Theories of Conditional Reasoning: A Developmental Examination of Competing Hypotheses.

Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Counterfactual and Semifactual Conditionals Prime Alternative Possibilities.

The authors examined in 3 experiments the comprehension of counterfactuals, such as "If it had rained, the plants would have bloomed," and semifactuals, such as "Even if it had rained, the plants would have bloomed," compared with indicative conditionals, "If it rained, the plants bloomed." The first experiment showed that people read the negative conjunction, "not p and not q" faster when it was primed by a counterfactual than when it was primed by an indicative conditional. They read the affirmative conjunction, "p and q" equally quickly when it was primed by either conditional. The 2nd experiment showed that people read the negated-antecedent conjunction, "not p and q" faster when it was primed by a semifactual conditional. The 3rd experiment corroborated these results in a direct comparison of counterfactuals and semifactuals. The authors discuss the implications of the results for the mental representations of different conditionals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The negated conditional: A litmus test for the suppositional conditional?

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability [P(q/p)]. In this paper, the authors examine a further implication of this analysis with respect to the wide-scope negation of conditional assertions, "it is not the case that if p then q." Under the suppositional account, nothing categorically follows from the negation of a conditional, other than a second conditional, "if p then not-q." In contrast, according to the mental model theory, a negated conditional is consistent only with the determinate state of affairs, p and not-q. In 4 experiments, the authors compare the contrasting predictions that arise from each of these accounts. The findings are consistent with the suppositional theory but are incongruent with the mental model theory of conditionals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities": Correction to Oberauer and Wilhelm (2003).

Reports an error in "The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities" by Klaus Oberauer and Oliver Wilhelm (Journal of Experimental Psychology: Learning, Memory, and Cognition, 2003[Jul], Vol 29[4], 680-693). On page 684, Table 4, all correlations should have been identified as having a p2003-06626-018.) Five experiments were conducted to test the hypothesis that people understand conditional statements ("if p then q") as indicating a high conditional probability P(q|p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p?q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conditional reasoning with inducements and advice

In an earlier study of conditional reasoning, Newstead et al. [Newstead, S.E., Ellis, C.E., Evans, J.St.B.T., Dennis, I., (1997). Conditional reasoning with realistic material. Thinking and Reasoning 3, 49-96] found that people drew more inferences from conditionals framed as inducements (threats and promises) than from conditionals phrased as advice (tips and warnings). The present study was designed to test the hypothesis that this difference arose from the fact that the speaker of an inducement is normally seen to have control over the consequent event whereas the giver of advice does not. In the experiment reported here, inducement and advice conditionals were constructed in brief contexts such that in either case the speaker could be seen to have high or low control. Participants drew many more conditional inferences of all kinds for high control than for low control conditionals in either context. A second finding of interest was that participants drew many more forward (antecedent to consequent) inferences than backward inferences with these kinds of realistic conditionals.     

The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities.

[Correction Notice: An erratum for this article was reported in Vol 29(6) of Journal of Experimental Psychology: Learning, Memory, and Cognition (see record 2007-16865-001). On page 684, Table 4, all correlations should have been identified as having a pp then q") as indicating a high conditional probability P(q|p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p?q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Processing of logically valid and logically invalid conditional inferences in discourse comprehension.

Two competing theories of processing of conditionals (if-then) were tested. Syntactic theories posit that people only draw inferences conforming to the logically valid modus ponens (MP) schema. Mental models theories predict that people draw MP and invalid affirming-the-consequent (AC) inferences. Three experiments tested these predictions. Participants read short stories that conformed to either the MP or AC form but without conclusions, and they completed either priming or recognition tasks. Results indicate that both MP and AC inferences occur during discourse processing: MP and AC premise forms prime their respective conclusions, participants erroneously judged that they had read the conclusions to MP and AC arguments, and AC inferences did not stem from a biconditional interpretation of conditionals. Findings support mental models theories. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conversational comprehension processes are responsible for reasoning fallacies in children as well as adults: If is not the biconditional.

