In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

This systematic investigation of computation and mental phenomena by a noted psychologist and computer scientist argues that cognition is a form of computation, that the semantic contents of mental states are encoded in the same general way as computer representations are encoded. It is a rich and sustained investigation of the assumptions underlying the directions cognitive science research is taking. 1 The Explanatory Vocabulary of Cognition 2 The Explanatory Role of Representations 3 The Relevance of Computation 4 The Psychological Reality (...) of Programs: Strong Equivalence 5 Constraining Functional Architecture 6 The Bridge from Physical to Symbolic: Transduction 7 Functional Architecture and Analogue Processes 8 Mental Imagery and Functional Architecture 9 Epilogue: What is Cognitive Science the Science of? (shrink)

In this influential study of central issues in the philosophy of science, Paul Horwich elaborates on an important conception of probability, diagnosing the failure of previous attempts to resolve these issues as stemming from a too-rigid conception of belief. Adopting a Bayesian strategy, he argues for a probabilistic approach, yielding a more complete understanding of the characteristics of scientific reasoning and methodology. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Colin Howson, illuminating its (...) enduring importance and relevance to philosophical enquiry, this engaging work has been revived for a new generation of readers. (shrink)

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given (...) a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results. (shrink)

Four experiments investigated the effects of probability manipulations on the indicative four card selection task (Wason, 1966, 1968). All looked at the effects of high and low probability antecedents (p) and consequents (q) on participants' data selections when determining the truth or falsity of a conditional rule, if p then q . Experiments 1 and 2 also manipulated believability. In Experiment 1, 128 participants performed the task using rules with varied contents pretested for probability of occurrence. Probabilistic effects were observed (...) which were partly consistent with some probabilistic accounts but not with non-probabilistic approaches to selection task performance. No effects of believability were observed, a finding replicated in Experiment 2 which used 80 participants with standardised and familiar contents. Some effects in this experiment appeared inconsistent with existing probabilistic approaches. To avoid possible effects of content, Experiments 3 (48 participants) and 4 (20 participants) used abstract material. Both experiments revealed probabilistic effects. In the Discussion we examine the compatibility of these results with the various models of selection task performance. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Byrne has demonstrated that although subjects can make deductively valid inferences of the modus ponens and modus tollens forms, these valid inferences can be suppressed by presenting an appropriate additional premise “If R then Q” with the original conditional “If P then Q”. This suppression effect challenges the assumption of all syntactic theories of conditional reasoning that formal rules of inference such as modus ponens is part of mental logic. This paper argues that both the syntactic and the mental model (...) accounts of the suppression effect are inadequate because they fail to give a principled account of the critical interpretive component involved in reasoning. In contrast, the relative salience model proposed in this study emphasized the centrality of the interpretative processes with the critical component being the relative salience of premises as judged by subjects on the basis of their prior knowledge activated in particular problem situations. Using 120 undergraduates and 120 policemen as subjects, predictions from the model were tested and confirmed in a suppression paradigm and evidence of convergent validity for the construct of salience were obtained. The results cannot be reconciled with either the syntactic view or the mental model view that have dominated theories of conditional reasoning. (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of universal or (...) conditional claims in everyday life. (shrink)

M. Oaksford and N. Chater presented a Bayesian analysis of the Wason selection task in which they proposed that people choose cards in order to maximize expected information gain as measured by reduction in uncertainty in the Shannon-Weaver information theory sense. It is argued that the EIG measure is both psychologically implausible and normatively inadequate as a measure of epistemic utility. The article is also concerned with the descriptive account of findings in the selection task literature offered by Oaksford and (...) Chater. First, it is shown that their analysis data reported in the recent article of K. N. Kirby is unsound; second, an EIG analysis is presented of the experiments of P. Pollard and J. St. B. T. Evans that provides a strong empirical disconfirmation of the theory. (shrink)

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then (...) show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning. (shrink)

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of the Antecedent, and (...) Affirmation of the Consequent . They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise If p then it is very probable that q and if p then it is not very probable that q of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed. (shrink)