Intentional inference: perceptual information and top-down prior knowledge

Explaining or predicting the behaviour of our conspecifics requires the ability to properly appreciate the causes that motivate it. As these causes are hidden – intentions, like beliefs or desires, are unobservable states –, it has long been a matter of speculation how one may infer them from patterns of visible behaviour alone. Indeed, visual information conveyed by the movement kinematics is often noisy, ambiguous or incomplete. As a result, visual information generally under-constraints the space of candidate causes (i.e. the many competing intentions) that are logically consistent with what is observed [1]–[3]. One way to solve this problem is to assume that this space of possible intentions is further constrained by the observer's prior expectations. These expectations are derived from prior knowledge that may originate from the past experience of the viewer (through expertise: [4], [5]; or learning of statistical regularities: [6]), from her intuitive theories [7], [8], or reputational knowledge [9], [10], as well as from contextual information surrounding the action scene [5], [11]. This prior knowledge has been demonstrated to be crucial to account for the robustness of our everyday inferences [12]. Indeed, it makes possible inductive inference about the agent's intentions, even in cases of noisy signals or incomplete data [13]–[15].

However, although most authors agree that prior knowledge and perceptual information both contribute to the process of inferring intentions, the precise contribution of each type of information remains controversial [16]–[23]. The controversy stems in part from the fact that “intention” is an umbrella term used in the empirical and philosophical literature to refer to representations of actions that can differ in both their content and format, as well as in their temporal properties and in the role they play in the guidance of actions [24]–[29]. Intentions can therefore be distinguished into several sub-types according to one or several of these factors. In the present study, we propose a typology of intentions and hypothesize that this typology might be a key element in understanding how perceptual information and prior knowledge contribute to the process by which intentions are inferred.

Varieties of intentions

The intentional typology we present below is primarily motivated by the necessity to take into account two dimensions of variation in the content of intentions that may make an important difference to the processes involved in their inference. The first dimension of variation concerns the scope of the intention; i.e., the more-or-less complex nature of its goal. Here we can draw a distinction between basic intentions and superordinate intentions. Basic intentions are directed at simple motor goals (i.e. goals that can be realized by basic actions such as lifting an arm, pressing a button, or reaching for an object). These intentions are sensorimotor representations where the goal is represented directly in terms of the motor commands needed to achieve it. The relation between basic intention and motor act is thus one-to-one when that act is successfully completed [17]. In contrast, superordinate intentions are intentions directed at somewhat more complex or general goals, the achievement of which typically involves the completion of a number of subgoals or substeps. Depending on the complexity of the general goal, these subgoals may themselves be decomposed into further subgoals, ultimately reaching the level of basic actions. The achievement of a superordinate intention will thus require the execution of a combination of basic actions each guided by a corresponding basic intention. Different combinations of motor acts can be used to accomplish the same general goal and, conversely, a same motor act (or even series of motor acts) can be part of combinations aimed at different general goals.

The second dimension of variation we were interested in concerns the target of the intentions. Neither basic nor superordinate intentions are necessarily directed at inanimate objects. They may also target a third party or be achieved in a context of social interaction [11], [30]–[33]. The content of intentions is thus also modulated by the relational structure in which an action takes place. We call intentions directed at an object, non-social intentions, and intentions directed at a third party, social intentions.

By combining these two dimensions, we obtain the following typology: i) non-social basic intention, ii) non-social superordinate intention, iii) social basic intention, and iv) social superordinate intention. Owing to their different scopes and targets, basic and superordinate, social and non-social, intentions are naturally assigned different functional roles, different types of content and different temporal scales. The present study aims at investigating whether these functional differences are reflected in the respective contribution of perceptual information and prior expectations to intentional judgments.

Overview of the present study

We conducted four experiments in which participants were requested to identify one intention underlying an action scene. Each experiment involved one type of intention with a specific scope (basic vs. superordinate) and a specific target (social vs. non-social). Interactions between prior expectations and visual information were examined within a Bayesian probabilistic framework. This conceptual framework is particularly well-suited to account for how accurate predictions on hidden world states are made in situations where available sensory information does not sufficiently constrain the number of potential solutions [13], [15], [34]. Before the onset of an action sequence, each of the agent's possible intentions was first assigned a certain ‘level of belief’, termed a priori probability (the probability that intention X is the real cause of the observed behaviour estimated from past experiences). Then the observer progressively gathers sensory information (visual input) as the action sequence is disclosed and both sources of information (sensory and a priori) are combined and used to infer the intention underlying the observed behaviour. Thus, the process by which intentions are inferred is considered as reflecting a trade-off between the sensory information and the prior probability of each candidate intention [14]. Finally, the chosen intention is that which maximizes the posterior probability value, i.e. the probability that intention X is true given what is observed.

