The Mental Models Theory of Reasoning

Refinements and Extensions

Walter Schaeken, Andre Vandierendonck, Walter Schroyens, Gery d'Ydewalle, Karl C. Klauer

• Publisher: Taylor & Francis
• Year: 2013
• Print ISBN: 9780805841831
• eBook ISBN: 9781134810819
• Edition: 1
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

The Mental Models Theory of Reasoning presents theoretical and empirical research on an area of growing interest, the status of mental models in deductive reasoning. As research in the framework of the mental models theory flourishes, this book answers a need to assess the contribution of the notion of training and content. It covers the central issues of propositional, relational, causal and probabilistic reasoning, and argumentation and development. In addition, this work presents data regarding strategies, argumentation, and the development of reasoning. Special features of this text include:
*sharp theoretical analyses as well as important new empirical data offered by theorists who work in the framework of the mental models theory;
*a critical and empirically driven account of content effects in conditional and linear reasoning; and
*an original account on the influence of pragmatics on reasoning. The Mental Models Theory of Reasoning will be of interest to researchers and advanced students of cognitive psychology, and will be valuable to individuals working in Artificial Intelligence, as it highlights theoretical and empirical data on how humans use mental models when tackling deductive puzzles.

1

Memory Retrieval and Content Effects in Conditional Reasoning: A Developmental Mental Models Account

Pierre Barrouillet

Nelly Grosset

The mental models theory assumes that conditional reasoning is mainly constrained by the number of models individuals can hold and process in working memory and the nature and the accessibility of knowledge used to construct these models. Both constraints result from the limitation of the cognitive resources available to activate knowledge from long-term memory and maintain it active for processing. Because the amount of cognitive resources increases with age, the mental models theory allows precise predictions about the way children, adolescents, and adults interpret conditional sentences and reason from them, and about how contents affect reasoning at different ages. These predictions have been tested in two experiments in which adolescents and adults were asked to reason from conditional sentences that involved either familiar or unfamiliar relations between the antecedent and the consequent. The results confirmed the main developmental predictions of the mental models theory and provided evidence that the fleshing-out process is achieved through a process of retrieval from long-term memory. Both developmental and content effects result from the same processes of constructing and manipulating mental models.

Introduction

Evidence in support of the mental models theory of conditional reasoning (Johnson-Laird, 1999; Johnson-Laird & Byrne, 1991, 2002) has been growing during the last 10 years. According to this theory, understanding an “If p then q” conditional sentence results in the construction of an initial representation of the following form:

(1)	p	q
…

that contains only one explicit model representing a state of affairs in which both p and q propositions are verified. The three dots refer to other possibilities that are kept in an implicit format and in which p would be false. Thus, this initial representation supports only affirmative inferences (i.e,. modus ponens [MP], from p conclude q, and affirmation of consequent [AC], from q conclude p). To draw denial inferences from a negative minor premise (i.e., either not p or not q) requires reasoners to flesh out this initial representation with additional models that explicitly represent negated values (¬ p · ¬q, and ¬ p · q).

The mental models theory assumes that this fleshing-out process is demanding and time-consuming. Accordingly, it has been shown that the production of denial inferences that require a fleshing-out process is slower than that of the affirmative inferences supported by the initial model (Barrouillet, Grosset, & Lecas, 2000). In the same way, it has been shown that modus tollens (MT; from not q conclude not p) is more often endorsed when the minor premise not q is presented before rather than after the conditional premise (Girotto, Mazzocco, & Tasso, 1997). Indeed, the preliminary presentation of negative information (i.e., not q) leads reasoners to focus on negative values and thus facilitates the explicit representation of the ¬ p · ¬ q model that supports MT. Furthermore, it has been suggested that the mental models theory provides an account of Wason’s selection task (Evans & Handley, 1999; Johnson-Laird & Byrne, 2002), probabilistic reasoning from conditional sentences (Johnson-Laird, Legrenzi, Girotto, Legrenzi, & Caverni, 1999), and the compelling illusory inferences that result from a disjunction of conditional statements (Johnson-Laird & Savary, 1999). Thus, the mental models theory is undoubtedly the most explanatory and heuristic among the available theories of propositional reasoning. However, we would suggest that the standard version of this theory still suffers from two gaps on which this chapter focuses.

