Kinematic mental simulations in abduction and deduction

Reasoning about possibilities: Modal logics, possible worlds, and mental models

Everyone reasons about possibilities. This article explains how they could do so using mental models. The theory makes four major claims: 1. Correct inferences are necessary, referring only to facts or possibilities to which the premises refer and not ruling any of them out, for example: She left or hid; Therefore, it's possible that she left and possible that she hid. 2. A possibility such as that she hid, which is represented in an intuitive model, presupposes the possibility that it did not occur, she did not hide, which, if reasoners deliberate, is represented in the resulting model. 3. Reasoners condense consistent possibilities, such as the earlier pair, into one possibility: it is possible that she left and she hid. 4. Inconsistencies, such as she left or hid, and she neither left nor hid, refer to no possibilities whatsoever - they have an empty model - and so their only effects are local. Hence, any inference can be withdrawn with impunity if there is knowledge to the contrary. Experiments have corroborated each of these principles. They are incompatible with four essentials of standard modal logics, which concern deductions based on "possible" or "necessary". Their formal deductions correspond to valid inferences, which have no counterexamples in which the premises are true but the conclusion is false. And so the article examines the differences between the two approaches, and explores the adaptation of a modal logic to account for correct human reasoning. Its feasibility is an open question.

How people think about the truth of hypothetical impossibilities

People can think about hypothetical impossibilities and a curious observation is that some impossible conditionals seem true and others do not. Four experiments test the proposal that people think about impossibilities just as they do possibilities, by attempting to construct a consistent simulation of the impossible conjecture with its suggested outcome, informed by their knowledge of the real world. The results show that participants judge some impossible conditionals true with one outcome, for example, "if people were made of steel, they would not bruise easily" and false with the opposite outcome, "if people were made of steel they would bruise easily", and others false with either outcome, for example, "if houses were made of spaghetti, their engines would (not) be noisy". However, they can sometimes judge impossible conditionals true with either outcome, for example, "if Plato were identical to Socrates, he would (not) have a small nose", or "if sheep and wolves were alike, they would (not) eat grass". The results were observed for judgments about what could be true (Experiments 1 and 4), judgments of degrees of truth (Experiment 2), and judgments of what is true (Experiment 3). The results rule out the idea that people evaluate the truth of a hypothetical impossibility by relying on cognitive processes that compare the probability of each conditional to its counterpart with the opposite outcome.

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.

Reasoning About Want

No present theory explains the inferences people draw about the real world when reasoning about "bouletic" relations, that is, predicates that express desires, such as want in "Lee wants to be in love". Linguistic accounts of want define it in terms of a relation to a desirer's beliefs, and how its complement is deemed desirable. In contrast, we describe a new model-based theory that posits that by default, desire predicates such as want contrast desires against facts. In particular, A wants P implies by default that P is not the case, because you cannot want what is already true. On further deliberation, reasoners may infer that A believes, but does not know for certain, that P is not the case. The theory makes several empirical predictions about how people interpret, assess the consistency of, and draw conclusions from desire predicates like want. Seven experiments tested and validated the theory's central predictions. We assess the theory in light of recent proposals of desire predicates.

How poetry evokes emotions

Poetry evokes emotions. It does so, according to the theory we present, from three sorts of simulation. They each can prompt emotions, which are communications both within the brain and among people. First, models of a poem's semantic contents can evoke emotions as do models that occur in depictions of all kinds, from novels to perceptions. Second, mimetic simulations of prosodic cues, such as meter, rhythm, and rhyme, yield particular emotional states. Third, people's simulations of themselves enable them to know that they are engaged with a poem, and an aesthetic emotion can occur as a result. The three simulations predict certain sorts of emotion, e.g., prosodic cues can evoke basic emotions of happiness, sadness, anger, and anxiety. Empirical evidence corroborates the theory, which we relate to other accounts of poetic emotions.

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.

Learning Intuitive Physics and One-Shot Imitation Using State-Action-Prediction Self-Organizing Maps

Human learning and intelligence work differently from the supervised pattern recognition approach adopted in most deep learning architectures. Humans seem to learn rich representations by exploration and imitation, build causal models of the world, and use both to flexibly solve new tasks. We suggest a simple but effective unsupervised model which develops such characteristics. The agent learns to represent the dynamical physical properties of its environment by intrinsically motivated exploration and performs inference on this representation to reach goals. For this, a set of self-organizing maps which represent state-action pairs is combined with a causal model for sequence prediction. The proposed system is evaluated in the cartpole environment. After an initial phase of playful exploration, the agent can execute kinematic simulations of the environment's future and use those for action planning. We demonstrate its performance on a set of several related, but different one-shot imitation tasks, which the agent flexibly solves in an active inference style.

