Relations between Associative and Structured Knowledge in Category-based Induction Eoin Travers (etravers01@qub.ac.uk) Jonathan Rolison (j.rolison@qub.ac.uk) School of Psychology, Queen’s University Belfast Belfast, BT7 1NN UK Aimée K. Bright (a.bright@qmul.ac.uk) Psychology Division, School of Biological and Chemical Sciences, Queen Mary University of London London E1 4NS, UK Aidan Feeney (a.feeney@qub.ac.uk) School of Psychology, Queen’s University Belfast Belfast, BT7 1NN UK Abstract relational models take advantage of more sophisticated knowledge about the world, including directional causal Theories of category-based human inductive reasoning typically rely on either associative or structured knowledge relationships, and domain specific rules (Griffiths & about relationships between categories. Here, we test a Tenenbaum, 2009; Heit, 1998; Kemp & Tenenbaum, 2009; prediction, derived from a hybrid theory that utilizes both Murphy & Medin, 1985; Osherson, Smith, Wilkie, Lopez, kinds of knowledge representation, that participants will & Shafir, 1990). experience conflict on a reasoning task in which associative Evaluating the strengths and weaknesses of structured and and structured knowledge support different responses. relational models, Bright and Feeney (2015) proposed that Participants completed a triad task that tested their ability to generalize a genetic property from a target species to a induction relies on two forms of knowledge: simple, taxonomically related response. The strength of association associative representations that are retrieved easily and between the target and an alternative non-taxonomic (i.e., automatically, and more complex, structured relational foil) response was manipulated across trials. Analysis of knowledge, including causal relationships, and domain participants’ mouse cursor trajectories revealed that they were specific intuitive theories, that require cognitive effort. A initially drawn toward strongly associated foil responses, even prediction of this hybrid model, investigated in the present when they ultimately chose the correct (taxonomic) option. article, is that when associative and structured knowledge Keywords: Category-based induction; Knowledge; Response come into conflict it often becomes necessary for the dynamics; Cognitive conflict; reasoner to inhibit an incorrect inference, generated automatically from associative knowledge, in order to Introduction reason on the basis of more complicated relational Inductive reasoning is among people’s most important information. To test this prediction, we employed a well- cognitive skills, allowing them to draw on prior knowledge established mouse-tracking paradigm (Freeman, Dale & to make predictions under uncertainty. Induction is both Farmer, 2011), allowing us to monitor participants' moment- simple and complex. Induction is simple in the sense that by-moment movements toward responses that are cued by we can easily and automatically associate causes with their associative and structured knowledge in a forced-choice effects, generalize properties to a category from a single inductive reasoning task. instance, or from one instance to another, and select actions in complex situations by recognizing commonalities with Knowledge types in category-based induction past experiences. Conversely, inductive reasoning can be Associative knowledge features most prominently in complex: how we generalize a property from a given connectionist, or neural network-based, models of category- exemplar depends on the nature of the property in question, based induction (Rogers & McClelland, 2004; Sloman, the circumstances under which the property is observed, and 1993; Sloutsky & Fisher, 2008). In Sloman's (1993) the nature of the relationships between categories. influential feature-based model, the known features of a Theories of category-based induction may be category can be represented as an activation vector applied distinguished in a similar manner. Simple, or associative, to the input nodes of a feed-forward neural network. Each models (Kruschke, 1992; Rescorla & Wagner, 1972; Rogers node is activated when its corresponding feature is & McClelland, 2004; Sloman, 1993; Sloutsky & Fisher, possessed by the target category. The network can be 2008) rely on similarity, contiguity, or co-occurrence presented with the premises of an inductive argument by between instances, and are often modelled using training it to activate its output node when presented with connectionist neural networks. Conversely, structured the features of categories which do have a novel property. 