First, the theory must account for content effects, which are ubiquitous in conditional reasoning, in a more effective and convincing way than it does. Bonatti (1994a, 1994b) argued that the mental models theory cannot account for content effects in propositional reasoning because this theory relies on a truth-table approach that is formal and ignores both the content and the context. Despite that Bonatti seems to neglect the role of the fleshing-out process in conditional reasoning (see Barrouillet & Lecas, 1998, for a discussion), it should be acknowledged that the standard theory lacks the precise machinery to account for content effects in a predictable way.

Second, the theory must account for the developmental phenomena that have been the focus of past psychological studies on thinking, reasoning, and rationality (Inhelder & Piaget, 1955; Piaget & Inhelder, 1959) because a developmental approach probably constitutes the best way to validate the theory. Indeed, if reasoning is a matter of constructing and manipulating mental models in working memory, these processes should be constrained in three ways. The first of these relates to the limited capacity of the working memory in which mental models are maintained and processed. The second concerns the structure and content of the semantic memory that provides reasoners with knowledge from which mental models are constructed. Finally, the third relates to the relative accessibility of this knowledge in long-term memory. The impact of these constraints on reasoning processes should evolve with age, thus leading to a predictable developmental trend. One of the main developmental changes that could have a direct influence on reasoning skills is the developmental increase in cognitive resources.

It is widely acknowledged that there is an age-related increase in cognitive capacities (Barrouillet & Camos, 2001; Case, 1985; Cowan, 1997; Halford, 1993; Halford, Wilson, & Phillips, 1998; Swanson, 1999). The most recent models of working memory conceive these capacities as a pool of attentional resources available to activate knowledge from long-term memory and to keep it active for processing (Anderson & Lebière, 1998; Cowan, 1995, 2001; Engle, Kane, & Tuholski, 1999; Rosen & Engle, 1997). As a consequence, any increase in cognitive capacities should have an impact both on the number of models that can be processed in working memory and on the accessibility of knowledge from long-term memory (i.e., the two main constraints on reasoning hypothesized by the mental models theory). This theory should thus make it possible to predict the form and content of the representations used at different ages as a function of the amount of available resources and knowledge. Thus, the mental models theory is not only more suited than others to account for content effects, as Johnson-Laird and Byrne (1991) claimed, but it is also developmental in nature.

The Development of Conditional Reasoning: A Model

Markovits and Barrouillet (2002) recently proposed a developmental reformulation of the mental models theory of the conditional based on two main assumptions. First, they assume that although advanced reasoners may develop or learn strategies specific to logical reasoning, children and probably many adults use processes that are general and rely on existing cognitive architectures. Second, they suggest that children (and adults) have an understanding of if-then propositions that is inherently relational and involves the application of a rich linguistic and pragmatic knowledge. More precisely, an “if p then q” statement is understood as introducing a directional relation between a variable P, one value of which is specified by the proposition p, and a variable Q, one value of which is specified by the proposition q. Thus, the “if p then q” relation defines a semantic space that depends both on the semantic nature of the terms used and on the reasoner’s knowledge about the relationship between them. For example, “if he is a postman, then he has a blue cap” would be understood not only as introducing a mapping between different kinds of people and different kinds of hats, but also as referring to hats of professional uniforms because we assume that mental models for conditionals represent not only specific elements but also how they are related (Thompson, 2000; Thompson & Mann, 1995).

In line with Johnson-Laird and Byrne’s (1991) theory, it is assumed that children construct an initial representation that contains only one model in which specific tokens represent both p and q propositions as verified. However, the authors suggest that this model does not represent the mere cooccurrence of p and q but takes the form of a relational schema in which p is understood as a hypothetical state of affairs and q as its resulting outcome:

(2)

p → q

The directionality of this relation, already suggested by Evans (1993), accounts for the fact that forward inferences (MP and denial of the antecedent, i.e., DA) are faster than backward inferences (AC and MT) from “if p then q” forms (Grosset & Barrouillet, 2003).

