Temporal and spatial relations in sentential reasoning

The mental model theory postulates that the meanings of assertions, and knowledge about their context can modulate the logical meaning of sentential connectives, such as "if" and "or". One known effect of modulation is to block the representation of possibilities to which a proposition refers. But, modulation should also add relational information, such as temporal order, to models of possibilities. Three experiments tested this prediction. Experiment 1 showed that individuals spontaneously matched the tense of their conclusions (in Portuguese) to embody implied, but unexpressed, temporal relations in conditional premises. Experiment 2 demonstrated the same phenomenon in inferences from disjunctions. Experiment 3 showed that the number of such implicit relations in inferences from conditionals affects both accuracy and the speed of reasoning. These results support the modulation hypothesis.     

On the generation and evaluation of inferences from single premises

A theory of how individuals construct mental models to draw inferences from single premises was tested in three experiments. Experiment 1 confirmed a counterintuitive prediction that it is easier to generate inferences between conditionals and disjunctions than it is to evaluate them. Experiment 2 replicated this finding, but an advantage found in the first experiment for conditional-to-disjunction over disjunction-to-conditional inferences was removed with different sentence contents. Experiment 3 showed that disjunction-to-conditional inferences were facilitated when premises expressed familiar indicative relations, whereas conditional-to-disjunction inferences were facilitated when premises expressed causal relations. The results indicate that small changes in task format can have large effects on the strategies that people use to represent and reason about different sentential connectives. We discuss the potential for theories other than mental models to account for these results. We argue that, despite the important role played by single-premise inferences in paraphrasing logical forms during inference, mental logic theories cannot account for the results reported here.     

Transitive and pseudo-transitive inferences

Given that A is longer than B, and that B is longer than C, even 5-year-old children can infer that A is longer than C. Theories of reasoning based on formal rules of inference invoke simple axioms ("meaning postulates") to capture such transitive inferences. An alternative theory proposes instead that reasoners construct mental models of the situation described by the premises in order to draw such inferences. An unexpected consequence of the model theory is that if adult reasoners construct simple models of typical situations, then they should infer transitive relations where, in certain cases, none exists. We report four studies corroborating the occurrence of these "pseudo-transitive" fallacies. Experiment 1 established that individuals' diagrams of certain non-transitive relations yield transitive conclusions. Experiment 2 showed that these premises also give rise to fallacious transitive inferences. Experiment 3 established that when the context suggested alternatives to the simple models, the participants made fewer errors. Experiment 4 showed that tense is an important aspect of meaning which affects whether individuals draw transitive conclusions. We discuss the implications of these results for various theories of reasoning.     

Illusions in quantified reasoning: How to make the impossible seem possible, and vice versa

The mental model theory postulates that reasoners build models of the situations described in premises, and that these models normally represent only what is true. The theory has an unexpected consequence. It predicts the existence of illusions in inferences. Certain inferences should have compelling but erroneous conclusions. Two experiments corroborated the occurrence of such illusions in inferences about what is possible from disjunctions of quantified assertions, such as, "at least some of the plastic beads are not red." Experiment 1 showed that participants erroneously inferred that impossible situations were possible, and that possible situations were impossible, but that they performed well with control problems based on the same premises. Experiment 2 corroborated these findings in inferences from assertions based on dyadic relations, such as, "all the boys played with the girls."     

Reasoning from connectives and relations between entities

This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals—for instance, Ann is taller than Beth if and only if Beth is taller than Cath—than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results.     

Mental simulation and argument

When a quantified premise such as: Everyone loves anyone who loves someone, occurs with a premise such as: Anne loves Beth, it follows immediately that everyone loves Anne. It also follows that Carol loves Diane, where these two individuals are in the domain of discourse. According to the theory of mental models, this inference requires the quantified premise to be used again to update a model of specific individuals. The paper reports four experiments examining such iterative inferences. Experiment 1 confirmed that they are harder than immediate inferences. Experiment 2 extended the finding to negative inferences, i.e., granted that Anne does not love Beth, it follows from the quantified premise that Carol does not love Diane. Experiment 3 established that intermediate steps referring to specific individuals are accepted more readily than intermediate steps referring to quantified variables. Experiment 4 showed that the participants' written justifications corroborated the model theory.     

Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared

The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. The strategy selection learning theory specifies how people select strategies from this repertoire. The theory assumes that individuals select strategies proportional to their subjective expectations of how well the strategies solve particular problems; such expectations are assumed to be updated by reinforcement learning. The theory is compared with an adaptive network model that assumes people make inferences by integrating information according to a connectionist network. The network's weights are modified by error correction learning. The theories were tested against each other in 2 experimental studies. Study 1 showed that people substantially improved their inferences through feedback, which was appropriately predicted by the strategy selection learning theory. Study 2 examined a dynamic environment in which the strategies' performances changed. In this situation a quick adaptation to the new situation was not observed; rather, individuals got stuck on the strategy they had successfully applied previously. This "inertia effect" was most strongly predicted by the strategy selection learning theory.     