In the present study, these two terms – a priori probability and sensory information – were manipulated using a two-step procedure. Prior expectations the participants had about the agent's possible intentions were manipulated by increasing the a priori probability that one intention (termed likely intention) was achieved, to the detriment of other intentions (unlikely intentions) with the same scope and target. Sensory information available from an action scene was then manipulated in a second step by modulating the degree of completeness (i.e. the duration) of the action sequences, resulting in actions scenes with varying amounts of visual information.

We first predicted that judgements about intentions would follow the general principles of Bayesian inference. Specifically, we expected that the amount of visual information would interact with participants' prior expectations such that the lower the reliability of the external visual input, the more participants' responses would depend upon their own internal expectations. That is, they should respond more frequently in the direction of the likely intention. And vice versa, the higher the amount of visual information, the less the participants should rely on their prior expectations.

Second, we predicted that the shape of the interaction between these two sources of information would be a function of the type of intention, depending on both its scope and target. Along the dimension of the scope, we hypothesised that participants' judgement about basic intentions should primarily rely on sensory information available from the action scene. This prediction is motivated by the pragmatic content of the basic intention: “grasping a glass of water” directly denotes the corresponding intention of “grasping that glass”. In this case, perceiving the action itself – i.e. processing the associated visual kinematics – is enough to successfully determine the nature of the underlying intention [35]. On the other hand, we expected performance in judging superordinate intentions to be significantly influenced by participants' prior expectations. As already mentioned, the same sequence of motor acts can be part of combinations aimed at different general goals or superordinate intentions. In this specific case, sensory information carried by movement kinematics is not sufficient to infer the corresponding intention, as it under-constraints the set of candidate intentions congruent with this movement [1], [2], [17], [36]. We consequently predicted that this perceptual uncertainty should encourage participants to ‘mistrust’ what they observe and, hence, to rely more on their prior expectations.

Along the dimension of target, finally, we expected participants' reliance on their prior expectations to increase when basic and superordinate intentions are directed at another agent. The structure of social interaction meets indeed particular, often irrepressible, expectations, such as those provided by reputational knowledge [9], [10], [37]. Indeed, knowledge about individual's reputation has been robustly demonstrated to have a strong impact on predicting how the observed agent will behave [12]. In line with other recent suggestions, we thus hypothesised that the weight of these a priori expectations would increase when the observed action fits into a context of social interaction.

Non-social experiments

In the first experiment, participants were instructed to infer the basic intention (to lift, to rotate, or to transport) of an actor manipulating meaningless objects (fig. 1, A). In the second experiment, participants were instructed to infer the superordinate intention (i.e. the general goal) underlying a sequence of motor acts (fig. 1, B).

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Figure 1. Examples of stimuli for each of the four experiments.

basic non-social intention experiment (A); superordinate non-social intention experiment (B); basic social intention experiment (C); superordinate social intention experiment (D). The black cross indicates the starting position of the hand.

https://doi.org/10.1371/journal.pone.0017133.g001

Social experiments

The third (fig. 1, C) and fourth experiments (fig. 1, D) presented two actors engaged in a social game in which they could either cooperate or defect by coordinating their action (joint-action condition) or by refusing to join their action to the achievement of a shared goal (defective condition). Participants were instructed to infer the nature of the second player's social intention (i.e. cooperative or defective intention). In both these experiments, the bias was assigned according to the way the second player responded to the strategy adopted by the opponent in the previous round. Participants were therefore biased towards the reputation of the second player rather than towards one particular type of social intention. Finally, as in the two previous non-social experiments, both basic intentions (single motor acts) and superordinate intentions (sequences of motor acts leading to the construction of a shape) were considered in the last two experiments.

Ethics Statement

All participants gave written informed consent for the study which was approved by the local Ethical Committee (Comité de Protection des Personnes SUD-EST IV, no. B80631-60).

Experiment 1: non-social basic intention

Procedure.

Participants were comfortably sat at a distance of 60 cm from a 19″ computer monitor. Each trial started with the observation of an incomplete movie, and then a response screen appeared for 2500 ms representing the first letter of each possible intention (T for ‘transport’, L for ‘lift’, or R for ‘rotate’). Participants were requested to respond by pressing, as quickly and accurately as possible, one of the three keyboard presses corresponding to the three possible intentions. Once a response was given, the next trial started.

The design was composed of two experimental sessions. A first baseline session was characterized by a flat (unbiased) prior probability distribution with all basic intentions having the same probability. In a second bias session, participants were biased towards one intention (likely intention, 55%) to the detriment of the others (unlikely intentions, 22% each). The bias was randomly assigned so that each basic intention was equally biased across participants.

In both sessions, trials were organized into OVERT blocks in which movies consisted of a constant and very high amount of visual information (1880 ms), alternating with COVERT blocks in which movies consisted of varying and lower amounts of visual information presented in a random order (low = 1480 ms, moderate = 1560 ms, and high = 1640) (see Supporting Text S1, part 2, for the selection of these amounts of visual information[58], [59]; Figure S2). Each experimental sequence (one overt block followed by one covert block) was repeated 9 times over each session (see figure 2, A) and each participant performed the trials in a different random order.

