We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a 6-sided die and were asked how sure they were that a conditional holds of the side landing upward when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto the sides of each die. In 2 experiments (N₁ = 66, N₂ = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional's antecedent and consequent: Participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: Conditional event interpretations took longer to process than conjunction interpretations (mean difference = 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning.

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We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.To empirically investigate human deductive inference one needs a description of what deductive inference is all about. Such a description specifies what the human mind should compute, which conclusions should be considered rational and which ones not. From Aristotle until the end of the twentieth century, classical logic was the standard reference in psychology. The emerging logical pluralism and the many new paradigms developed in computer science cast doubts upon the general appropriateness of classical logic as the standard frame in the psychology of thinking and reasoning. Recently, a strong trend in psychology emerged to consider probability to be relevant even in tasks in which uncertainties are not explicitly mentioned.The present contribution takes probability logic based on the coherence approach of subjective probability as the basic reference theory. It gives a brief overview of the recent developments of combining logic and probability to build normative and descriptive models of human deductive reasoning. It explains the reasons why we think that the coherence approach offers advantages for psychological model building. We also describe results of our own experimental studies.Coherence is a key concept in subjective probability theory. In the betting interpretation, coherence guarantees the avoidance of sure losses (often called a "Dutch book"). From a psychological perspective, the coherence approach provides several advantages. Most importantly, the coherence approach is based on the subjective interpretation of probabilities. Subjective probabilities are degrees of belief and are conceived as coherent descriptions of incomplete knowledge states. While human reasoning may be more or less coherent, it in any case involves degrees of belief and descriptions of incomplete knowledge states. It would be an unwise research strategy to take a reference theory that is ✩ Supported by the Austrian Recearch Fonds, FWF (project P20209, Mental probability logic).

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We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults