Linguistic factors in conditional reasoning

An experiment is reported which demonstrates the influence of three cognitive variables on adults' abilities to reason with conditional arguments embedded in either causal-temporal or class inclusion content. The three variables are the linguistic form of the conditional rule, the principle of conditional reasoning, and the order of the components in the conditional rule. The results showed considerable similarity in the effects of these factors for the two types of concrete content, but some interesting differences were found. The findings are discussed in relation to the results of recent investigations which involved abstract content and/or other deductive reasoning paradigms.     

Language and reasoning: a study of temporal factors

The paper is concerned with the testing of psycholinguistic hypotheses by the use of deductive reasoning tasks. After reviewing some of the problems of interpretation which have arisen with particular reference to conditional rules, an experiment is presented which measures comprehension and verification latencies in addition to response frequencies in a truth table evaluation task.The experiment tests a psycholinguistic hypothesis concerning the different usage of the logically equivalent forms of sentence: If p then q and p only if q with respect to the temporal order of the events p and q. It is proposed that the former sentence is more natural when the event p precedes the event q in time, and the latter more natural when the opposite temporal relation holds.Although significant support is found for the hypothesis in the analysis of the latency data, it is only distinguished from an alternative explanation by detailed analysis of response frequencies, thus indicating the general usefulness of the paradigm adopted.     

Working memory and conditional reasoning

Little is known about the role of working memory in conditional reasoning. This paper reports three experiments that examine the contributions of the visuo-spatial scratch pad (VSSP), the articulatory loop, and the central executive components of Baddeley and Hitch's (1974) model of working memory to conditional reasoning. The first experiment employs a spatial memory task that is presented concurrently with two putative spatial interference tasks (tapping and tracking), articulatory suppression, and a verbal memory load. Only the tracking and memory load impaired performance, suggesting that these tap the VSSP and central executive, respectively. Having established the potency of these interference tasks two further experiments examined the effects of tapping and tracking (Experiment 2) and articulation and memory load (Experiment 3) on a conditional reasoning task. Neither tracking nor tapping affected the number of inferences accepted or response latency. Articulation also failed to affect conditional reasoning but memory load selectively reduced acceptance of modus tollens inferences. These results are discussed in terms of both rule-based and mental models theories of reasoning. While these data cannot discriminate between the two perspectives they provide support for one of the central assumptions in each: that some errors in reasoning are attributable directly to working memory demands. Taken together these experiments suggest that conditional reasoning requires an abstract working memory medium for representation; it does not require either the VSSP or the articulatory loop. It is concluded that the central executive provides the necessary substrate.     

Pragmatic schemas and conditional reasoning in children

Solving problems involving conditional relationships has been postulated to play a central role in the development of deductive reasoning, which itself underpins much cognitive developmental theory. The traditional Piagetian and “natural logic” approaches to this topic have more recently been challenged by findings that are more readily explained in terms of the concept of pragmatic schemas. On this basis it was predicted that even young “pre-formal” children would be able to succeed in a Reduced Array Selection Task if the test statement (referring to a previously told story about bees living in a hive) was couched in such a way as to evoke an authorization or permission schema. This proved to be the case in the present study involving 54 nine- and ten-year-old children: The permission condition elicited 70% globally correct solutions, compared to the 11% elicited by the formal control condition. Moreover, this facilitatory effect of the permission condition carried over to a second trial conducted in a standard way across all the conditions.     

Necessity and sufficiency in abstract conditional reasoning

The necessity and sufficiency of the cause relates to the conclusions people draw on everyday conditional inference problems. The current research explores the effects of necessity and sufficiency in an abstract causal context. Three experiments showed that the subjective ratings of necessity and sufficiency diverge from the objective levels: A sufficient and necessary cause is more often labelled as sufficient than a sufficient and not-necessary cause. Likewise, a necessary and sufficient cause is more often labelled necessary than a necessary and not-sufficient cause. In Experiments 1 and 2 we observed that the robust effects of sufficiency on MP and MT, and of necessity on AC and DA found on everyday reasoning generalise to abstract conditionals. There were also partial effects of sufficiency on AC and DA, and of necessity on MP and MT. When the problem presentation is simplified, as in Experiment 3, these partial effects on reasoning disappear. The reasoning results then relate to the objective levels and less to the subjective levels of necessity and sufficiency. This divergence sheds doubt on the idea that reasoners base their inferences on an active assessment of the necessity and/or sufficiency of the causal relation.     

Age,schooling and conditional reasoning

This study estimated the independent effects of age and schooling in grades 7–9 on scores obtained on invalid conditional and class syllogisms. The results, which point to a negative, albeit small, effect of out-of-school experience and to a sizeable positive effect of schooling, replicate previous findings in a different age range and support the counterintuitive hypothesis that accumulated daily experience with conditionals has a negative effect on the development of conditional reasoning, and that improved performance on invalid problems with age is entirely attributable to schooling. Contrary to most cognitive tasks, therefore, in which schooling operates in the same direction as out-of-school experience, in this case, schooling breaks daily-life interpretational habits, and therefore, is critical for development.     

Role of responsibility in conditional reasoning

A series of recent studies showed that facilitation on the Wason Selection Task could be produced by perceived utilities. The present work was aimed at testing whether a similar factor could also be involved in human reasoning performance in the context of responsibility. We supposed that the motivation of the subject assuming responsibility is affected by normative goals. These goals prescribe the actions and the results to be achieved, also considering the different social roles. In this experiment the responses of different groups of subjects (N = 270) to a selection task were compared in two different conditions involving different responsibility contexts. The results show that the subjects' strategies in searching for possible violators depended on the condition (responsibility vs no responsibility). In particular, only in the context of responsibility were the performances elicited by conditional rules characterised by a falsification strategy.     

Strategies in temporal reasoning

Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with determinate relations and not with indeterminate ones. However, (a) there is no reason to presuppose that a rule-based procedure could not deal with indeterminate relations, and (b) applying a rule-based procedure to indeterminate relations should result in greater difficulty. Hence, none of the recent articles devoted to relational reasoning currently presents a conclusive case for discarding IRA by using the well-known determinate vs indeterminate problems comparison.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Content and context effects in children's and adults' conditional reasoning

We have recently shown that children interpret conditional sentences with binary terms (e.g., male/female) in both the antecedent and the consequent as biconditionals (Barrouillet & Lecas, 1998). We hypothesized that the same effect can be obtained with conditionals that do not contain binary terms provided that they are embedded in a context that restricts to only two the possible values on both the antecedent and the consequent. In the present experiment, we asked 12-year-old children, 15-year-old children, and adults to draw conclusions from conditional syllogisms that involved three types of conditional sentence: (1) conditionals with binary terms (BB), (2) conditionals with non-binary terms (NN), and (3) conditionals with non-binary terms embedded in a restrictive context (NNR). As we predicted, BB conditionals elicited more biconditional response patterns than did NN conditionals in all age groups. On the other hand, manipulating the context had the same effect in children but not in adults. Content and context constraints on conditional reasoning along with developmental issues are discussed within the framework of the mental models theory.     

A dual-process specification of causal conditional reasoning

There are two accounts describing causal conditional reasoning: the probabilistic and the mental models account. According to the probabilistic account, the tendency to accept a conclusion is related to the probability by which cause and effect covary. According to the mental models account, the tendency to accept a conclusion relates to the availability of counterexamples. These two accounts are brought together in a dual-process theory: It is argued that the probabilistic reasoning process can be considered as a heuristic process whereas the mental models account can be seen as its analytic counterpart. Experiment 1 showed that the two processes differ on a temporal dimension: The variation in fast responses was best predicted by the variation in likelihood information, while the variation in slow responses was best predicted by variation in counterexample information. Experiments 2 and 3 validate the override principle: The likelihood conclusion can be overwritten when specific counterexamples are retrieved in time. In Experiment 2 both accounts were compared based on their difference in input. In Experiment 3 we used a verbal protocol analysis to validate the dual-process idea at the output level. The data of the three experiments provide converging support for framing the two reasoning accounts in a dual-process theory.     