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Figure 2. Experimental designs.

Examples of a typical experimental sequence (one OVERT block followed by one COVERT block) used in both the baseline and the bias sessions. OVERT blocks (O): 18 movies with a very high and constant amount of visual information (1880 ms). COVERT blocks (C): 9 movies with three amounts of visual information (1480, 1560, and 1640 ms). In the 4 experiments, the probability of all intentions was held equal across the block, except in overt blocks of the bias session, where one particular intention had a greater probability to be accomplished than the other ones. In the BASIC exp., subjects had to identify a single action (labels: L: “lift” action; R: “rotate” action; T: “transport” action). In the SUPERORDINATE exp., subjects had to identify the final action (red letter) of a sequence leading to shape 1, 2, or 3 (s1: shape 1). In the SUPERORD. SOCIAL exp., subjects had to identify the action of the second player (red letter) leading to configuration 1, 2, 3, or 4 (c1: configuration 1). In both BASIC and SUPERORD. SOCIAL exp., the action or the configuration achieved by each player indicated either a cooperative or a defective strategy (CO: cooperate; DF: defect). In each experiment, a probabilistic bias was assigned to one particular action (basic), shape (superordinate) or strategy (social). The red interrogation mark indicates the action (basic: single action; superordinate: last action of the sequence) for which the amount of visual information varied.

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The reason for block interleaving was that it enabled us to maintain the bias constant across the bias session. Indeed, by regularly inserting overt blocks of movies with different probabilities, we ensured that participants were continuously biased towards one intention over the whole session. Furthermore, even though the baseline session did not include any bias assignment, and therefore was not concerned with bias maintenance, it contained the same trial organization (block interleaving) to allow a direct comparison of the performance between the two sessions.

Prior to running the experiment, participants undertook a training session to get familiar with the task. The training consisted of 3 baseline experimental sequences (non-biased probability distribution) with interleaved blocks. The 72 movies (3×24) presented during the training session were distinct from those used in the experiment.

Experiment 2: non-social superordinate intention

Experiment 3: social basic intention

Experiment 4: social superordinate intention

‘Bias effect’: between-experiment comparisons

Finally, some analyses were conducted to directly assess whether the contribution of prior knowledge to the inference of an intention depended upon the target (basic vs. superordinate) and the scope (non-social vs. social) of the intention. Student tests were first conducted on the overall performance in the bias session between the basic experiments and the superordinate ones, and between the non-social experiments and the social ones. Second, the bias effects for each dimension (scope and target) were compared with each other. A score reflecting the effect of each type of intention (basic, superordinate, social, non-social intention) was calculated by subtracting, in each experiment, participants' hit rate for the likely intention from the hit rate for the unlikely intentions. The resulting scores were then entered in a 2 (basic vs. superordinate) ×2 (social vs. non-social) ×3 (amounts of information) factorial ANOVA.

Experiment 1: non-social basic intention

For each session, two-tailed t-tests were performed between the two unlikely intentions on both RTs and hits. As no significant differences appeared (all p>.05), performances for these two unlikely intentions were pooled for subsequent analyses.

Overt blocks.

As expected, participants performed the task well when the amount of visual information was very high (percentage of mean correct responses  = 98%, S.D. = 2.4, and 96.8%, S.D. = 3.4 in the baseline and the bias sessions, respectively). Furthermore, in the baseline session, there were no significant differences among hits and RTs between the (future) ‘likely intention’ (i.e. the one towards which participants will be biased in the subsequent bias session) and the ‘unlikely intention’, indicating that prior to biasing participants, there was no a priori bias towards one intention rather than another (two-tailed t-tests, all p>0.2, see figure 3, ‘Basic exp.’, baseline session).

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Figure 3. OVERT blocks: mean reaction times of the likely and the unlikely intentions across time.

Baseline and bias sessions: (1-3): the first three overt blocks of the session; (4-6) the intermediate three blocks; and (7-9) the three last blocks of the session.

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The only significant difference was found in the bias session, with faster RTs for the likely intention vs. unlikely intentions (two-tailed t-tests, all p<.001). Subsequent analyses of RTs across time were carried out by independently comparing RTs for likely basic intention and RTs for unlikely basic intentions across the different blocks. The bias was found to have a cumulative effect over time, with RTs for the likely intention progressively decreasing up to block 8 (minimal RT = 337 ms) and then remaining constant until the end of the session (blocks 1–3 vs. blocks 4–6: t = 3.09, p<.005; blocks 4–6 vs. blocks 7–9: t = 2.08, p<.05) (see figure 3, ‘Basic exp.’).

Covert Blocks.

The 3 (amounts of information) ×2 (likely vs. unlikely intentions) repeated-measures ANOVA revealed significant effects on both participants' RTs and hits. In the baseline session, a significant effect of the amount of visual information was obtained (RTs: F(2,116) = 167.13, p<.001,  = 0.74, and hits: F(2,116) = 277.44, p<.001,  = 0.82). As expected, RTs were found to decrease and hits to improve as the amount of visual information increased. There were, however, no significant effects of the intention presented (future ‘likely’ or future ‘unlikely’ intention) nor of the interaction between the intention and the amount of visual information (both p>0.05), showing that improved performance for higher amounts of information was independent of the presented intention (Im1, Im2, or Im3) (see table 1 and figure 4, ‘Baseline session’).

