in) piano because it is way too expensive. Implicated-Premise cond: e'. Further, he cannot play (take classes in) drums because it is way too expensive. f. He says: "I will start taking (classes on) the guitar." g. He hopes he will improve quickly.

Comprehension question:

In your opinion, does Michael want to play a music instrument? Justification question:

In your opinion, is Michael justified to think that he has to start playing the guitar?

Filler story a. Jennifer just bought a new camera.

b. She wants to unpack it immediately.

c. It would be easier with a sharp knife.

d. She goes to the kitchen to pick up a sharp knife.

e. After a few minutes, she retrieves the camera from the package.

f. She decides to read the instructions before using it.

g. She is very excited to start taking pictures.

Comprehension question:

In your opinion, is Jennifer happy with what she bought?

  (a) introduced the context, sentence (b) introduced the disjunctive argument, and sentences (c)

  Italian, Portuguese, or Spanish. (d) It's not Portuguese because my Mom speaks Portuguese, Camille declares.

  Twenty-eight typically developing children participated in this fMRI experiment. All children included in the fMRI study (1) were native French speakers, (2) had no MRI counterindications, (3) had no history of neurological and psychiatric disorder, (4) had no diagnosis of mental retardation or high intellectual potential and a full-scale IQ between 70 and 130 as measured by the NEMI-2 (Nouvelle Echelle Metrique de l'Intelligence)(Cognet, 2006), (5) had no diagnosis of autism and a score lower than 32 on the Autism Quotient test[START_REF] Baron-Cohen | The autismspectrum quotient (AQ): Evidence from asperger syndrome/high-functioning autism, males and females, scientists and mathematicians[END_REF], and (

  may underlie the development of pragmatic processing in younger children. In other words, although the present study suggests that the development of ToM mechanisms is unlikely to account for the development of pragmatic inference-making from 8 to 14, future research might investigate to what extent it might for younger children.

Figure 1

 1 Figure 1

Figure 2

 2 Figure2

Figure 3

 3 Figure 3

Figure 4

 4 Figure 4

Figure 5

 5 Figure5

  https://neurovault.org/collections/3040/. Associated behavioral data are available at Mendeley Data: http://dx.doi.org/10.17632/fd7t5h3grb.2. The Matlab scripts used to analyze fMRI data are available upon request.

Table 2 . MNI Coordinates of ROIs from the inference-making and ToM networks

 2 . = left; R. = right; ∼BA = approximate Brodmann's area.

	Anatomical Location	∼BA		MNI Coordinates
	Inference-making network
	L. RLPFC	10	-36	56	7
	L. DLPFC	9	-48	23	37
	L. IPL	40	-42	-58	52
	R. RLPFC	10	33	59	4
	R. DLPFC	9	42	17	46
	R. IPL	40	48	-55	46
	ToM network
	L. TPJ	40	-50	-55	25
	R. TPJ	40	50	-55	25
	mPFC	9	0	55	6
	PC	7	-1	-56	33

L

Table 3 . Analysis of effects for the Bayesian ANOVA with the effects Story version (Implicated-Premise versus Fully-Deductive), Network (Inference-making versus ToM) and Age.

 3

	Effects	P(incl)	P(incl|data)	BF Inclusion
	Story version	0.737	1.000	2.957e +10
	Network	0.737	0.983	20.552
	Age	0.737	0.955	7.553
	Story version × Network	0.316	0.948	39.833
	Story version × Age	0.316	0.639	3.829
	Network × Age	0.316	0.914	22.923
	Story version × Network × Age	0.053	0.218	5.005

Note that for illustration purpose descriptive analyses are presented by age-group in all figures.

For 9 th graders, the random slope structure was simplified by removing the by-story random slope for Story version because the full model did not converge.

The authors declare no competing financial interests. This research was supported by grants from the CNRS and the Ministère de la Recherche to IN, as well as from the Fondation de France (2012-00033701) and the Agence Nationale de la Recherche (ANR-14-CE30-0002) to JP. We thank the Hospices Civils de Lyon for sponsoring the research, as well as Romain Mathieu and the MRI technicians (Sylvaine Couderc and Philippe Combet) at the Lyon neurological hospital for their assistance in collecting the fMRI data. Finally,

To evaluate how specific these relationships were to Implicated-Premise stories, we then used Bayesian Pearson correlations to estimate the strength of evidence for H1 versus H0 in Fully-Deductive stories. For conclusions of Fully-Deductive stories, we found anecdotal evidence for H0 versus H1 in the inference-making network (r = 0.29, BF10 = 0.55) (see Fig. 4A), and substantial evidence for H0 versus H1 in the ToM network (r = 0.03, BF10 = 0.29) (see Fig. 4B,left). The SBF procedure indicated that substantial evidence for H0 versus H1 was obtained with about 15 participants in the ToM network (see Fig. 4B,right). Therefore, in the inference-making and ToM networks, there was anecdotal to substantial evidence for a lack of relationship between age and activity associated with conclusions of Fully-Deductive stories.

Change of brain activity with age was then directly compared between story versions and networks using a Bayesian ANOVA with default prior scales. The ANOVA included the within-subject factors Story version (Fully-Deductive versus Implicated-Premise) and Network (inference-making versus ToM), as well as the between-subject factor Age. In a Bayesian ANOVA, different models that include versus do not include each factor and interaction are created 4 . A BF10 is then calculated for each model (i.e., reflecting the evidence in favor of that model versus the null model) and Bayesian Model Averaging (BMA) is used to estimate evidence in favor of main effects and interactions [START_REF] Hoeting | Bayesian model averaging: A tutorial[END_REF]. Critically, this analysis revealed substantial evidence for the Story version × Network × Age interaction (BF10 = 5). That is, there was substantial evidence for a stronger relationship between activity for Implicated-Premise conclusions and age in the inference-making than in the ToM network (correlation between age and difference in activity between inference-making and ToM network for Implicated-Premise conclusions: r = 0.59, BF10 = 6.20). In contrast, there was anecdotal evidence for an equal relationship between activity for Fully-Deductive conclusions 4 Interactions were only included when the component main effects were present [START_REF] Rouder | Bayesian analysis of factorial designs[END_REF].

Correlations between age and difference in activity between inference-making and ToM networks for Implicated-Premise and Fully-Deductive conclusions.