66 The outcomes of the trained network (i.e., its inferences) ratings of the strength of inductive arguments made under can be elicited by probing the input nodes with the features cognitive load, and under time pressure. Conversely, a of a novel category. The activation of the output node measure of structured knowledge predicts ratings of corresponds to the degree to which the network believes the argument strength otherwise novel category will have the property in question. Simple associative architectures are capable of capturing Conflict in category-based induction many aspects of human performance (Rolison, Evans, If both associative and structured knowledge play a role in Dennis, & Walsh, 2012). For instance, like human subjects, induction, a natural question is how associative and an associative network can be trained to rate similar structured knowledge interact when they support conflicting categories (which share many features) as more likely to beliefs. For instance, upon learning that a biological share a novel property, and properties that are present in a property is true of salmon, does one decide that this is also diverse range of categories as more likely to be found in a true of grizzly bears (strongly associated, but no structured novel category. Adding additional layers to the neural means of transmission for biological properties) or of networks allows them to account for further characteristics goldfish (weakly associated, but related taxonomically)? of human inference, such as sensitivity to different property Clearly, the decision depends on what kind of knowledge is types, such as “is a” and “has a” properties (Rogers & recruited, with purely associative knowledge in this case McClelland, 2004), as well as basic context-dependent leading to a non-normative inference. One possibility is that inferences (Sloutsky & Fisher, 2008). one or other representation is activated, depending on Murphy and Medin (1985) argue, however, that available time and cognitive capacity, in what Evans (2007) similarity-based approaches fail to capture the full flexibility labels a “preemptive conflict resolution” model. of people's intuitive theories about the relationships between Alternatively, both representations may compete, either with categories in specific domains. In particular, participants associative knowledge being recruited by default, which have been shown to be sensitive to property effects when must be inhibited in order for structured representations to reasoning inductively, such that the strength of an argument come online (“default interventionist models”), or with both is dependent on the kind of property projected. (Heit & representations activated in parallel (“parallel-competitive Rubinstein, 1994; Shafto, Coley, & Baldwin, 2007; Shafto, models”), leading to a conflict. Bright and Feeney (in prep.) Kemp, Baraff, Coley, & Tenenbaum, 2005). For instance, offer evidence that associative and structured knowledge do transmittable properties such as infectious diseases are conflict during category-based induction. In a triad task thought to be shared by animals that are related (Gelman & Markman, 1986), in which participants were ecologically, such as predators and prey in a food chain, asked which of two target species was most likely to share a whereas biological properties such as genes are shared only biological property given that it was found in a third base by animals that are close together in their evolutionary species, participants were more likely to fail to select a taxonomic tree. Such intuitions, in one domain, are captured structurally (i.e. taxonomically) related target when the by the similarity-coverage model (Osherson et al., 1990), alternative response was strongly associated to the base. which uses a taxonomic tree to capture intuitions about how Crucially, participants were less able to inhibit the properties are shared by related species in the natural world. association-driven response under cognitive load, or when More recently, structured Bayesian models have been lacking in semantic inhibitory control or working memory introduced (Griffiths & Tenenbaum, 2009; Kemp & capacity. Tenenbaum, 2009; Shafto, Kemp, Bonawitz, Coley, & Although the above results provide some support for a Tenenbaum, 2008; Tenenbaum, Griffiths, & Kemp, 2006), proposal that associative and structured knowledge can which are capable of describing flexible human performance compete during inductive reasoning, these conclusions are in a range of domains. These models require that, for each drawn from analysis of participants' responses – the end domain, a specific structure is generated to capture product of the reasoning process – and thus constitute only relationships between categories, such as food chains or an indirect measure of the underlying processes. The mouse- taxonomic trees, along with a generic probabilistic process tracking paradigm (Spivey, Grosjean, and Knoblich, 2005; by which properties can be transmitted. In the biological Freeman et al., 2011), on the other hand, provides a domain, such structures include unidirectional causal links powerful tool for measuring these processes as they unfold connecting prey to predators, or distance from a common during cognition. Monitoring the location of the mouse ancestor in a biological taxonomy. cursor whilst participants are choosing between choice Bright and Feeney (2015) argue that neither associative options located on opposite sides of the computer