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Figure 4. Non-social basic intention experiment (COVERT blocks).

Mean percentage of correct responses (± SD) for likely (red) and unlikely (blue) intentions for each amount of visual information (low, moderate, high).

https://doi.org/10.1371/journal.pone.0017133.g004

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Table 1. Non-social basic intention experiment (COVERT blocks).

https://doi.org/10.1371/journal.pone.0017133.t001

In the bias session, in addition to the effect of amount of visual information (RTs: F(2,116) = 98.8, p<.001,  = 0.62; hits: (F(2,116) = 190.92, p<.001,  = 0.76), an effect of the bias (RTs: F(1,58) = 18.51, p<.001,  = 0.24; hits: (F(1,58) = 19.81, p<.001,  = 0.25) as well as of the interaction (RTs: F(2,116) = 13.98, p<.001,  = 0.19; hits: F(2,116) = 5.44, p = .005,  = 0.08) were also observed. Post-hoc tests indicated that participants were more accurate and faster in recognizing the likely intention in low information condition only (LSD Fisher tests, RTs: low  = p<.001; moderate  =  p<.005 and high  =  ns; Hits: low  = p<.001; moderate  =  ns. and high  =  ns.) (see table 1 and figure 4, ‘Bias session’).

Experiment 2: non-social superordinate intention

Statistical analyses were similar to those conducted in the first experiment. Responses for the two unlikely superordinate intentions were pooled for subsequent analyses as there were no significant differences among both hits and RTs between these responses (for each session, two-tailed t-tests, p>0.15).

Covert blocks.

In both the baseline and the bias sessions, the amount of visual information significantly affected participants' hits and latencies with decreased RTs (baseline: F(2,116) = 423,68, p<.001,  = 0.87; bias session: (F(2,116) = 523.9, p<.001;  = 0.9) and a greater number of hits as the amount of visual information increased (baseline: F(2,116) = 249.18, p<.001,  = 0.81; bias session: (F(2,116) = 199.03, p<.001;  = 0.77) (see table 2 and figure 5).

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Figure 5. Non-social superordinate intention experiment (COVERT blocks).

Mean percentage of correct responses (± SD) for likely (red) and unlikely (blue) intentions for each amount of visual information (low, moderate, high).

https://doi.org/10.1371/journal.pone.0017133.g005

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Table 2. Non-social superordinate intention experiment (COVERT blocks).

https://doi.org/10.1371/journal.pone.0017133.t002

In the bias session, a significant effect of the bias was also observed with faster RTs and increased hits for actions congruent with the likely superordinate intention (RTs: F(1,58) = 47.04, p<.001,  = 0.44; and hits: F(1,58) = 62.09, p<.001,  = 0.51). Finally, the bias was found to significantly interact with the amount of visual information in such a way that the number of hits was significantly higher and RTs faster for the likely intention as the amount of visual information decreased (RTs: F(2,116) = 15.3, p<.001,  = 0.2; and hits: F(2,116) = 9.28, p<.001;  = 0.13). Post-hoc tests further indicated that participants were more accurate and faster in recognizing the likely intention in both low and moderate amount of visual information conditions (LSD Fisher: low, p<.001; moderate, p = .005, high, p<.05 for RTs; and low, p<.001; moderate, p<.001; high  =  ns. for hits) (see table 2 and figure 5, ‘Bias session’).

Experiment 3: social basic intention

Statistical analyses were similar to those conducted in the previous experiments. Two-tailed t-tests revealed no significant differences among both participants' RTs and hits between the TFT intentions (coop/coop vs. def/def: two-tailed t-tests, all p>.2) and between the alternative ones (coop/def vs. def/coop, two-tailed t-tests, all p>.15). Performances for def/def were therefore pooled with those of coop/coop (i.e. TFT or likely intentions) and performances for def/coop were pooled with those of coop/def (i.e. alternative or unlikely intentions) for the subsequent analyses.

Covert blocks.

Baseline session. ANOVAs performed on both hits and RTs showed a significant main effect of the amount of visual information with decreased RTs (F(2,116) = 80.44, p<.001;  = .58) and a greater number of hits (F(2,116) = 209.02, p<.001,  = .78) as the amount of visual information increased. In addition, the main effect of the type of reputation – previously observed in the overt blocks – was also significant in the covert blocks among RTs only (F (1, 58)  = 4.7, p<.05,  = .07). The second player's action was more rapidly inferred when it was embedded within a TFT intention than within an “always defecting” or an “always cooperating” intention. The type of reputation did not, however, interact with the amount of visual information (see table 3 and figure 6, ‘Baseline session”).