Disjunctive illusory inferences and how to eliminate them

The mental model theory of reasoning postulates that individuals construct mental models of the possibilities in which the premises of an inference hold and that these models represent what is true but not what is false. An unexpected consequence of this assumption is that certain premises should yield systematically invalid inferences. This prediction is unique among current theories of reasoning, because no alternative theory, whether based on formal rules of inference or on probabilistic considerations, predicts these illusory inferences. We report three studies of novel illusory inferences that depend on embedded disjunctions—for example, premises of this sort: A or else (B or else C). The theory distinguishes between those embedded disjunctions that should yield illusions and those that should not. In Experiment 1, we corroborated this distinction. In Experiment 2, we extended the illusory inferences to a more stringently controlled set of problems. In Experiment 3, we established a novel method for reducing illusions by calling for participants to make auxiliary inferences.     

Probabilistically Valid Inference of Covariation From a Single x,y Observation When Univariate Characteristics Are Known

Participants were asked to draw inferences about correlation from single x,y observations. In Experiment 1 statistically sophisticated participants were given the univariate characteristics of distributions of x and y and asked to infer whether a single x, y observation came from a correlated or an uncorrelated population. In Experiment 2, students with a variety of statistical backgrounds assigned posterior probabilities to five possible populations based on single x, y observations, again given knowledge of the univariate statistics. In Experiment 3, statistically naïve participants were given a problem analogous to that given in Experiment 1, framed verbally. Experiment 4 replicated Experiment 3 but added an "impossible to determine" response option. Models that rely on computing sample correlations make no predictions about these investigations. From a Bayesian perspective, participants' inferences in all four experiments tended to make probabilistically valid inferences as long as the single datum was directional. The results are discussed in light of the Brunswikian notion of vicarious functioning.     

Deductive rationality in validating and testing conditional inferences

We asked people to validate conditional inferences (e.g., "A, therefore C" with "if A then C"). People are more likely to look for falsifications ("A and not-C") versus confirmations ("A and C") given a forced choice. Second, falsification rates are lower for logically valid versus invalid inferences. Logically valid inferences are inferences that follow necessarily. Experiment 1 (N = 96) shows that emphasising this logicality constraint increases falsification rates in the validation task and corroborates that validation-by-falsification increases logically correct inference evaluations. Experiment 2 (N = 41) corroborates the other way round that people who are more likely to make logically correct evaluations, show higher falsification performance in the validation task. The results support mental-models theory and suggest alternative theories similarly need to specify how people would go about looking for counterexamples. We proffer such a specification for two alternatives to the model theory. (PsycINFO Database Record (c) 2008 APA, all rights reserved).     

Concessive and semifactual interpretations during reasoning with multiple conditionals

The present research evaluates how people integrate factual ‘if then’ and semifactual ‘even if’ conditional premises in an inference task. The theory of mental models establishes that semifactual statements are represented by two mental models with different epistemic status: ‘A & B’ is conjectured and ‘not-A & B’ is presupposed. However, following the principle of cognitive economy in tasks with a high working memory load such as reasoning with multiple conditionals, people could simplify the deduction process in two ways, by discarding: (a) the presupposed case and/or (b) the epistemic status information. In Experiment 1 and Experiment 2, we evaluated each of these hypotheses. In Experiment 1, participants make inferences from two conditionals: two factual conditionals or one factual and one semifactual, with different representations. In Experiment 2, participants make inferences with a factual conditional followed by two different semifactual conditionals that share the same representations but differ in their epistemic status. Accuracy and latency data suggest that people think of both the conjectured and the presupposed situations, but do not codify the epistemic status of either when the task does not require it. The results are discussed through theoretical predictions about how people make inferences from different connected conditionals.     

Inferences from memory: strategy- and exemplar-based judgment models compared

What are the cognitive processes underlying people's inferences from memory? To provide an answer, the exemplar-based approach to predicting people's inferences is tested against the strategy-based approach. Exemplar models assume that people make inferences about objects by retrieving similar objects from memory. In contrast, the strategy-based approach assumes that people select cognitive strategies that make inferences based on abstracted knowledge and information the inference situation provides. In Experiment 1, in which dichotomous feedback on the level of pair-comparisons was provided, almost all participants were classified as using a simple lexicographic strategy. In Experiment 2, in which continuous feedback for single objects was provided, most participants were classified as using a compensatory strategy. Both experiments suggest that the strategy-based approach is more suitable for predicting people's inferences from memory than the exemplar-based approach. The strategy-based approach shows how people adapt to inference situations by selecting different cognitive strategies.     