monitor, nor structured models are sufficient to account for all of the this method allows us to track the time-course of reasoning phenomena observed in category-based induction. They that leads to an inference. Mouse-tracking has been used to propose a hybrid theory in which both associative and reveal parallel competition effects on a range of simple structured knowledge can be used in reasoning. They cognitive and perceptual tasks (i.e. Freeman, Ambady, Rule, provide evidence that the two kinds of knowledge can be & Johnson, 2008; O’Hora, Dale, Piiroinen, & Connolly, dissociated. Namely, measures of the strength of the 2013; Spivey et al., 2005), in which participants are shown association between two categories predicts participant to be attracted simultaneously to competing response 67 options. In more complicated tasks, participants also have On each trial, participants were first primed with the kind been found to exhibit more discrete “changes of mind” of property they were to reason about: “gene” for tendencies by switching between choice options mid-trial experimental trials or “disease” for fillers. This prime (Dale & Duran, 2011; Freeman, 2013). In the present study, appeared in the center of the monitor for one second. For we use this technique to test for conflict between associative each experimental trial, participants were then informed that and structured knowledge in the triad task. Participants were the given gene (i.e. “Gene r3P”) is found in the bodies of asked to choose between projecting a biological property one of the two target species, which appeared as labeled from a base species to a correct target species belonging to images in the top left and right corners of the screen (Figure the same taxonomic group, or to an unrelated foil species. 1). The two species were randomly assigned to the left and Critically, the strength of the association between the base right positions on each trial and appeared for 1.6 seconds and the foil species is varied within subjects. If, as each. The targets then remained visible and participants suggested by Bright and Feeney (2015), responses cued by were asked which species they believed was most likely to associative knowledge must be inhibited in order to reason possess the gene, given that it was possessed by another on the basis of structured relations, we should expect to species. Participants were then instructed to click a observe an initial attraction toward the foil that is “START” button located in the bottom center of the proportional to the strength of the associative connection monitor, after which a fixation cross appeared for 1.5 between the foil and the target. On the other hand, if seconds, which was then replaced by a labeled image of the participants recruit one or other form of knowledge, we base species (Figure 1). At this point, the mouse cursor was should not expect to find an initial attraction to the foil, reset to the center of the start button and participants were regardless of the strength of association between the target given five seconds to respond by selecting one of the two and foil. target species labels with their mouse cursor. Participants were given five seconds to respond following presentation Method of the base category. Additionally, in line with previous mouse-tracking research, on trials in which participants did Stimuli not move the cursor away from the start button within 1.5 Participants were presented with a version of the inductive seconds of the onset of the base, they were shown a message triad task (Gelman & Markman, 1986). On each trial, reminding them that they were under time pressure. This participants were informed that a particular gene is was done to encourage participants to make their decision possessed by a given base species and were asked to decide while the mouse cursor was in motion. which of two candidate target species was most likely to possess the same gene (see Figure 1). The correct response was the species belonging to the same taxonomic group as the base (mammals, birds, insects, reptiles, or plants). The foil response belonged to a different taxonomic group than the base and was weakly, moderately, or strongly associated with the base. The strength of association was determined by prior testing. Across 27 experimental trials, nine base species were each presented three times, paired with the same correct response species but a different foil species on each occasion. An additional 27 filler trials were included, in which the property to be generalized was susceptibility to a given disease. Design and Procedure Forty four undergraduate students at Queen's University Belfast participated for course credit. Stimuli were custom programmed using the OpenSesame software package Figure 1: Screenshot of the experiment screen following (Mathôt, Schreij, & Theeuwes, 2011) and were presented on onset of the base species (“Killer Whales”). a computer monitor. The 27 experimental trials were presented in three blocks of nine trials each, interspersed Analysis with