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Figure 6. Social basic intention experiment (COVERT blocks).

Mean percentage of correct responses (± SD) for likely (red) and unlikely (blue) intentions for each amount of visual information (low, moderate, high).

https://doi.org/10.1371/journal.pone.0017133.g006

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Table 3. Social basic intention experiment (COVERT blocks).

https://doi.org/10.1371/journal.pone.0017133.t003

Bias session. There were significant main effects of the amount of visual information and of the bias on both the RTs (main effect of amount of visual information: F(2,116) = 114.49, p<.001,  = .66; main effect of the bias, F(1,58) = 25.29, p<.001,  = .3) and the hits (main effect of amount of visual information: F(2,116) = 170.34, p<.001,  = .74; main effect of the bias, F(1,58) = 34.75, p<.001,  = .37), as well as a significant effect of the interaction between these two factors (RTs: F(2,116) = 9.23, p<.001,  = .13; hits: F(2,116) = 8.28, p<.001,  = .12). Participants' performance (slower RTs and higher hits) for actions congruent with a biased (i.e. likely) social intention improved as the amount of visual information decreased. Furthermore, the bias significantly affected participants' hits for all amounts of information (LSD Fisher: low, p<.001; moderate, p = .005; high, p =  ns for RTs; low, p<.001; moderate, p = .05; high, p = .05 for hits) (see table 3 and figure 6, ‘Bias session’).

Experiment 4: social superordinate intention

Statistical analyses were similar to those conducted in the first three experiments. Two-tailed t-tests revealed no significant differences among both participants' RTs and hits between the two likely combinations (coop/coop vs. def/def: two-tailed t-tests, all p>.2) and between the two unlikely combinations (coop/def vs. def/coop, two-tailed t-tests, all p>.15). Performances for def/def were therefore pooled with those of coop/coop (TFT or likely intentions) and performances for def/coop were pooled with those of coop/def (unlikely intentions).

Covert blocks.

Baseline session. As the amount of visual information increased, decreased RTs (F(2,116) = 93.23, p<.001,  = .61) and increased hits (F(2,116) = 281.6, p<.001,  = .82) were observed for actions accomplishing the likely social intention. In addition, as in the overt blocks, actions were better and more rapidly inferred when they were embedded within a tit-for-tat strategy than within an alternative strategy (RTs: F(1,58,) = 4.16, p<.05,  = .06, and hits: F(1,58) = 7.96, p<.01,  = .12). The effect of reputation did not, however, interact with the amount of visual information showing that the type of strategy affected participants' performance independently of the amount of visual information (see table 4 and figure 7, ‘Baseline session’).

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Figure 7. Social superordinate intention experiment (COVERT blocks).

Mean percentage of correct responses (± SD) for likely (red) and unlikely (blue) intentions for each amount of visual information (low, moderate, high).

https://doi.org/10.1371/journal.pone.0017133.g007

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Table 4. Social superordinate intention experiment (COVERT blocks).

https://doi.org/10.1371/journal.pone.0017133.t004

Bias session. There were significant main effects of the amount of visual information and of the bias on both the RTs (main effect of amount of visual information: F(2,116) = 163.11, p<.001,  = .73; main effect of the bias F(1,58) = 52.03, p<.001,  = .47) and the hits (main effect of amount of visual information: F(2,116) = 198.77, p<.001,  = .77; main effect of the bias F(1,58) = 92.16, p<.001,  = .61), as well as a significant effect of the interaction between these two factors (RTs: F(2,116) = 27.74, p<.001,  = .32, and hits: F(2,116) = 4.41, p = .01,  = .07). Participants' performance (slower RTs and higher percentage of hits) for likely social intentions improved to a large extent as the amount of visual information decreased, although the bias effect was observed for all amounts of visual information as revealed by the Post-hoc (LSD Fisher: low, p<.001; moderate, p<.001; high, p = .01 for RTs and low, p<.001; moderate, p<.001; high, p<.001 for hits) (see table 4 and figure 7, ‘Bias session’).

‘Bias effect’: between-experiment comparisons

Contrasting the overall performance between experiments revealed no significant differences, showing that overall participants performed at comparable levels across the four experiments. Comparing the bias effect between experiments revealed significant effects of both the scope and the target of the intention. The bias effect was indeed significantly increased for the superordinate intention compared with the basic intention (F(1,116) = 8.36, p<.005,  = .81) and for the social intention compared with the non-social intention (F(1,116) = 5.06, p = .02,  = .61). Furthermore, these differences were observed for different amounts of information according to the dimension itself. Indeed, along the scope dimension, the bias had a significantly greater effect when inferring a superordinate intention than a basic one in the conditions with a moderate amount of visual information (post-hoc Fisher test, p = .014). Along the target dimension, on the other hand, the only significant difference was observed for a high amount of visual information with a greater bias effect for inferring social intentions than non-social ones (post-hoc Fisher test, p = .0035) (see figure 8).