When a minor premise is given and an inference required, this initial representation could be enriched through a fleshing-out process. Markovits (1993; Markovits & Vachon, 1990) suggested that this fleshing out is the result of an automatic process of the activation and retrieval of knowledge from long-term memory. This process would provide the reasoner with information that makes it possible to construct additional models that represent the values of Q that could result from alternative hypotheses on P that differ from p. In children, at least, these models would then represent specific values of the variables P and Q rather than negated values using propositional-like tags (represented as ¬ in the standard theory).

The outcome of this fleshing-out process and the resulting representation depend on several factors, including children’s ability to maintain complex representations in working memory, the efficiency of the retrieval process, the semantic structure of the concepts the conditional sentence involves, the nature of the relation between the antecedent and the consequent, the amount of available knowledge in long-term memory concerning both these concepts and this relation and finally, the context of enunciation. Though this theoretical framework might seem rather complex, it permits several precise predictions about the way children understand conditional sentences and draw inferences, how this understanding evolves with age, and how contents affect reasoning at different ages.

A first distinction must be made between familiar and unfamiliar relations between the antecedent and the consequent. Indeed, in the first case, retrieval from long-term memory provides the reasoner with knowledge about cases that link possible values of the two variables. For example, on the basis of the conditional premise “if the petrol tank is empty, then the car breaks down,” reasoners can retrieve knowledge about the fact that, usually, cars with full tanks run, or that if the spark plugs are dirty cars also fail to start. Such cases constitute ready-made models in which different possible values of P (i.e., possible causes of cars breaking down or running) are already linked to their resulting outcome (the car either runs or it does not). On the other hand, when unfamiliar relations are presented, the retrieval process can only provide reasoners with values from the variables P and Q that must be combined to form models. For example, from an artificial relation such as “if the piece is a square, then it is red,” individuals must combine alternative shapes (circle, triangle, etc.) with possible colors. However, there is no available knowledge about this relationship that could direct this construction and help reasoners to keep the constructed models active for processing. Thus, constructing and maintaining models should be easier from familiar rather than unfamiliar relations. As a consequence, the developmental impact of a limitation in cognitive resources depends on the type of conditional relation that is being investigated.

As far as reasoning from artificial relations is concerned, both the construction and maintenance of mental models should be particularly difficult for young children who have limited working memory capacities. As a consequence, the most primitive level in understanding the conditional should involve the construction of only one explicit model of the form p · q, the content of which is directly provided by the conditional sentence. This representation leads to a conjunctive-like interpretation of “if p then q.” The developmental increase in cognitive capacities should allow children to construct more complex representations that involve an increasing number of models. Thus, the next step in the development of conditional reasoning should involve the construction of a two-model representation in which a not-p–not-q model is added to the initial model. Indeed, this additional model maximizes the relevance of the conditional statement (i.e., the amount of information it provides; Sperber & Wilson, 1986). This level corresponds to a biconditional interpretation. Finally, adolescents and adults should be able to construct and process three-model representations that correspond to the complete conditional representation hypothesized by Johnson-Laird and Byrne (1991).

This predicted developmental trend from a conjunctive to a biconditional and then to a conditional interpretation of the conditional sentences involving artificial relations has been observed in many experiments (Barrouillet, 1997; Barrouillet et al., 2000; Barrouillet & Lecas, 1998; Lecas & Barrouillet, 1999). It has also been demonstrated that both developmental and individual differences in understanding conditionals rely on differences in working memory capacity (Barrouillet...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright
• Contents
• List of Contributors
• Preface
• 1. Memory Retrieval and Content Effects in Conditional Reasoning: A Developmental Mental Models Account
• 2. Representation, Pragmatics, and Process in Model-Based Reasoning
• 3. Whether, Although, and Other Conditionals
• 4. Rethinking the Model Theory of Conditionals
• 5. Mental Models and Falsification: It Depends on the Task
• 6. Modeling Something That Is Believed to Be False: The Competition of Scripts and Models in Linear Reasoning
• 7. The Mental Models Theory of Relational Reasoning: Premises’ Relevance, Conclusions’ Phrasing, and Cognitive Economy
• 8. Extensional Reasoning About Chances
• 9. Models of Cause and Effect
• 10. A Mental Model Theory of Informal Argument
• 11. Training Effects in Deductive Reasoning: A Theory-Based Review
• Author Index
• Subject Index