Human verifications: Computable with truth values outside logic.

Cognitive scientists treat verification as a computation in which descriptions that match the relevant situation are true, but otherwise false. The claim is controversial: The logician Gödel and the physicist Penrose have argued that human verifications are not computable. In contrast, the theory of mental models treats verification as computable, but the two truth values of standard logics, true and false, as insufficient. Three online experiments (n = 208) examined participants' verifications of disjunctive assertions about a location of an individual or a journey, such as: 'You arrived at Exeter or Perth'. The results showed that their verifications depended on observation of a match with one of the locations but also on the status of other locations (Experiment 1). Likewise, when they reached one destination and the alternative one was impossible, their use of the truth value: could be true and could be false increased (Experiment 2). And, when they reached one destination and the only alternative one was possible, they used the truth value, true and it couldn't have been false, and when the alternative one was impossible, they used the truth value: true but it could have been false (Experiment 3). These truth values and those for falsity embody counterfactuals. We implemented a computer program that constructs models of disjunctions, represents possible destinations, and verifies the disjunctions using the truth values in our experiments. Whether an awareness of a verification's outcome is computable remains an open question.

Recursion in programs, thought, and language.

This article presents a theory of recursion in thinking and language. In the logic of computability, a function maps one or more sets to another, and it can have a recursive definition that is semi-circular, i.e., referring in part to the function itself. Any function that is computable - and many are not - can be computed in an infinite number of distinct programs. Some of these programs are semi-circular too, but they needn't be, because repeated loops of instructions can compute any recursive function. Our theory aims to explain how naive individuals devise informal programs in natural language, and is itself implemented in a computer program that creates programs. Participants in our experiments spontaneously simulate loops of instructions in kinematic mental models. They rely on such loops to compute recursive functions for rearranging the order of cars in trains on a track with a siding. Kolmogorov complexity predicts the relative difficulty of abducing such programs - for easy rearrangements, such as reversing the order of the cars, to difficult ones, such as splitting a train in two and interleaving the two resulting halves (equivalent to a faro shuffle). This rearrangement uses both the siding and part of the track as working memories, shuffling cars between them, and so it relies on the power of a linear-bounded computer. Linguistic evidence implies that this power is more than necessary to compose the meanings of sentences in natural language from those of their grammatical constituents.

Facts and Possibilities: A Model-Based Theory of Sentential Reasoning.

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities.

Episodes, events, and models.

We describe a novel computational theory of how individuals segment perceptual information into representations of events. The theory is inspired by recent findings in the cognitive science and cognitive neuroscience of event segmentation. In line with recent theories, it holds that online event segmentation is automatic, and that event segmentation yields mental simulations of events. But it posits two novel principles as well: first, discrete episodic markers track perceptual and conceptual changes, and can be retrieved to construct event models. Second, the process of retrieving and reconstructing those episodic markers is constrained and prioritized. We describe a computational implementation of the theory, as well as a robotic extension of the theory that demonstrates the processes of online event segmentation and event model construction. The theory is the first unified computational account of event segmentation and temporal inference. We conclude by demonstrating now neuroimaging data can constrain and inspire the construction of process-level theories of human reasoning.

Logic, probability, and human reasoning.

This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction.

Naive Probability: Model-Based Estimates of Unique Events.

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.

Causal reasoning with mental models.

This paper outlines the model-based theory of causal reasoning. It postulates that the core meanings of causal assertions are deterministic and refer to temporally-ordered sets of possibilities: A causes B to occur means that given A, B occurs, whereas A enables B to occur means that given A, it is possible for B to occur. The paper shows how mental models represent such assertions, and how these models underlie deductive, inductive, and abductive reasoning yielding explanations. It reviews evidence both to corroborate the theory and to account for phenomena sometimes taken to be incompatible with it. Finally, it reviews neuroscience evidence indicating that mental models for causal inference are implemented within lateral prefrontal cortex.

The probabilities of unique events.

Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable.

Hidden conflicts: explanations make inconsistencies harder to detect.

A rational response to an inconsistent set of propositions is to revise it in a minimal way to restore consistency. A more important psychological goal is usually to create an explanation that resolves the inconsistency. We report five studies showing that once individuals have done so, they find inconsistencies harder to detect. Experiment 1 established the effect when participants explained inconsistencies, and Experiment 2 eliminated the possibility that the effect was a result of demand characteristics. Experiments 3a and 3b replicated the result, and showed that it did not occur in control groups that evaluated (or justified) which events in the pairs of assertions were more surprising. Experiment 4 replicated the previous findings, but the participants carried out all the conditions acting as their own controls. In all five studies, control conditions established that participants were able to detect comparable inconsistencies. Their explanations led them to re-interpret the generalizations as holding by default, and so they were less likely to treat the pairs of assertions as inconsistent. Explanations can accordingly undo the devastating consequences of logical inconsistencies, but at the cost of a subsequent failure to detect them.

