We present a framework for the rational analysis of elemental causal induction – learning about the existence of a relationship between a single cause and effect – based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, ∆P and causal power, both estimate causal strength, and introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between ∆P and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either ∆P or causal power.

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. You reason about conditional relations because much of your knowledge is conditional. If you get caught speeding, then you pay a fine. If you have an operation, then you need time to recuperate. If you have money in the bank, then you can cash a check. Conditional reasoning is a central part of thinking, yet people do not always reason correctly. The lawyer Jan Schlictmann in a celebrated trial (see Harr, 1995, pp. 361–362) elicited the following information from an expert witness about the source of a chemical pollutant trichloroethylene (TCE):

The dynamics model, which is based on L. Talmy’s (1988) theory of force dynamics, characterizes causation as a pattern of forces and a position vector. In contrast to counterfactual and probabilistic models, the dynamics model naturally distinguishes between different cause-related concepts and explains the induction of causal relationships from single observations. Support for the model is provided in experiments in which participants categorized 3-D animations of realistically rendered objects with trajectories that were wholly determined by the force vectors entered into a physics simulator. Experiments 1–3 showed that causal judgments are based on several forces, not just one. Experiment 4 demonstrated that people compute the resultant of forces using a qualitative decision rule. Experiments 5 and 6 showed that a dynamics approach extends to the representation of social causation. Implications for the relationship between causation and time are discussed.

Research suggests that causal judgment is influenced primarily by counterfactual or covariational reasoning. In contrast, the author of this article develops judgment dissociation theory (JDT), which predicts that these types of reasoning differ in function and can lead to divergent judgments. The actuality principle proposes that causal selections focus on antecedents that are sufficient to generate the actual outcome. The substitution principle proposes that ad hoc categorization plays a key role in counterfactual and covariational reasoning such that counterfactual selections focus on antecedents that would have been sufficient to prevent the outcome or something like it and covariational selections focus on antecedents that yield the largest increase in the probability of the outcome or something like it. The findings of 4 experiments support JDT but not the competing counterfactual and covariational accounts. If causation is the cement of the universe, as the philosopher David Hume (1740/1938) put it, then it is fair to say that causal knowledge is the cement that binds together each person’s representational universe. Causal reasoning—the process that generates this glue—confers many functional advantages. In virtually every sphere of human interest, our abilities to learn and categorize

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 principles.

According to the transitive dynamics model, people can construct causal structures by linking together configurations of force. The predictions of the model were tested in two experiments in which participants generated new causal relationships by chaining together two (Experiment 1) or three (Experiment 2) causal relations. The predictions of the transitive dynamics model were compared against those of Goldvarg and Johnson-Laird’s model theory (Goldvarg & Johnson-Laird, 2001). The transitive dynamics model consistently predicted the overall causal relationship drawn by participants for both types of causal chains, and, when compared to the model theory, provided a better fit to the data. The results suggest that certain kinds of causal reasoning may depend on force dynamic—rather than on purely logical or statistical—representations.

Dynamics and the perception of causal events To imagine possible events, we use our knowledge of causal relationships. To look deep into the past and infer events that were not witnessed, we use causal relationships as well. We also use causal knowledge to infer what can not be directly seen in the present, for instance, the existence of planets around distant stars, or the presence of subatomic particles. Knowledge of causal relationships allows us to go beyond the immediate here and now. In this chapter I introduce a new theoretical framework for how this very basic concept might be mentally represented. In effect, I propose an epistemological theory of causation, that is, a theory that specifies the nature of people’s knowledge of causation, the notion of causation used in everyday language and reasoning. In philosophy, epistemological theories are often contrasted with metaphysical theories, theories about the nature of reality. Since people’s concepts of causation are assumed to be in error, most metaphysical theories of causation seek to reform rather than describe the concept of CAUSE in people’s heads, (see Mackie, 1974; Dowe, 2000). Theories of causation in psychology have followed suit by linking people’s representations of causation to the outward

A normative framework for modeling causal and counterfactual reasoning has been proposed by Spirtes, Glymour, and Scheines (1993; cf. Pearl, 2000). The framework takes as fundamental that reasoning from observation and intervention differ. Intervention includes actual manipulation as well as counterfactual manipulation of a model via thought. To represent intervention, Pearl employed the do operator that simplifies the structure of a causal model by disconnecting an intervened-on variable from its normal causes. Construing the do operator as a psychological function affords predictions about how people reason when asked counterfactual questions about causal relations that we refer to as undoing, a family of effects that derive from the claim that intervened-on variables become independent of their normal causes. Six studies support the prediction for causal (A causes B) arguments but not consistently for parallel conditional (if A then B) ones. Two of the studies show that effects are treated as diagnostic when their values are observed but nondiagnostic when they are intervened on. These results cannot be explained by theories that do not distinguish interventions from other sorts of events.

This paper proposes a new model of causal meaning, the Vector Model, which formalizes a model of causation based on Talmys notions of force dynamics (Wolff, Song, & Driscoll, 2002). In the Vector Model, the concepts of CAUSE, ENABLE and PREVENT are distinguished from one another in terms of force vectors, their resultant and the relationship of each force vector to a target vector. The predictions of the model were tested in two experiments in which participants saw realistic 3D-animations of an inflatable boat moving through a pool of water. The boats movements were completely determined by the force vectors entered into a physics simulator. Participants linguistic descriptions of the animations were closely matched by those predicted by the model given the same force vectors as those used to produce the animations. Our model may have implications for the semantics of causal verbs as well as the perception of causal events.

We report 4 studies which show that there are systematic quantitative patterns in the way we reason with uncertainty during causal and counterfactual inference.