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Figure 8. Mean score (± SD) of the bias effect expressed as a percentage of correct responses.

Left panel: comparison between intentions with same target but different scopes (BASIC vs. SUPERORD.). Right panel: comparison between intentions with same scope but different targets (SOCIAL vs. NON-SOCIAL).

https://doi.org/10.1371/journal.pone.0017133.g008

Interaction between perceptual and prior information

In the 4 experiments in the present study, the degree to which prior expectations contributed strongly depended on the reliability of the visual information conveyed by the video scenes. In low amount of visual information conditions, whatever the type of intention, participants tended to give priority to likely intentions at the expense of unlikely intentions; that is, they relied mostly on the intention they estimated to be the most likely cause of what was observed. This tendency towards favouring prior knowledge over perceptual information may further be accounted for by considering intentional inference as an inverse problem [1]–[3], [14]. Inverse problems characterise situations in which the same sensory input can have different causes. This type of problem is commonly encountered in ambiguous perceptual tasks – such as those using bi-stable or degraded stimuli – the resolution of which requires appealing to prior knowledge or making further assumptions about the nature of the observed phenomenon [43]. The significant contribution of prior expectations in conditions of high visual ambiguity precisely suggests that when sensory information was not sufficient to unambiguously infer one intention, participants compensated by massively appealing to their prior knowledge (i.e. about the space of the agent's possible intentions). This strategy resulted in preferentially selecting actions achieving the intention with the highest probability to occur.

Overall, this result reinforces the idea that in situations of sparse or incomplete data a successful inference depends on an adaptive integration between bottom-up information (from the observation of behaviour) and top-down prior knowledge about goals or intentions [13]. This integration is consistent with a mechanism complementing the available perceptual information when it does not sufficiently constrain the number of potential solutions, namely, the many competing intentions congruent with what is observed. In line with this assumption, some authors have suggested that inferring another person's intention necessarily requires sensorimotor information to be complemented with information about mental states and attitudes [23]. It has been demonstrated that prior expectations are already used frequently by children, even at a very early age. This tendency combines with a tendency to interpret actions as being directed towards a goal (‘teleological obsession’, [3]). When the visual information is not sufficient for interpreting the action as a goal directed one [44], or when the action is incomplete [45], children posit states of the world occasionally counterfactual to the perceptual evidence (such as the presence of occluded physical objects). The results of the present study are consistent with the existence of such a mechanism of data completion/correction operating through the default use of prior expectations. Crucially, however, we further show that reliance on this mechanism also depends on the type of the intention to be inferred, according to its scope (basic vs. superordinate) or its target (non-social vs. social).

Basic vs. superordinate intentions

Both non-social basic and superordinate experiments required recognising one motor act, with the superordinate condition also requiring the final goal of the sequence (i.e. the shape being constructed) to be taken into account. Yet, across both experiments, prior expectations were found to differentially contribute to the participants' responses. In the basic non-social experiment, a bias response towards the likely intention was only observed in the condition where the amount of visual information was low. When participants were exposed to a moderate amount of visual information, these expectations no longer exerted an influence on performance, which then substantially depended upon the processing of the visual information alone. On the other hand, a heightened contribution of these expectations is observed in the superordinate experiments since they significantly influenced participants' performance in conditions of both low and moderate amounts of visual information.

The increase in response bias in the superordinate experiment cannot be explained by differences in complexity between both tasks since participants performed at comparable levels across basic and superordinate experiments showing that the differences between both experiments in terms of contribution of prior information are accounted for by the type of intention being considered. This result may be explained by differences in the relationship between these two types of intentions and action. While basic intention stands to action in a one-to-one relation (basic intentions like ‘transport’, ‘rotate’, or ‘lift’ an object are indeed directly accessible to the viewer from mere observation of the motor acts), superordinate intention stands to action in a many-to-one relation since the very same intention can be achieved by several distinct (commutative) sequences of actions. In the present study, this commutative property resulted in an ability of participants to infer the underlying intention solely on the basis of visual information arising from the first two actions. However, the present results also suggest that, despite the unpredictability of the sequence, participants still initiated a response, before observing the last action, by appealing massively to their prior expectations. Participants' dependence on priors in this condition could precisely account for the fact that simulating the motor acts composing the sequence (through motor mirroring, [46]–[47]) was of little help to infer the final superordinate intention. Those motor acts were indeed interchangeable within the sequence itself, and, as a consequence, they did predict neither the subsequent action nor the intention eventually achieved.

This early use of prior expectations might be accounted for by the existence of a system that pre-processes the current action chain depending on the sequences previously encountered. Observing the beginning of an action, or a sequence of actions, would automatically activate a representation of the likely intention that would be progressively suppressed or reinforced as the amount of visual information increases. Such a pre-processing would be particularly salient in superordinate conditions, where the beginning of the act chain proved to be of little importance for inferring the final intention it achieved. As such, it would explain why selecting an unlikely intention in bias sessions induced a significant cost on participants' performance. In these sessions, selecting an unlikely intention would indeed imply disengaging from the early activation of a likely intention. Finally, such pre-processing may account for why prior expectations are favoured over visual information in conditions of moderate perceptual uncertainty, as it would account for the role that priors continue to play when the amount of perceptual information increases. In superordinate conditions, the current sequence of actions would pre-activate the representation of the likely intention (i.e. the intention with the highest probability) to such an extent that a greater amount of visual information would be required to counteract it.