The need to explain.

How do reasoners deal with inconsistencies? James (1907) believed that the rational solution is to revise your beliefs and to do so in a minimal way. We propose an alternative: You explain the origins of an inconsistency, which has the side effect of a revision to your beliefs. This hypothesis predicts that individuals should spontaneously create explanations of inconsistencies rather than refute one of the assertions and that they should rate explanations as more probable than refutations. A pilot study showed that participants spontaneously explain inconsistencies when they are asked what follows from inconsistent premises. In three subsequent experiments, participants were asked to compare explanations of inconsistencies against minimal refutations of the inconsistent premises. In Experiment 1, participants chose which conclusion was most probable; in Experiment 2 they rank ordered the conclusions based on their probability; and in Experiment 3 they estimated the mean probability of the conclusions' occurrence. In all three studies, participants rated explanations as more probable than refutations. The results imply that individuals create explanations to resolve an inconsistency and that these explanations lead to changes in belief. Changes in belief are therefore of secondary importance to the primary goal of explanation.

Harry Potter and the sorcerer's scope: latent scope biases in explanatory reasoning.

What makes a good explanation? We examine the function of latent scope, i.e., the number of unobserved phenomena that an explanation can account for. We show that individuals prefer narrow latent scope explanations-those that account for fewer unobserved effects-to broader explanations. In Experiments 1a-d, participants found narrow latent scope explanations to be both more satisfying and more likely. In Experiment 2 we directly manipulated base rate information and again found a preference for narrow latent scope explanations. Participants in Experiment 3 evaluated more natural explanations of unexpected observations, and again displayed a bias for narrow latent scope explanations. We conclude by considering what this novel bias tells us about how humans evaluate explanations and engage in causal reasoning.

When one model casts doubt on another: a levels-of-analysis approach to causal discounting.

Discounting is a phenomenon in causal reasoning in which the presence of one cause casts doubt on another. We provide a survey of the descriptive and formal models that attempt to explain the discounting process and summarize what current models do not account for and where room for improvement exists. We propose a levels-of-analysis framework organized around 2 types of models of causal discounting: computational and algorithmic models. Theories of causal discounting at the computational level attempt to provide normative, prescriptive explanations for discounting behavior, and they build on other normative frameworks like formal logic and probability theory. However, they tend not to focus on how those computations are carried out. Theories of discounting at the algorithmic level focus on the functions and representations from which discounting behavior emerges (i.e., they examine how problems are solved). We use this framework to identify gaps in the current literature and avenues for future model development.

Determinants of cognitive variability.

Henrich et al. address how culture leads to cognitive variability and recommend that researchers be critical about the samples they investigate. However, there are other sources of variability, such as individual strategies in reasoning and the content and context on which processes operate. Because strategy and content drive variability, those factors are of primary interest, while culture is merely incidental.

The function and representation of concepts.

Machery has usefully organized the vast heterogeneity in conceptual representation. However, we believe his argument is too narrow in tacitly assuming that concepts are comprised of only prototypes, exemplars, and theories, and also that its eliminative aspect is too strong. We examine two exceptions to Machery's representational taxonomy before considering whether doing without concepts is a good idea.

Feedback design for the control of a dynamic multitasking system: dissociating outcome feedback from control feedback.

OBJECTIVE: We distinguish outcome feedback from control feedback to show that suboptimal performance in a dynamic multitasking system may be caused by limits inherent to the information provided rather than human resource limits. BACKGROUND: Tardast is a paradigm for investigating human multitasking behavior, complex system management, and supervisory control. Prior research attributed the suboptimal performance of Tardast operators to poor strategic task management. METHODS: We varied the nature of performance feedback in the Tardast paradigm to compare continuous, cumulative feedback (global feedback) on performance outcome with feedback limited to the most recent system state (local feedback). RESULTS: Participants in both conditions improved with practice, but those with local feedback performed better than those with global feedback. An eye gaze analysis showed increased visual attention directed toward the feedback display in the local feedback condition. CONCLUSION: Predicting performance in the control of a dynamic multitasking system requires understanding the interactions between embodied cognition, the task being performed, and characteristics of performance feedback. In the current case, at least part of what had been diagnosed as a deficit caused by limited cognitive resources has been shown to be data limited. APPLICATION: Perfect outcome feedback can provide inadequate control feedback. Instances of suboptimal performance can be alleviated by better feedback design that takes into account the temporal dynamics of the human-system interaction.