Young children infer causal strength from probabilities and interventions

We examine the interaction of two cues that children use to make judgments about cause-effect relations: probabilities and interventions. Children were shown a "detector" that lit up and played music when a block was placed on its surface. We varied the probabilistic effectiveness of the block, as well as whether the experimenter or the child was performing the interventions. In Experiment 1, we found that children can use probabilistic evidence to make inferences about causal strength. However, when the results of their own interventions are in conflict with the overall frequencies, preschoolers favor the results of their own interventions. In Experiment 2, children used probabilistic evidence to infer a hidden causal mechanism. Though they again gave preference to their own interventions, they did not do so when their interventions were explicitly confounded by an alternative cause.     

Working memory for relations among objects

Across many areas of study in cognition, the capacity of working memory (WM) is widely agreed to be roughly three to five items: three to five objects (i.e., bound collections of object features) in the literature on visual WM or three to five role bindings (i.e., objects in specific relational roles) in the literature on memory and reasoning. Three experiments investigated the capacity of observers’ WM for the spatial relations among objects in a visual display, and the results suggest that the “items” in WM are neither simply objects nor simply role bindings. The results of Experiment 1 are most consistent with a model that treats an “item” in visual WM as an object, along with the roles of all its relations to one other object. Experiment 2 compared observers’ WM for object size with their memory for relative size and provided evidence that observers compute and store objects’ relations per se (rather than just absolute size) in WM. Experiment 3 tested and confirmed several more nuanced predictions of the model supported by Experiment 1. Together, these findings suggest that objects are stored in visual WM in pairs (along with all the relations between the objects in a pair) and that, from the perspective of WM, a given object in one pair is not the same “item” as that same object in a different pair.     

Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference.     

Adjusting Social Inferences in Familiar and Unfamiliar Domains: The Generality of Response to Situational Pragmatics

Two experiments investigated the influence of situational pragmatics on the selective use of specific instances and generalized knowledge structures to make social inferences. In Experiment 1, social inferences were made in an unfamiliar domain similar in structure to a typical situation of social greetings and address, but devoid of useful cues to social schemas. Participants were told that either one or another of the features of the situation was more pragmatically important for deriving inferences about appropriate social behaviour; consistent with predictions from a computational model of analogical mapping (ACME), they made reliable inferences based on analogies to specific instances, with the situational importance of relations guiding the selection of the optimal analogue. In Experiment 2, social inferences were examined in the more familiar domain of predicting social behavior between low and high status persons and between members of an ingroup and an outgroup in Japan. The availability of specific examples was varied, as was the perceived importance of status and group membership. The situation was isomorphic to that in the first experiment, except for the availability of generalized knowledge structures to guide inferences. Participants made relatively veridical inferences that were sensitive to variations in the pragmatic importance of dimensions. Provision of specific analogues had little impact on inferences, suggesting that participants were relying instead on more general and cross-culturally applicable knowledge about adjusting social relations according to situational pragmatics.     

Reasoning about relations

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. (a) The structure of mental models is iconic as far as possible. (b) The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. (c) Individuals tend to construct only a single, typical model. (d) They spontaneously develop their own strategies for relational reasoning. (e) Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle.     

Infants learn about objects from statistics and people

In laboratory experiments, infants are sensitive to patterns of visual features that co-occur (e.g., Fiser & Aslin, 2002). Once infants learn the statistical regularities, however, what do they do with that knowledge? Moreover, which patterns do infants learn in the cluttered world outside of the laboratory? Across 4 experiments, we show that 9-month-olds use this sensitivity to make inferences about object properties. In Experiment 1, 9-month-old infants expected co-occurring visual features to remain fused (i.e., infants looked longer when co-occurring features split apart than when they stayed together). Forming such expectations can help identify integral object parts for object individuation, recognition, and categorization. In Experiment 2, we increased the task difficulty by presenting the test stimuli simultaneously with a different spatial layout from the familiarization trials to provide a more ecologically valid condition. Infants did not make similar inferences in this more distracting test condition. However, Experiment 3 showed that a social cue did allow inferences in this more difficult test condition, and Experiment 4 showed that social cues helped infants choose patterns among distractor patterns during learning as well as during test. These findings suggest that infants can use feature co-occurrence to learn about objects and that social cues shape such foundational learning in distraction-filled environments.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.