nine filler trials. Trials were randomly assigned to each Mouse trajectories were normalized to a standard co- block with the constraints that each base species appeared ordinate system, with all trials beginning at point [0, 0], and once in each block and each block contained three weakly, ending at point [1, 1.5] in the top right corner. Trajectories three moderately, and three strongly associated foil trials. in which the chosen response was on the left were reflected Trial order within blocks was randomized with the through the y-axis. For each trial, we calculated the time constraint that the same base could not appear twice within from target onset to a response (response time), the time three trials. from target onset to the beginning of the mouse movement 68 (initiation time), the deviation of mouse trajectory away changed direction toward the taxonomic option mid-trial. from a straight line to the response, measured in the Analysis of the distribution of the maximum deviation standard co-ordinate system (maximum deviation), and the statistic (Figure 2) revealed two normally-distributed frequency of changes of mouse trajectory direction on the x- subpopulations of responses, one centered on a deviation axis (x-flips). close to 0 (measured in the standard co-ordinate system) that Our analysis was restricted to trials on which the corresponded to movements directly toward the taxonomic taxonomically-related species was chosen. Thus, our data option, and a second centered around 1.4. The bimodality of set was unbalanced. Therefore, we conducted random this distribution was confirmed by calculating its bimodality effects linear regression modeling on our data. This analysis coefficient (Freeman & Dale, 2012), yielding a value of accounted for the clustering in our data by allowing for .636, well above the threshold of .555 usually interpreted as random intercepts at the subject and base species level indicating bimodality. We therefore fitted a two-sample (Baayen, Davidson & Bates, 2008). Main effects were finite mixture model to these maximum deviation values, in assessed on the basis of the -2 log-likelihood model fit order to classify trajectories as either “changes of mind” improvement, tested using the chi-square statistic. Main (maximum deviation > .827), or “direct to taxonomic effects were followed-up with Tukey pairwise comparisons option”. The two kinds of mouse trajectories are shown in between each group, with p values calculated using the Figure 3. normal approximation. Condition means and statistical tests for the measures Log transformations were used for analyses of response described above are shown in table 1. time, initiation time, and maximum deviation due to violations of normality. A Poisson regression model was used for the count of x-flips. A logistic random effects model was used for the analysis of choices in each condition. Results Results did not differ appreciably between the stimuli blocks, and so data were collapsed across blocks for analysis. Participants selected the correct taxonomically- related response on 81% of trials when the foil was weakly associated with the base, 61% of trials when moderately associated, and 57% when strongly associated. This suggests that participants were influenced by the associative strength of the foil option, such that stronger associations competed with structural knowledge. A logistic mixed effects model indicated a main effect of foil strength (ΔAIC Figure 2: Distribution of the maximum deviation from a = -86.4, -2LL χ2(2) = 90.4, p < .001). Pairwise comparisons straight line for all correct responses. revealed significant differences between the weak and moderate (t = 7.310, p < .001), and weak and strong foils (t Significant main effects were observed for maximum = 8.489, p < .001), but not between moderate and strong deviation (ΔAIC = -2.33, χ2(2) = 6.33, p = .042) and for foils (t = 1.428, p > .3). changes of mind (ΔAIC = -5.0, χ2(2) = 9.012, p = .011), with a marginally significant main effect for x-flips (ΔAIC Table 1: Descriptive statistics by condition and statistical = -1.471, χ2(2) = 5.471, p = .065). Pairwise comparisons tests assessing the main effects of condition. showed significant differences between weakly and strongly associated foils, with greater signs of conflict when strongly Foil associated, for maximum deviation (t = 2.44, p = .038), and association RT IT MD X-flips CoM for changes of mind (t = 2.69, p = .023), and a marginal Weak 1517 572 0.37 0.34 21.4% difference for x-flips (t = 2.23, p = .067). There was an Moderate 1493 583 0.35 0.32 19.3% additional significant difference between moderately and Strong 1513 567 0.45 0.41 27.8% strongly associated foils for changes of mind only (t = p .883 .558 .042 .065 .011 2.673, p = .020), with more changes of mind for strongly Note: RT = Response Time (msec); IT = Initiation Time associated foils. (msec); MD = Maximum Deviation; CoM = Percentage of trials classed as changes of mind. Discussion Inspection of the mouse cursor data revealed two kinds of