Open and closed models of understanding in conditional reasoning (original) (raw)
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The initial representation in reasoning towards an interpretation of conditional sentences
Quarterly journal of experimental psychology (2006), 2011
All accounts of human reasoning (whether presented at the symbolic or subsymbolic level) have to reckon with the temporal organization of the human processing systems and the ephemeral nature of the representations it uses. We present three new empirical tests for the hypothesis that people commence the interpretational process by constructing a minimal initial representation. In the case of if A then C the initial representation captures the occurrence of the consequent, C, within the context of the antecedent, A. Conditional inference problems are created by a categorical premise that affirms or denies A or C. The initial representation allows an inference when the explicitly represented information matches (e.g., the categorical premise A affirms the antecedent “A”) but not when it mismatches (e.g., “not-A” denies A). Experiments 1 and 2 confirmed that people tend to accept the conclusion that “nothing follows” for the denial problems, as indeed they do not have a determinate initial-model conclusion. Experiment 3 demonstrated the other way round that the effect of problem type (affirmation versus denial) is reduced when we impede the possibility of inferring a determinate conclusion on the basis of the initial representation of both the affirmation and the denial problems.
All accounts of human reasoning (whether presented at the symbolic or subsymbolic level) have to reckon with the temporal organization of the human processing systems and the ephemeral nature of the representations it uses. We present three new empirical tests for the hypothesis that people commence the interpretational process by constructing a minimal initial representation. In the case of if A then C the initial representation captures the occurrence of the consequent, C, within the context of the antecedent, A. Conditional inference problems are created by a categorical premise that affirms or denies A or C. The initial representation allows an inference when the explicitly represented information matches (e.g., the categorical premise A affirms the antecedent “A”) but not when it mismatches (e.g., “not-A” denies A). Experiments 1 and 2 confirmed that people tend to accept the conclusion that “nothing follows” for the denial problems, as indeed they do not have a determinate initial-model conclusion. Experiment 3 demonstrated the other way round that the effect of problem type (affirmation versus denial) is reduced when we impede the possibility of inferring a determinate conclusion on the basis of the initial representation of both the affirmation and the denial problems.
Interpretational factors in conditional reasoning
Memory & Cognition, 1994
on perceived necessity and sufficiency have consistently been shown to be important factors in making and evaluating conditional inferences (e.g., Cummins et al., 1991; Digdon, 1986; Markovits, 1984, 1986; Staudenmayer, 1975; Thompson, in press), we do not know how the use of necessity/sufficiency information may be modified by other interpretational variables, such as pragmatic, contextual relations (e.g., Cheng & Holyoak, 1985) or logical, syntactic relations. Thus, the following experiments examined the role of perceived necessity and sufficiency in the making of inferences about a variety of pragmatic and syntactic relationships. Conditional Reasoning Conditional relationships are often expressed in the generic form "if p, then q," where p and q are referred to as the antecedent and consequent, respectively. In a conditional reasoning task, subjects are typically asked to make inferences about the occurrence of one event, given the occurrence or nonoccurrence ofthe other event. For example, in a conditional arguments task, subjects are asked to indicate the validity of four inferences derived from a conditional statement (e.g., if the car is out of gas, then it stalls). The modus ponens (MP) inference entails concluding q, given p (e.g., the car is out of gas; therefore, it stalls), and modus tollens (MT) entails concluding-p, given-q (e.g., the car has not stalled; therefore, it did not run out ofgas). The denying-the-antecedent (DA) and affirming-the-consequent arguments (AC) involve the inference from 'P to-q (e.g., ifthe car does not run out of gas, it will not stall) and from q to p (the car has stalled; therefore, it has run out of gas), respectively. Logically speaking, the validity of an argument is determined only by its syntactic form; by this criterion, the MP and MT arguments are considered to be valid, and the DA and AC arguments are considered to be fallacies
CONDITIONAL REASONING: THE IMPORTANCE OF INDIVIDUAL DIFFERENCES.
SYMPOSIUM ON MENTAL MODELS IN REASONING. UNED, November, 1998
An extended version of this paper was published in the chapter "CONDITIONAL REASONING : THE IMPORTANCE OF INDIVIDUAL DIFFERENCES" in the book MENTAL MODELS IN REASONING (J.A. GARCÍA MADRUGA, N.CARRIEDO & JM GONZÁLEZ- LABRA, 2000). This book is a collection of the papers presented at the "SYMPOSIUM ON MENTAL MODELS IN REASONING", which took place in Madrid in November,1998. This occasion enabled the spanish experts in reasoning with of their European colleagues with the common aim to celebrate the awards the UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA (UNED) of an Honoris Causa Doctorate Degree to PHIL N JONHNSON.LAIRD..