Proposes that children do poorly on reasoning from premises of the form if p then q not because they construe if as a biconditional but rather because they use discourse comprehension processes that lead them to accept the invited inferences if not p then not q and if q then p. This hypothesis predicts that children should respond appropriately to premises in which the invited inferences are countermanded. In Exp I, 24 undergraduates and 44 10-yr-olds were given conditional reasoning problems. Some of these had a major premise consisting of a single if–then sentence, while others had a more elaborate major premise in which the invited inferences were explicitly countermanded. In Exp II, Ss were 24 undergraduates, 20 10-yr-olds, and 34 7-yr-olds. In some problems the major premise consisted of a single if–then statement; in others, the major premise consisted of 3 such statements, 2 of which shared the same consequent, thus implicitly countermanding the invited inferences. In both experiments, all age groups committed the fallacies in the simple condition but not in the more complex condition. It is concluded that children's representation of if distinguishes necessary from merely invited inferences. Data suggest a collection of countermandable context-dependent inferences of varying degrees of invitingness associated with if. (19 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conditions for the Acceptance of Deontic Conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How people interpret conditionals: Shifts toward the conditional event.

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 (N? = 66, N? = 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. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Conditional reasoning, causality, and the structure of semantic memory: strength of association as a predictive factor for content effects

Available evidence indicates that responses to conditional inferences using concrete causal premises is affected by the relative number of available alternate causes (Cummins, D.D., 1995. Memory and Cognition 23 (5), 646-658). We propose that another important factor that may influence the kinds of inferences made to causal conditionals is the relative strength of association between such causes and the consequent term. We present a study with adult participants that examines the effect of strength of association on performance on a conditional reasoning task using causal premises for which there exist one highly associated potential cause for the given consequent term. We predicted that adults would produce a greater proportion of biconditional responses to invalid forms with strongly associated premises than weakly associated ones, while valid forms would not be affected by strength of association. The results are consistent with this hypothesis.     

Roles of symbolic knowledge and problem-information context in solving word problems.

In 4 experiments, the effects of symbolic knowledge (i.e., knowledge about the meaning of mathematical notation) and problem-information context (PIC) on translating relational statements (e.g., "There are 6 times as many students as professors") into math equations were examined. College students were more likely to construct correct equations when symbolic knowledge was presented than they were when they only received a single relational statement. Ss who received a PIC that more closely resembled a complete word problem did better on the equation-writing task than did those who only received a relational statement. Results indicated that the effects of the two factors are not separate. When Ss had the appropriate PIC, performance on the equation-writing task was enhanced because Ss' own memory representations for symbolic knowledge were more accessible. Contextual constraints in the access and use of knowledge in problem solving are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Counterfactual and Prefactual Conditionals.

We consider reasoning about prefactual possibilities in the future, for example, "if I were to win the lottery next year I would buy a yacht" and counterfactual possibilities, for example, "if I had won the lottery last year, I would have bought a yacht." People may reason about indicative conditionals, for example, "if I won the lottery I bought a yacht" by keeping in mind a few true possibilities, for example, "I won the lottery and I bought a yacht." They understand counterfactuals by keeping in mind two possibilities, the conjecture, "I won the lottery and I bought a yacht" and the presupposed facts, "I did not win the lottery and I did not buy a yacht." We report the results of three experiments on prefactuals that examine what people judge them to imply, the possibilities they judge to be consistent with them, and the inferences they judge to follow from them. The results show that reasoners keep a single possibility in mind to understand a prefactual. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On-line evidence for elaborative logical inferences in text.

A model of propositional-logic reasoning proposed by M. D. S. Braine, B. J. Reiser, and B. Rumain (1984) claims that inferences such as "p or q; not p /∴ q" are made spontaneously by readers at the moment both premises are available. This claim is inconsistent with some evidence in the text-processing literature that suggests that only those inferences necessary for textual coherence are made spontaneously. In the present study, participants read stories in which a logical inference was not necessary to maintain textual coherence, and inference making was assessed with on-line probes. Two experiments tested logical forms central to Braine et al's model, and both indicated that participants were making the logical inferences. Two further experiments replicated this result with stories that did not begin with thematic titles. These findings support Braine et al.'s prediction that some propositional-logic inferences are made routinely in texts that do not require them for coherence. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Schema congruence and depression: Loss of objectivity in self- and other-inferences.