Deductive temporal reasoning with constraints

When modelling realistic systems, physical constraints on the resources available are often required. For example, we might say that at most N processes can access a particular resource at any moment, exactly M participants are needed for an agreement, or an agent can be in exactly one mode at any moment. Such situations are concisely modelled where literals are constrained such that at most N, or exactly M, can hold at any moment in time. In this paper we consider a logic which is a combination of standard propositional linear time temporal logic with cardinality constraints restricting the numbers of literals that can be satisfied at any moment in time. We present the logic and show how to represent a number of case studies using this logic. We propose a tableau-like algorithm for checking the satisfiability of formulae in this logic, provide details of a prototype implementation and present experimental results using the prover.     

A mixed Rasch model of dual-process conditional reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.     

Effects of order of presentation on conditional reasoning

ABSTRACT

The main goal of this research is to study whether or not the order of presentation of the premises in a logical argument form, such as a conditional reasoning task, could affect the processing time of premises and conclusion and the conclusions that participants accept as valid in an evaluation task. One experiment is reported in which participants are asked to evaluate computer-presented conditionals. Half of the problems were presented in traditional order (“if p then q, p, therefore q”) and half in inverse order (“p, if p then q, therefore q”). The experiment showed that there was an order effect in processing the premises and conclusion: participants took longer to read the premises in traditional order than in inverse order, but they took longer to read the conclusion in inverse order than in traditional order. The finding is discussed with respect to the main theories of conditional reasoning.     

On the nature and development of conditional reasoning in early adolescence

Two studies investigated the conditional reasoning capabilities of eighth grade learners. In Study 1, we analysed conditional reasoning performances for differences in learners' abilities to solve problems correctly and propensities to be tricked into responding to problems in a biconditional manner. There seemed to be a developmental progression in conditional reasoning ability. Most young adolescents reason using memory of domain-specific memories. However, pragmatic inferential rules may serve as an intermediate level of abstration in reasoners as they progress from the ability to reason using only domain-specific experience to the ability to use content-free syntactic rules. In addition, correlation between scores on the Test of Logical Thinking and conditional reasoning performances suggested that ability to reason deductively using inferential rules at progressively higher levels of abstraction is related to cognitive development. In Study 2, we assessed the effectiveness of an instructional application of pragmatic inferential rule theory for development of conditional reasoning abilities. Pragmatic reasoning skill was developed throug engagement in Prolog programming activities involving hierarchical knowledge domains.     

Linguistic factors in reasoning

An experiment is reported which attempts to demonstrate the effects of manipulating two linguistic variables on a propositional reasoning task, one relating to the linguistic form of the logical rule, and the other to the presence and absence of negative components. The results are discussed in relation to Evans' (1972a) distinction between interpretational and operational factors in reasoning. Problems arising from the application of this distinction are discussed in detail.     

Response options and presentation format as contributors to conditional reasoning

The present study examines whether students' inability to solve conditional reasoning problems, shown in previous studies, is at least partially attributable to having to choose among logically incorrect response options. In two experiments, students evaluated conclusions to conditional reasoning problems where one of several response options was either the standard, Sometimes true, or the more logically appropriate, Could be true. Decision accuracy was related to the logical appropriateness of the response options available. This relationship was replicated across different problem types and formats.     

Partition-edit-count: naive extensional reasoning in judgment of conditional probability

The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total events. Participants' responses to conditional probability problems were influenced by irrelevant information (Study 1), small variations in problem wording (Study 2), and grouping of events (Study 3), as predicted by the partition-edit-count model. Informal protocol analysis also supports the authors' interpretation. A 4th study extends this account from situations where events are treated as interchangeable (chance and ignorance) to situations where participants have information they can use to distinguish among events (uncertainty).