Non-social vs. social intentions

Social experiments were characterized by participants' responses over-relying on prior expectations as revealed by responses massively shifting towards likely intentions (i.e. ‘tit-for-tat” intention: cooperation if previous cooperation, defection if previous defection) whatever the amount of visual information available from the action scene. This increased reliance on prior knowledge cannot be accounted for by differences in terms of complexity between non-social and social experiments, namely a greater memory load due to the requirement of tracking two successive intentions – the first and the second player's ones. Indeed, participants performed equally well, in terms of correct responses and reaction times, in both the social and non-social experiments. Additionally, the effect of facilitation associated with TFT strategy in the basic social experiment cannot be explained by a visual priming effect of the first player's action on the second player's one, which could have occurred when the latter performed the same action as the former. Indeed, TFT strategy was also found to be favoured in the superordinate social experiment; yet in this study TFT strategy did not necessarily imply that the action of the first player should be reproduced by the second player.

The dependence of the participants on their prior knowledge appears to reflect some expectations driven by the social context of the task. It is well-known that even basic movements, like the relative movements of geometrical figures, automatically induce participants to perceive the figures as socially interacting [48]–[50], and elicit strong expectations about the intentional causes of their movements (e.g. striking, kissing, etc.). Situations identified as involving social interactions are generally prone to trigger specific expectations concerning the way agents are likely to behave in such situations [12]. These expectations may be derived from perceiving the other as an interaction partner rather than a competitor in a joint-action task [51], and from knowledge of diverse origins, such as that provided by group stereotypes [52], social-specific naive theories [53], or an individual's reputation acquired from experience of reciprocal social interactions [10]. In the present experiment, increased dependence on prior knowledge for inferring social intentions, regardless of their scope, seems precisely to fall within this type of expectation. Indeed, during the whole task, increasing the frequency of the second player adopting a TFT strategy amounted to progressively assigning a specific reputation to that player. A bias in the response towards a “tit-for-tat” mode of reciprocation reveals that participants did integrate this reputational knowledge and made their response accordingly.

The pervasive effect of these specific expectations is also well illustrated in the baseline condition by the early preference of participants for the TFT reciprocation. Even before being biased in this direction, participants tended to infer more rapidly that the second player was more inclined to mirror the first player's strategy. This early preference was probabilistically reinforced in the bias session and, as a consequence, exerted a greater influence on the participants' performance since it persisted even when the reliability of the visual information was high. Indeed, while in the basic non-social experiment the very same motor act presented alone was inferred from a much lower amount of visual information, in the social experiment a bias response towards the likely social intention was still observed for a higher amount of visual information. This shows that the influence of these expectations in the bias session was such that the participants had difficulty disengaging from their a priori expectations, resulting in predicting a play congruent with prior expectations but counterfactual to perceptual evidence. Similarly, these difficulties could account for the cost in performance associated with the selection of intentions that did not meet these expectations. In the bias session, participants were indeed significantly less accurate and were slower to select an unlikely intention (i.e. always defect, always cooperate) when this selection required concomitantly inhibiting the competing tit-for-tat intention.

Simulation vs. reasoning accounts of action understanding

The two main results of the present study (interaction between prior expectations and perceptual information and the modulation of this interaction as a function of the type of intention) may help reconcile the two major accounts of action understanding developed over the last decade. On the simulation account, we understand our conspecifics' intention by literally simulating their action via the activation of our own motor planning system. The result of this process of internal replication is the selection, in the observer's own repertoire, of the intention that would have caused the very same action. This type of explanation stresses the role of sensory information, derived from the kinematics of the movement, in action understanding [35]– irrespective of whether the action is complete (the goal achieved is fully visible) or only partially performed (the goal is hidden but can be predicted from the unfolding action) [see 46]. In contrast, the “theory theory” account postulates that action understanding is based on specialized inferential processes and mostly emphasizes the contribution of the context-related prior knowledge. This knowledge can either be derived from our intuitive theories of human behaviour, or from the subject's past experiences and rules she has drawn from them [8], [54], [55].

A wealth of empirical data and theoretical works nowadays converges on the idea that these two major classes of mechanisms play a complementary role in intention inference [10], [22], [23], [56]. The results of the present study comfort these observations. By suggesting that intentional judgment relies on a relative balance of bottom-up sensory and top-down prior information, they plead in favour of a hybrid model of action understanding. In such a model, the observer would mobilize either low-level simulation or high-order inferential mechanisms depending on whether the current sensory evidence is, or is not, reliable enough to elicit simulation from observation.