Causal conflicts produce domino effects

Inconsistent beliefs call for revision-but which of them should individuals revise? A long-standing view is that they should make minimal changes that restore consistency. An alternative view is that their primary task is to explain how the inconsistency arose. Hence, they are likely to violate minimalism in two ways: they should infer more information than is strictly necessary to establish consistency and they should reject more information than is strictly necessary to establish consistency. Previous studies corroborated the first effect: reasoners use causal simulations to build explanations that resolve inconsistencies. Here, we show that the second effect is true too: they use causal simulations to reject more information than is strictly necessary to establish consistency. When they abandon a cause, the effects of the cause topple like dominos: Reasoners tend to deny the occurrence of each subsequent event in the chain. Four studies corroborated this prediction.

Explanatory completeness

All explanations are incomplete, but reasoners think some explanations are more complete than others. To explain this behavior, we propose a novel theory of how people assess explanatory incompleteness. The account assumes that reasoners represent explanations as causal mental models - iconic representations of possible arrangements of causes and effects. A complete explanation refers to a single integrated model, whereas an incomplete explanation refers to multiple models. The theory predicts that if there exists an unspecified causal relation - a gap - anywhere within an explanation, reasoners must maintain multiple models to handle the gap. They should treat such explanations as less complete than those without a gap. Four experiments provided participants with causal descriptions, some of which yield one explanatory model, e.g., A causes B and B causes C, and some of which demand multiple models, e.g., A causes X and B causes C. Participants across the studies preferred one-model descriptions to multiple-model ones on tasks that implicitly and explicitly required them to assess explanatory completeness. The studies corroborate the theory. They are the first to reveal the mental processes that underlie the assessment of explanatory completeness. We conclude by reviewing the theory in light of extant accounts of causal reasoning.

Reasoning about Durations

A set of assertions is consistent provided they can all be true at the same time. Naive individuals could prove consistency using the formal rules of a logical calculus, but it calls for them to fail to prove the negation of one assertion from the remainder in the set. An alternative procedure is for them to use an intuitive system (System 1) to construct a mental model of all the assertions. The task should be easy in this case. However, some sets of consistent assertions have no intuitive models and call for a deliberative system (System 2) to construct an alternative model. Formal rules and mental models therefore make different predictions. We report three experiments that tested their respective merits. The participants assessed the consistency of temporal descriptions based on statements using "during" and "before." They were more accurate for consistent problems with intuitive models than for those that called for deliberative models. There was no robust difference in accuracy between consistent and inconsistent problems. The results therefore corroborated the model theory.

Possibilities and the parallel meanings of factual and counterfactual conditionals

The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

Updating and reasoning: Different processes, different models, different functions

Two issues should be addressed to refine and extend the distinction between temporal updating and reasoning advocated by Hoerl & McCormack. First, do the mental representations constructed during updating differ from those used for reasoning? Second, are updating and reasoning the only two processes relevant to temporal thinking? If not, is a dual-systems framework sensible? We address both issues below.

Possibilities as the foundation of reasoning

Reasoning about possibilities is fundamental in daily life. Yet, it has been little studied in psychology. We present a psychological theory in which it is the foundation of human reasoning. The theory explains how possibilities have distinct interpretations (deontic, epistemic, and alethic), how people represent them in models, and how these models yield inferences. Key principles are that the semantics of possibilities are the same finitary alternatives underlying probabilities, that speech acts can create obligations inexpressible as probabilities, that compound assertions - conditionals and disjunctions - refer to conjunctions of possibilities holding in default of knowledge to the contrary, and that mental models condense multiple consistent possibilities into one. The theory is incompatible with all normal modal logics and with probabilistic logic. Yet, experiments have corroborated its predictions. The article discusses its precursors, rivals, and potentials.

Simulation in children's conscious recursive reasoning

When do children acquire the ability to understand recursion-that is, repeated loops of actions, as in cookery recipes or computer programs? Hitherto, studies have focused either on unconscious recursions in language and vision or on the difficulty of conscious recursions-even for adults-when learning to program. In contrast, we examined 10- to 11-year-old fifth-graders' ability to deduce the consequences of loops of actions in informal algorithms and to create such algorithms for themselves. In our experiments, the children tackled problems requiring the rearrangement of cars on a toy railway with a single track and a siding-an environment that in principle allows for the execution of any algorithm-that is, it has the power of a universal Turing machine. The children were not allowed to move the cars, so each problem's solution called for them to envision the movements of cars on the track. We describe a theory of recursive thinking, which is based on kinematic simulations and which we have implemented in a computer program embodying mental models of the cars and track. Experiment 1 tested children's ability to deduce rearrangements of the cars in a train from descriptions of algorithms containing a single loop of actions. Experiment 2 assessed children's spontaneous creation of similar sorts of algorithms. The results showed that fifth-grade children with no training in computer programming have systematic abilities to deduce from and to create informal recursive algorithms.

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.

Fiction: Simulation of Social Worlds

Fiction is the simulation of selves in interaction. People who read it improve their understanding of others. This effect is especially marked with literary fiction, which also enables people to change themselves. These effects are due partly to the process of engagement in stories, which includes making inferences and becoming emotionally involved, and partly to the contents of fiction, which include complex characters and circumstances that we might not encounter in daily life. Fiction can be thought of as a form of consciousness of selves and others that can be passed from an author to a reader or spectator, and can be internalized to augment everyday cognition.

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.

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.