Depressed and nondepressed students judged the plausibility of positive and negative inferences ostensibly made either by themselves or by others. Negative self-inferences were judged by depressed students as more plausible, and positive other-inferences as less plausible. The results were in accord with Beck's (1967) theory of schema-based distortion in depression, which proposes that persons vulnerable to the development of depression are prone to make erroneous negative inferences and to then regard those inferences as plausible and correct. The results also suggested that depressed persons responded differentially depending on whether they were instructed to consider the inferences as their own or another's, whereas nondepressed persons did not. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The framing of relative performance feedback: Seeing the glass as half empty or half full.

It was proposed that individuals' responses to information regarding their relative position in a performance distribution would depend on how they frame the information. To the degree that they focus selectively on the positive features of the feedback (i.e., the number of others who performed worse than them) rather than the negative features (i.e., the number of others who performed better than them) they should report higher ability levels and more positive affective reactions. In Study I, Ss received feedback indicating that they occupied a particular percentile standing in either a large or small distribution. Individuals with negative orientations (depressives and pessimists) reported lower ability levels as a function of increases in comparison group size, whereas individuals with positive orientations (nondepressives and optimists) reported higher ability levels. Presumably, these effects occurred because negatively oriented persons focused on the negative features of the feedback and positively oriented persons focused on the positive features of the feedback. The results of Study 2 support this explanation. Implications for the social comparison literature are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Semantic constraints on word learning: proper names and adjectives

4 experiments examined 3- and 4-year-olds' interpretations of novel words applied to familial objects in the sentence frame, "This Y is X," where X is a novel word, and Y is a familiar basic-level count noun (e.g., "dog," "cup"). These novel words are ambiguous and could be interpreted either as proper names (e.g., "Fred") or as adjectives/mass nouns (e.g., "red"/"lead"). The experiments addressed 2 questions. First, do children appreciate that the words can be construed either as proper names referring to individuals or as adjectives/mass nouns referring to salient properties/material kinds? The results showed that children could easily make either interpretation. Second, what factors affect children's tendency to make either a proper name or an adjective/mass noun interpretation? In the experiments, children learned the novel words for a range of animals and artifacts. Most children who learned the words for typical pets (e.g., a bird) made proper name interpretations, as did the majority of those who learned the words for certain non-pet animals (e.g., a caterpillar) described as possessed by someone, but only about half of those who learned the words for such non-pet animals not so described. Very few children who learned the words for either simple (e.g., a shoe) or complex (e.g., a boat) artifacts made proper name interpretations. The results provide clear evidence of the role of semantic information in constraining children's interpretation of a novel word, and they help to refine an understanding of what counts as a nameable individual for preschoolers.     

Representations as mediators of adolescent deductive reasoning

In Experiment 1, preadolescents, middle adolescents, and late adolescents were presented 3 deductive reasoning tasks. With some important exceptions, conditional reasoning improved with age on problems containing permission conditional relations, and reasoning fallacies increased with age on problems containing causal conditional relations. The results of Experiments 2a and 2b indicated that problem type (i.e., permission or causal) does not mediate the activation of conditional reasoning skills. Rather, valid conditional inferences are more common on problems for which plausible alternative antecedents can be generated than on problems for which alternative antecedent generation is difficult. Conditional rules for which alternative antecedent generation is difficult may be misrepresented as biconditionals, resulting in biconditional rather than conditional reasoning.     

Multidimensional scaling of the causes for negative interpersonal behavior.

Conducted studies to determine empirically the dimensions underlying attributions made for negative behavior in a close interpersonal relationship (a marriage). 96 university students rated the similarity of 13 causes given either by the enactor of a negative behavior (i.e., the actor) or by the person affected by the behavior (the partner or spouse). A multidimensional scaling analysis of these data yielded 2 dimensions in each condition. The interpretation of these dimensions was guided by data from 68 additional Ss who rated the 13 causes on bipolar scales (e.g., temporary–permanent). Dimension 1 in both conditions was interpreted as "positive vs negative attitude toward spouse." Dimension 2 of the actor condition was interpreted as "intentional vs unintentional" and Dimension 2 of the partner condition as "actor's traits vs circumstances or states." These dimensions are discussed in relation to the a priori causal distinctions made in current attribution writings and previous findings concerning actor–observer biases. (18 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)