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16
How people interpret conditionals: Shifts towards the conditional event
 JOURNAL OF EXPERIMENTAL PSYCHOLOGY: LEARNING, MEMORY, AND COGNITION
, 2011
"... 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 sixsided die, and were asked how sure they were that a conditional holds of the side landing upwards when the die is ..."
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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 sixsided die, and were asked how sure they were that a conditional holds of the side landing upwards 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 two 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.
The Conditional in Mental Probability Logic
, 2007
"... Since Störring’s [63] pioneering experiments on syllogistic reasoning at the beginning of last century, experimental psychology has investigated deductive reasoning in the framework of classical logic. The most prominent ..."
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Cited by 9 (4 self)
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Since Störring’s [63] pioneering experiments on syllogistic reasoning at the beginning of last century, experimental psychology has investigated deductive reasoning in the framework of classical logic. The most prominent
Is human reasoning about nonmonotonic conditionals probabilistically coherent
 In Proceedings of the 7 th Workshop on Uncertainty Processing
, 2006
"... Nonmonotonic conditionals (A  ∼ B) are formalizations of common sense expressions of the form “if A, normally B”. The nonmonotonic conditional is interpreted by a “high ” coherent conditional probability, P (BA)>.5. Two important properties are closely related to the nonmonotonic conditional: F ..."
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Cited by 9 (8 self)
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Nonmonotonic conditionals (A  ∼ B) are formalizations of common sense expressions of the form “if A, normally B”. The nonmonotonic conditional is interpreted by a “high ” coherent conditional probability, P (BA)>.5. Two important properties are closely related to the nonmonotonic conditional: First, A  ∼ B allows for exceptions. Second, the rules of the nonmonotonic system p guiding A  ∼ B allow for withdrawing conclusions in the light of new premises. This study reports a series of three experiments on reasoning with inference rules about nonmonotonic conditionals in the framework of coherence. We investigated the cut, and the right weakening rule of system p. As a critical condition, we investigated basic monotonic properties of classical (monotone) logic, namely monotonicity, transitivity, and contraposition. The results suggest that people reason nonmonotonically rather than monotonically. We propose nonmonotonic reasoning as a competence model of human reasoning. 1
Uncertain deductive reasoning
"... Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or ..."
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Cited by 6 (4 self)
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Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals). This contribution consists of two parts. In the first part we discuss general features of reasoning systems including consequence relations, how uncertainty may enter argument forms, probability intervals, and probabilistic informativeness. These concepts are of central importance for the psychological task analysis. In the second part we report new experimental data on the paradoxes of the material conditional, the probabilistic modus ponens, the complement task, and data on the probabilistic truth table task. The results of the experiments provide evidence for the hypothesis that people represent indicative conditionals by conditional probability assertions.
The modulation of conditional assertions and its effects on reasoning
 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY
, 2010
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Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent
 In 5 th International Symposium on Imprecise Probability: Theories and Applications
, 2007
"... The modus ponens (A → B, A ∴ B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A → B, ¬A ∴ ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports th ..."
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The modus ponens (A → B, A ∴ B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A → B, ¬A ∴ ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities. In the modus ponens tasks the participants inferred probabilities that agreed much better with the coherent normative values than in the denying the antecedent tasks, a result that mirrors results found with the classical argument versions. For modus ponens a surprisingly high number of lower and upper probabilities agreed perfectly with the conjugacy property (upper probabilities equal one complements of the lower probabilities). When the probabilities of the premises are imprecise the participants do not ignore irrelevant (“silent”) boundary probabilities. The results show that human mental probability logic is close to predictions derived from probability logic for the most elementary argument form, but has considerable difficulties with the more complex forms involving negations.
Towards a probability logic based on statistical reasoning
 In Proceedings of the 11 th IPMU Conference (Information Processing and Management of Uncertainty in KnowledgeBased Systems
, 2006
"... Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then t ..."
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Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (PólyaEggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.
Rational Argumentation under Uncertainty
, 2007
"... Common sense arguments are practically always about incomplete and uncertain information. We distinguish two aspects or kinds of uncertainty. The one is defined as a persons’ uncertainty about the truth of a sentence. The other uncertainty is defined as a persons ’ uncertainty of his assessment of ..."
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Cited by 2 (2 self)
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Common sense arguments are practically always about incomplete and uncertain information. We distinguish two aspects or kinds of uncertainty. The one is defined as a persons’ uncertainty about the truth of a sentence. The other uncertainty is defined as a persons ’ uncertainty of his assessment of the truth of a sentence. In everyday life argumentation we are often faced with both kinds of uncertainty which should be distinguished to avoid misunderstandings among discussants. The paper presents a probabilistic account of both kinds of uncertainty in the framework of coherence. Furthermore, intuitions about the evaluation of the strength of arguments are explored. Both reasoning about uncertainty and the development of a theory of argument strength are central for a realistic theory of rational argumentation.
Inductive logic and empirical psychology
 In
"... An inductive logic is a system for reasoning that derives conclusions which are plausible or credible, but are nonetheless not certain. Thus, inductive logic goes beyond the more familiar systems of deductive logic, in which the truth of the premises requires the truth of the conclusions. Thus, from ..."
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An inductive logic is a system for reasoning that derives conclusions which are plausible or credible, but are nonetheless not certain. Thus, inductive logic goes beyond the more familiar systems of deductive logic, in which the truth of the premises requires the truth of the conclusions. Thus, from All people are mortal,
Logic, models, and paradoxical inferences
 Mind & Language
, 2012
"... Abstract: People reject ‘paradoxical ’ inferences, such as: Luisa didn’t play music; therefore, if Luisa played soccer, then she didn’t play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unaccep ..."
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Cited by 1 (1 self)
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Abstract: People reject ‘paradoxical ’ inferences, such as: Luisa didn’t play music; therefore, if Luisa played soccer, then she didn’t play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn’t play soccer; therefore, if Luisa played a game then she didn’t play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. 1.