Strategies in sentential reasoning

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagrams corresponding to mental models, and the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e., the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams.     

Adding possibilities can reduce the Gambler's Fallacy: A naïve-probability paradox

This paper reports a novel paradox of intuitive probabilistic reasoning detected in naïve reasoners’ responses in two separate experiments where we manipulated the number of sets (or possibilities) of the problem keeping constant the probability of the critical set. Experiment 1 showed that the incidence of the Gambler's Fallacy (GF) was reduced when the number of sets was increased. In Experiment 2, a reduction of the GF also occurred but, more importantly, the percentage of correct responses of the participants increased when three sets of possibilities instead of two were used. Therefore, both Experiments 1 and 2 demonstrated that an increase in the extensional complexity of a problem can, under certain circumstances, lead to facilitation. These results support the importance of the extensional features in solving chance problems and are consistent with the model theory of reasoning.     

Phonological coding in reading comprehension: The importance of individual differences

Abstract

In two experiments, texts were presented word by word at a fixed pace to subjects high or low in test anxiety, under various concurrent interference conditions: no interference, articulatory suppression, finger tapping, unattended meaningful speech, reversed (meaningless) speech and nonword (meaningless) speech. High-anxiety subjects produced overt articulation more frequently than low-anxiety subjects, especially in the speech conditions. There was an interaction between anxiety and interference on comprehension performance: Conditions thought to interfere with phonological coding (i.e. articulatory suppression and nonword speech) were detrimental to comprehension for high but not for low-anxiety subjects; in contrast, there were no differences in comprehension performance as a function of anxiety under conditions causing no (proper) phonological interference (i.e. no interference, finger tapping and reversed speech). There were mixed results in the meaningful speech condition, partly attributable to its semantic interference component. These findings reveal that the use and importance of phonological coding in reading comprehension vary with differences in test anxiety-high-anxiety subjects are vulnerable to disruptive effects on phonological coding. This suggests that high-anxiety individuals are especially likely to resort to speech-based coding during reading, and that phonological coding has a compensatory role for them.     

Mental models and other misconceptions in children’s understanding of the earth

This study investigated the claim (e.g., Vosniadou & Brewer’s, 1992) that children have naive “mental models” of the earth and believe, for example, that the earth is flat or hollow. It tested the proposal that children appear to have these misconceptions because they find the researchers’ tasks and questions to be confusing and ambiguous. Participants were 6- and 7-year-olds (N = 127) who were given either the mental model theorists’ original drawing task or a new version in which the same instructions and questions were rephrased to minimize ambiguity and, thus, possible misinterpretation. In response to the new version, children gave substantially more indication of having scientific understanding and less of having naive mental models, suggesting that the misconceptions reported by the mental model theorists are largely methodological artifacts. There were also differences between the responses to the original version and those reported by Vosniadou and Brewer, indicating that other factors, such as cohort and cultural effects, are also likely to help explain the discrepant findings of previous research.     

Transitive and pseudo-transitive inferences

Given that A is longer than B, and that B is longer than C, even 5-year-old children can infer that A is longer than C. Theories of reasoning based on formal rules of inference invoke simple axioms ("meaning postulates") to capture such transitive inferences. An alternative theory proposes instead that reasoners construct mental models of the situation described by the premises in order to draw such inferences. An unexpected consequence of the model theory is that if adult reasoners construct simple models of typical situations, then they should infer transitive relations where, in certain cases, none exists. We report four studies corroborating the occurrence of these "pseudo-transitive" fallacies. Experiment 1 established that individuals' diagrams of certain non-transitive relations yield transitive conclusions. Experiment 2 showed that these premises also give rise to fallacious transitive inferences. Experiment 3 established that when the context suggested alternatives to the simple models, the participants made fewer errors. Experiment 4 showed that tense is an important aspect of meaning which affects whether individuals draw transitive conclusions. We discuss the implications of these results for various theories of reasoning.     

Reasoning with conditionals: a test of formal models of four theories

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. Psychological Review, 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press), a dual-process variant of the model theory (Verschueren, N., Schaeken, W., & d'Ydewalle, G. (2005). A dual-process specification of causal conditional reasoning. Thinking &Reasoning, 11, 278-293), and the probabilistic theory (Oaksford, M., Chater, N., & Larkin, J. (2000). Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 883-899). The first three theories are formalized as multinomial models. The models are applied to the frequencies of patterns of acceptance or rejection across the four basic inferences modus ponens, acceptance of the consequent, denial of the antecedent, and modus tollens. Model fits are assessed for two large data sets, one representing reasoning with abstract, basic conditionals, the other reflecting reasoning with pseudo-realistic causal and non-causal conditionals. The best account of the data was provided by a modified version of the mental-model theory, augmented by directionality, and by the dual-process model.     

How our brains reason logically

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic.

Mathematical concepts for analyzing ambiguous situations

Abstract

We examine some mathematical tools for dealing with ambiguous situations. The main tool is the use of non-standard logic with truth-values in what is called a locale. This approach is related to fuzzy set theory, which we briefly discuss. We also consider probabilistic concepts. We include specific examples and describe the way a researcher can set up a suitable locale to analyse a concrete situation.     

Facts and Possibilities: A Model‐Based Theory of Sentential Reasoning

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities.     