Bright and Feeney (2015) showed that both associative and mouse trajectory: movements directly toward the taxonomic structured knowledge can serve as the basis for inductive option, and initial movements toward the foil option that reasoning. Bright and Feeney (in prep.) provide evidence 69 that both kinds of knowledge can conflict during reasoning. consistent with Bright and Feeney's (2015) demonstration Here, we found that participants generalized biological that reasoning is consistent with the structured Bayesian properties from a base species to a target species from the model when people have adequate time and mental same taxonomic group, rather than to a foil species, on the resources, but is driven by simpler associative knowledge majority of trials when the target was weakly associated otherwise. with the foil. The stronger the association between the base Our results may be challenged by theorists who favor and foil species, however, the more likely participants were purely associative models of induction (Rogers & to generalize the property to the foil instead. This was McClelland, 2004; Sloman, 1993; Sloutsky & Fisher, 2008). despite the base and foil species belonging to different Neural network models have been shown to capture some taxonomic groups. Analysis of the mouse cursor trajectories context sensitivity effects by means of input nodes encoding revealed that many participants were initially drawn to contextual features (Sloutsky & Fisher, 2008). However, the strongly-associated foil responses, even when they “change of mind” movements which characterized our ultimately selected the option that corresponded to mouse trajectory data are difficult to explain within this structured knowledge. framework. Simple feedforward neural networks of the type used in models of induction are static, in that they are probed once, and produce a single output pattern, providing no mechanism for reversals during a trial. More complex recurrent networks, on the other hand, with input and output changing over time, can capture the evolution of choices. However, extensive mouse-tracking research has demonstrated that conflict in such networks is continuous, with participants partially drawn toward two competing responses, selecting one response but curving toward the alternative (i.e. Freeman & Ambady, 2011; Freeman et al., 2008; Spivey et al., 2005). Discrete reversals have been demonstrated on tasks thought to involve the sequential operation of two processes (Barca & Pezzulo, 2015; Dale & Duran, 2011; Freeman, 2013; Freeman & Dale, 2012; Hindy Figure 3: Direct and “change of mind” mouse trajectories. & Spivey, 2008; Tomlinson, Bailey, & Bott, 2013), Averaged trajectories are shown in bold. suggesting that our results reflect the initial activation of associative knowledge and the subsequent retrieval of Our findings provide evidence against theories of structured knowledge. inductive reasoning that describe either an associative or To conclude, we believe that neither associative nor structured knowledge account. Rather, our present findings structured models alone are capable of describing the suggest that both forms of knowledge are engaged during processes underlying human inductive reasoning. Instead, reasoning, and that both can influence a single decision. At people draw upon two forms of knowledge representation, the outset, we raised the question of how precisely the two one associative, and easily accessed, and one structured, and forms of knowledge interact. Although our data do not requiring mental effort to utilize. Making use of structured provide a definitive answer, the patterns in the mouse knowledge appears to require the inhibition of associative trajectory data shown in Figure 3 suggest that the majority information, and as a result, participants were more likely to of trajectories went directly to the taxonomically related select a foil response if it was strongly associated with the target without any evidence of conflict. To the extent that base. Uniquely, our mouse trajectory results reflect the participants detect conflict between the choice options, such online inhibition of association-driven responses, necessary trajectories are consistent with pre-emptive conflict to reason according to structured knowledge. resolution (Evans, 2007). “Change of mind” responses, on the other hand, indicate online resolution of conflict. Further Acknowledgments research will be required to determine (a) why conflict is Eoin Travers is funded by a PhD studentship from the sometimes resolved pre-emptively and sometimes online, Department for Employment and Learning in Northern and (b) whether, when conflict is resolved online, both types Ireland. of knowledge are activated in parallel or in sequence. Bayesian models of inductive reasoning claim that people References represent structured relations between categories when reasoning, appropriate to the domain in question. By placing Baayen, R. H., Davidson, D. J., & Bates, D. M. 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