Recently, Kilner and colleagues proposed a theoretical framework that attempts to further account for how these two classes of mechanisms may interact to enable one's understanding of other people's intentions [1]. This framework relies on the hierarchical architecture of action representations ranging from the intention level to the kinematics level (see also [57]). In this architecture, the selection of one type of action representation would result from the resolution of the inverse problem at each level of the hierarchy. Basically, each level uses a model to generate a prediction of the representations in the level below. This prediction is then compared with the representation at the subordinate level and prediction errors arising from that comparison are returned to the higher level to adjust its representation. This adjustment is generalised to the different levels of the hierarchy (intention, motor command and kinematics). The most likely cause of the observed action is then inferred by minimising the prediction error at all the levels of this hierarchy [1], [2]. Given visual kinematics, goal expectations are first generated, from these goal representations motor commands are then predicted and given these motor commands, kinematics are in turn predicted. In this framework, top-down influences are therefore dynamically generated since the estimates produced at the higher levels become prior expectations for the lower levels.

Our results can be consistently interpreted in the light of the Kilner's hierarchical model. A basic intention can be directly predicted from the observation of the current motor act, provided the related visual information is sufficient to enable comparison with expected kinematics at higher levels. In this case, participants' performance is strongly dependent on minimising the prediction error that arises from this comparison. However, this comparison also closely depends on the reliability of the current movement kinematics; when the amount of visual information is too low, this comparison cannot be made, and, as a result, subordinate levels cannot adjust their representation to higher estimates of the hierarchy. We observed that, when this comparison could not be carried out, participants consistently appealed to their prior knowledge. In a hierarchical model of action representations, such an over-reliance on priors could be made possible by the existence of a short circuitry of recursive loops between subordinate and higher levels of the cortical hierarchy. These recursive loops would be mobilized when data is sparse to shortcut the automatic comparison process between observed and expected kinematics movement. Importantly, the engagement of this mechanism proved to be dependent on the amount of visual information available from the action scene, but independent from the scope and target of the intention, since it was observed to operate at the lowest levels of visual information in each of the four experimental conditions.

Noteworthily, the engagement of these recursive loops is also sensitive to variations in the relationship between the observed action and its goal. Superordinate conditions indeed involved a greater recourse to participants' prior expectations even when the visual information significantly increased to a moderate (non-social) or even a high level (social). This greater dependence on prior expectations can be explained by the fact that, in superordinate conditions, many competing intentions are congruent with the visual information conveyed by the current motor act. Thus, whereas minimising the prediction error between expected and current kinematics may be sufficient to predict the agent's single act (e.g. to rotate), it may not be to infer unambiguously which of the multiple superordinate intentions (e.g. final shapes) it contributes to accomplish. As a consequence, we found the weight of the decision to be mostly carried by participants' prior expectations, suggesting, in this situation of accrued perceptual uncertainty, an early shortcut of the comparison process between levels of the action representation hierarchy. Crucially, this shortcut was independent of the amount of information, since it occurred even when the visual information was high enough for the participant to be normally confident about what she is seeing. This observation suggests that recursive loops of this kind could be mostly recruited in contexts where relying on one's prior expectations is a better guarantee for accurate inference, even if such expectations can occasionally go against perceptual evidence.

Conclusion

Our results shed light on how sensory information, derived from the kinematics of the observed action, interacts with prior expectations to enable one's understanding of other people's intentions. We first showed that the contribution of participants' prior knowledge was sensitive to the availability of the sensory information from the action scene. A greater contribution of this knowledge was observed in conditions of sparse visual information, suggesting the engagement of a mechanism of data completion operating through the default use of prior expectations.

Second, we found that the priors' contribution also depended on the type of intention that was inferred. An increased reliance on priors was indeed observed in conditions where the agent's intention could not be predicted by the sole visible, current motor act, but further required estimating the superordinate goal this act contributed to achieve. In this case, participants' expectations – being progressively acquired from observation – were found to most frequently supersede the visual information conveyed by the current motor kinematics. Thus, the more participants responded towards the biased (e.g. expected) intentions, the more the visual information tended to play a confirmatory, rather than a predictive role. Such a shift in the contribution of visual evidence is likely to account for why participants, in this condition, mostly over-relied on their priors to make their decision, even though it ran counter to the perceptual evidence.

Crucially, an over-reliance on priors was also massively observed in social conditions. We suggested that the early influence of social-specific expectations (e.g. expectations on how agents are the most likely to behave in a context of reciprocal interaction) may account for this important shift in the response toward participants' priors. Contexts of social interaction are indeed prone to elicit modular, high-level expectations, which may contribute to giving priority to some intentional causes (e.g. cooperation if previous cooperation, defection if previous defection) at the expense of other competing causes. These a priori expectations, being acquired from experience (probabilistic bias) or derived from domain-specific knowledge (TFT reciprocation), were found to favour some action representations so that less sensory evidence was needed for the participants to be confident about their decision, i.e. about which kind of intention was most likely the cause of the observed action.