Using phenomenal concepts to explain away the intuition of contingency

Humans can think about their conscious experiences using a special class of “phenomenal” concepts. Psychophysical identity statements formulated using phenomenal concepts appear to be contingent. Kripke argued that this intuited contingency could not be explained away, in contrast to ordinary theoretical identities where it can. If the contingency is real, property dualism follows. Physicalists have attempted to answer this challenge by pointing to special features of phenomenal concepts that explain the intuition of contingency. However no physicalist account of their distinguishing features has proven to be satisfactory. Leading accounts rely on there being a phenomenological difference between tokening a physical-functional concept and tokening a phenomenal concept. This paper shows that existing psychological data undermine that claim. The paper goes on to suggest that the recalcitrance of the intuition of contingency may instead by explained by the limited means people typically have for applying their phenomenal concepts. Ways of testing that suggestion empirically are proposed.     

Mental models in the brain: On context-dependent neural correlates of mental models

In this paper, the concept of context-dependent realisation of mental models is introduced and discussed. Literature from neuroscience is discussed showing that different types of mental models can use different types of brain areas. Moreover, it is discussed that the same occurs for the formation and adaptation of mental models and the control of these processes. This makes that it is hard to claim that all mental models use the same brain mechanisms and areas. Instead, the notion of context-dependent realisation is proposed here as a better manner to relate neural correlates to mental models. It is shown in some formal detail how this context-dependent realisation approach can be related to well-known perspectives based on bridge principle realisation and interpretation mapping realisation.     

A catalog of Boolean concepts

Boolean concepts are concepts whose membership is determined by a Boolean function, such as that expressed by a formula of propositional logic. Certain Boolean concepts have been much studied in the psychological literature, in particular with regard to their ease of learning. But research attention has been somewhat uneven, with a great deal of attention paid to certain concepts and little to others, in part because of the unavailability of a comprehensive catalog. This paper gives a complete classification of Boolean concepts up to congruence (isomorphism of logical form). Tables give complete details of all concepts determined by up to four Boolean variables. For each concept type, the tables give a canonic logical expression, an approximately minimal logical expression, the Boolean complexity (length of the minimal expression), the number of distinct Boolean concepts of that type, and a pictorial depiction of the concept as a set of vertices in Boolean D-space. Some psychological properties of Boolean concepts are also discussed.     

An Investigation of Singaporean Clergy Treatment Models for Mental Problems

While clergy are recognized by their faith communities as important sources of mental health care, questions persist as to the treatment strategies they employ and endorse. This has implication for their likelihood to encourage their members to utilize professional mental health care resources. In this study, a modified version of the treatment portion of the Opinions about Psychological Problems (OPP, Barker, Pistrang & Shapiro, 1983) is used to examine the treatment strategies endorsed by a representative sample of Singaporean clergymen. Besides attempting to show the usefulness of this modified scale, this study highlights that clergy endorse psychological models the most when these models are congruent to their theological belief system. Organic and popular Charismatic deliverance treatment models received less support. Mathew Mathews recently submitted his Ph.D. thesis entitled Clergy & Counsellors: Mental health care in Singapore. He is actively researching issues at the intersection of religion and health including the role of religion in help seeking intentions.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Complexity of categorical syllogisms: An integration of two metrics

The complexity of categorical syllogisms was assessed using the relational complexity metric, which is based on the number of entities that are related in a single cognitive representation. This was compared with number of mental models in an experiment in which adult participants solved all 64 syllogisms. Both metrics accounted for similarly large proportions of the variance, showing that complexity depends on the number of categories that are related in a representation of the combined premises, whether represented in multiple mental models, or by a single model. This obviates the difficulty with mental models theory due to equivocal evidence for construction of more than one mental model. The “no valid conclusion” response was used for complex syllogisms that had valid conclusions. The results are interpreted as showing that the relational complexity metric can be applied to syllogistic reasoning, and can be integrated with mental models theory, which together account for a wide range of cognitive performances.     

Mental abilities and school achievement: A test of a mediation hypothesis

This study analyzes the interplay of four cognitive abilities - reasoning, divergent thinking, mental speed, and short-term memory - and their impact on academic achievement in school in a sample of adolescents in grades seven to 10 (N = 1135). Based on information processing approaches to intelligence, we tested a mediation hypothesis, which states that the complex cognitive abilities of reasoning and divergent thinking mediate the influence of the basic cognitive abilities of mental speed and short-term memory on achievement. We administered a comprehensive test battery and analyzed the data through structural equation modeling while controlling for the cluster structure of the data. Our findings support the notion that mental speed and short-term memory, as ability factors reflecting basic cognitive processes, exert an indirect influence on academic achievement by affecting reasoning and divergent thinking (total indirect effects: β = .22 and .24, respectively). Short-term memory also directly affects achievement (β = .22).     

Negation: A theory of its meaning,representation, and use

This article presents a model-based theory of what negation means, how it is mentally represented, and how it is understood. The theory postulates that negation takes a single argument that refers to a set of possibilities and returns the complement of that set. Individuals therefore tend to assign a small scope to negation in order to minimize the number of models of possibilities that they have to consider. Individuals untrained in logic do not know the possibilities corresponding to the negation of compound assertions formed with if, or, and and, and have to infer the possibilities one by one. It follows that negations are easier to understand, and to formulate, when individuals already have in mind the possibilities to be negated. The paper shows that the evidence, including the results of recent studies, corroborates the theory.