In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology (...) and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external (...) graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson‐Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

Modern logic provides accounts of both interpretation and derivation which work together to provide abstract frameworks for modelling the sensitivity of human reasoning to task, context and content. Cognitive theories have underplayed the importance of interpretative processes. We illustrate, using Wason's [Q. J. Exp. Psychol. 20 (1968) 273] selection task, how better empirical cognitive investigations and theories can be built directly on logical accounts when this imbalance is redressed. Subjects quite reasonably experience great difficulty in assigning logical form to descriptively (...) interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contrasts in reasoning performance are precisely between these interpretations, so better semantic theory can explain the main empirical effects. However, a more adequate notion of logical form than that typically employed in the psychology of reasoning is required, and we offer a richer alternative. Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predictions. The results bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. © 2004 Cognitive Science Society, Inc. All rights reserved.Subjects quite reasonably experience great difficulty in assigning logical form to descriptively interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contracts in reasoning performance are precisely between these interpretatins, so better semantic theory can explain the main empirical effects. Howevers, a more adequate nation of logical from than that typically employed in the psychology of reasoning in required, and we offer a richer alternative.Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predications.The resluts bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed‐world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine‐grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3‐valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

Festschrift for Michiel van Lambalgen on the occasion of his retirement as professor of logic and cognitive science at the University of Amsterdam.

Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and how contrasting sub-components of executive function are involved across disorders. This analysis reveals (...) how logical analysis is as applicable to fast, automatic and unconscious reasoning as it is to slow deliberate cogitation. (shrink)

Classical symbolic computational models of cognition are at variance with the empirical findings in the cognitive psychology of memory and inference. Standard symbolic computers are well suited to remembering arbitrary lists of symbols and performing logical inferences. In contrast, human performance on such tasks is extremely limited. Standard models donot easily capture content addressable memory or context sensitive defeasible inference, which are natural and effortless for people. We argue that Connectionism provides a more natural framework in which to model this (...) behaviour. In addition to capturing the gross human performance profile, Connectionist systems seem well suited to accounting for the systematic patterns of errors observed in the human data. We take these arguments to counter Fodor and Pylyshyn's (1988) recent claim that Connectionism is, in principle, irrelevant to psychology. (shrink)

Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and how contrasting sub-components of executive function are involved across disorders. This analysis reveals (...) how logical analysis is as applicable to fast, automatic and unconscious reasoning as it is to slow deliberate cogitation. (shrink)

Several of Beller, Bender, and Medin’s (2012) issues are as relevant within cognitive science as between it and anthropology. Knowledge-rich human mental processes impose hermeneutic tasks, both on subjects and researchers. Psychology's current philosophy of science is ill suited to analyzing these: Its demand for ‘‘stimulus control’’ needs to give way to ‘‘negotiation of mutual interpretation.’’ Cognitive science has ways to address these issues, as does anthropology. An example from my own work is about how defeasible logics are mathematical models (...) of some aspects of simple hermeneutic processes. They explain processing relative to databases of knowledge and belief—that is, content. A specific example is syllogistic reasoning, which raises issues of experimenters’ interpretations of subjects’ reasoning. Science, especially since the advent of understandings of computation, does not have to be reductive. How does this approach transfer onto anthropological topics? Recent cognitive science approaches to anthropological topics have taken a reductive stance in terms of modules. We end with some speculations about a different cognitive approach to, for example, religion. (shrink)

This reply to Oaksford and Chater’s ’s critical discussion of our use of logic programming to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work (...) shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings. (shrink)

It is neither desirable nor possible to eliminate normative concerns from the psychology of reasoning. Norms define the most fundamental psychological questions: What are people trying to do, and how? Even if no one system of reasoning can be the norm, pure descriptivism is as undesirable and unobtainable in the psychology of reasoning as elsewhere in science.