Individual differences in conditional reasoning: A dual-process account
Thinking & Reasoning, 2005
Dual-process theories of conditional reasoning predict that relationships among four basic logical forms, and to intellectual ability and thinking predictions, are most evident when conflict arises between experiential and analytic processing (e.g., Stanovich & West, 2000). To test these predictions, 210 undergraduates were presented with conditionals for which the consequents were either weakly or strongly associated with alternative antecedents (i.e., WA and SA problems, respectively). Consistent with predictions, modus ponens inferences were not related to inferences on the uncertain forms (affirmation of the consequent, denial of the antecedent). On WA problems, modus tollens, affirmation of the consequent, and denial of the antecedent were related to each other and to verbal ability. Modus ponens was linked to verbal ability only when disabling conditions were activated. In accord with the predictions of Stanovich and West (2000), on most problems, thinking dispositions predicted variance in inferences independently from verbal ability. We argue that a largely automatic experiential processing system governs performance on modus ponens, unless disablers are activated. Consciously controlled analytic processing predominates on the uncertain forms and, under some conditions, on modus tollens. Studies of conditional inferences have frequently concentrated on the conditions that elicit determinate and indeterminate inferences on four basic logical forms. The four forms share the major premise, if p, then q. Modus ponens (MP) involves the minor premise ''p is true'', and the conclusion ''q is true''. For modus tollens (MT), the minor premise is ''q is not true'' and
The modulation of conditional assertions and its effects on reasoning
The Quarterly Journal of Experimental Psychology, 2010
The theory of mental models postulates that conditionals of the sort, if A then C, have a "core" meaning referring to three possibilities: A and C, not-A and C, and not-A and not-C. The meaning of a conditional's clauses and general knowledge can modulate this meaning, blocking certain possibilities or adding relations between the clauses. Four experiments investigated such interpretations in factual and deontic domains. In Experiment 1, the participants constructed instances of what was possible and what was impossible according to various conditionals. The results corroborated the general predictions of the model theory and also the occurrence of modulation. The resulting interpretations governed the conclusions that participants accepted in Experiment 2, which also yielded the predicted effects of a time limit on responding. In Experiment 3, the participants drew the predicted conclusions for themselves. In Experiment 4, modulation led to predicted temporal relations between A and C. We relate these results to current theories of conditionals.
Reasoning with three Types of Conditional: Biases and Mental Models
The Quarterly Journal of Experimental Psychology Section A, 1993
Two experiments are reported which compare conditional reasoning with three types of rule. These consist of two types of rule that have been widely studied previously, if p then q and p only if q, together with a third type, q if p. In both experiments, the p only if q type of rule yields a different pattern of performance from the two other types of rule. Experiment 1 is an abstract rule-evaluation task and demonstrates differential effects of temporal order and of suppositional bias. Experiment 2 investigates rule generation, rephrasing, and comparison, and demonstrates differential effects of temporal order and of thematic content. An analysis of the results is offered in terms of biases and mental models. Effects of rule form and context can be explained as reflecting the different sequences in which mental models are created for each rule form. However, it is necessary to consider the internal structure of individual mental models to account for effects arising from temporal or...
In two studies we examined the role of contextual cues and logical training in differentiating conditional from biconditional statements (i.e. the statements of the form ―if p then q‖ from the statements of the form ―if and only if p then q‖) in deductive inference task (i.e. establishing which conclusions necessarily follow from syllogisms whose major premise is formed by a conditional clause). We assume that the well-documented tendency to interpret conditionals as biconditionals is due not only to pragmatic factors, such as a large amount of literature posits, but also to cognitive factors: it is much easier to understand a symmetrical (biconditional) relation between two states of affairs rather than an asymmetrical (conditional) one. We expected that this tendency would be inhibited not only by the presence of contextual cues -as alternative antecedents (e.g. c, m, r) showing that the consequent (q) can be implied by other states of affairs besides the one (p) presented in cond...
Transfer of conditional reasoning: Effects explanations and initial problem types
Memory & Cognition, 1989
Transfer of reasoning on Wason's (1966) selection task was explored in three experiments. Experiment 1 tested the effects of problem explanations and verbalization instructions on transfer from abstract or thematic problems to abstract problems. Explanations facilitated transfer only when the initial problems were abstract; verbalization did not produce transfer between problems. Experiment 2 explored the effects of problem similarity and explanations on transfer between problems. Although transfer occurred following explanations, no effect of similarity was found for thematic problems. In both of these experiments, the thematic effect (Wason & Shapiro, 1971) was observed. Experiment 3 examined the effects of explanations to abstract or thematic problems on transfer to subsequent abstract or thematic problems. Transfer of reasoning occurred from both initial problem types, particularly to problems of the same type; however, transfer occurred to a greater extent from abstract problems than from thematic problems. The results are discussed in terms of problem similarity and Cheng and Holyoak's (1985)pragmatic reasoning schema hypothesis.