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty ; and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: logic programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of input/output logic for dealing with uncertainty in dynamic (...) normative contexts. (shrink)

The notion of “bounded rationality” was introduced by Simon as an appropriate framework for explaining how agents reason and make decisions in accordance with their computational limitations and the characteristics of the environments in which they exist (seen metaphorically as two complementary scissor blades).We elaborate on how bounded rationality is usually conceived in psychology and on its relationship with logic. We focus on the relationship between heuristics and some non-monotonic logical systems. These two categories of cognitive tools share fundamental features. (...) As a step further, we show that in some cases heuristics themselves can be formalized from this logic perspective. We have therefore two main aims: on the one hand, to demonstrate the relationship between the bounded rationality programme and logic, understood in a broad sense; on the other hand, to provide logical tools of analysis of already known heuristics. This may lead to results such as the characterization of fast and frugal binary trees in terms of their associated logic program here provided. (shrink)

(2013). Statistical models as cognitive models of individual differences in reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 89-102. doi: 10.1080/19462166.2012.674061.

Machine generated contents note: -- Preface -- Acknowledgements -- Notes on Contributors -- PART I: COMPLEXITY IN ANIMAL MINDS -- Introduction: M.McGonigle-Chalmers -- Relational and Absolute Discrimination Learning by Squirrel Monkeys: Establishing a Common Ground with Human Cognition; B.T.Jones -- Serial List Retention by Non-Human Primates: Complexity and Cognitive Continuity; F.R.Treichler -- The Use of Spatial Structure in Working Memory: A Comparative Standpoint; C.De Lillo -- The Emergence of Linear Sequencing in Children: A Continuity Account and a Formal Model; M.McGonigle-Chalmers&I.Kusel (...) -- Sensitivity to Quantity: What Counts Across Species?; S.T.Boysen&A.M.Yocom -- PART II: COMPLEXITY IN ROBOTS -- Editorial Introduction; D.McFarland -- Towards Cognitive Robotics: Robotics, Biology and Developmental Psychology; M.Lee, U.Nehmzow&M.Rodriguez -- Structuring Intelligence: The Role of Hierarchy, Modularity and Learning in Generating Intelligent Behaviour; J.J.Bryson -- Epistemology, Access, and Computational Models; G.Luger -- Reasoning About Representations in Autonomous Systems: What P´Olya and Lakatos Have To Say; A.Bundy -- PART III: LANGUAGE, EVOLUTION AND THE COMPLEX MIND -- Editorial Introduction; K.Stenning -- How to Qualify for a Cognitive Upgrade: Executive Control, Glass Ceilings, and the Limits of Simian Success; A.Clark -- Private Codes and Public Structures; C.Allen -- The Emergence of Complex Language; W.Hinzen -- Language Evolution: Enlarging the Picture; K.Stenning&M.Van Lambalgen -- Epilogue: Reminiscences of Brendan McGonigle -- Index. (shrink)

Subjects exhibiting logical competence choices, for example, in Wason's selection task, are exhibiting an important skill. We take issue with the idea that this skill is individualistic and must be selected for at some different level than System 1 skills. Our case redraws System 1/2 boundaries, and reconsiders the relationship of competence model to skill.

Oaksford & Chater (O&C) advocate Bayesian probability as a way to deal formally with the pervasive nonmonotonicity of common sense reasoning. We show that some forms of nonmonotonicity cannot be treated by Bayesian methods.

We review the various explanations that have been offered toaccount for subjects'' behaviour in Wason ''s famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects'' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject''s cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with excerpts from tutorialdialogues which motivate the kinds of (...) analysis proposed. Our long termgoal is an integration of the various insights about conditionalreasoning on offer from different cognitive science methodologies. Thepurpose of this paper is to try to draw the attention of logicians andsemanticists to this area, since we believe that empirical investigationof the cognitive processes involved could benefit from semanticanalyses. (shrink)

Theories of diagrams and diagrammatic reasoning typically seek to account for either the formal semantics of diagrams, or for the advantages which diagrammatic representations hold for the reasoner over other forms of representation. Regrettably, almost no theory exists which accounts for both of these issues together, nor how they affect one another. We do not attempt to provide such an account here. We do, however, seek to lay out larger context than is generally used for examining the processes of using (...) diagrams in reasoning or communication. A context in which detailed studies of sub-problems, such as the formal semantics or cognitive impact of specific diagrammatic systems, may be embedded.Accounts of the embedding of sentential logics in the computational processes of reasoners and communicators are relatively well developed from several decades of research in AI. Analogies between the sentential and the graphical cases are quite revealing about both similarities and differences. To provide a structure for the 'grand context' of diagrammatic representation and reasoning, and to clarify the relations between its component problems, we examine carefully these analogies and the decomposition they provide of subproblems for analysing diagrammatic reasoning. (shrink)