Simple Heuristics That Make Us Smart invites readers to embark on a new journey into a land of rationality that differs from the familiar territory of cognitive science and economics. Traditional views of rationality tend to see decision makers as possessing superhuman powers of reason, limitless knowledge, and all of eternity in which to ponder choices. To understand decisions in the real world, we need a different, more psychologically plausible notion of rationality, and this book provides it. It is about (...) fast and frugal heuristics--simple rules for making decisions when time is pressing and deep thought an unaffordable luxury. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? Can judgments based simply on one good reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? Simple Heuristics explores these questions, developing computational models of heuristics and testing them through experiments and analyses. It shows how fast and frugal heuristics can produce adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop out rates, and playing the stock market. As an interdisciplinary work that is both useful and engaging, this book will appeal to a wide audience. It is ideal for researchers in cognitive psychology, evolutionary psychology, and cognitive science, as well as in economics and artificial intelligence. It will also inspire anyone interested in simply making good decisions. (shrink)

The human cognitive architecture consists of a set of largely independent modules associated with different brain regions. This book discusses in detail how these various modules can combine to produce behaviours as varied as driving a car and solving an algebraic equation.

Modern logic is undergoing a cognitive turn, side-stepping Frege’s ‘antipsychologism’. Collaborations between logicians and colleagues in more empirical fields are growing, especially in research on reasoning and information update by intelligent agents. We place this border-crossing research in the context of long-standing contacts between logic and empirical facts, since pure normativity has never been a plausible stance. We also discuss what the fall of Frege’s Wall means for a new agenda of logic as a theory of rational agency, and what (...) might then be a viable understanding of ‘psychologism’ as a friend rather than an enemy of logical theory. (shrink)

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight (...) in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems. (shrink)

Many social situations require a mental model of the knowledge, beliefs, goals, and intentions of others: a Theory of Mind (ToM). If a person can reason about other people’s beliefs about his own beliefs or intentions, he is demonstrating second-order ToM reasoning. A standard task to test second-order ToM reasoning is the second-order false belief task. A different approach to investigating ToM reasoning is through its application in a strategic game. Another task that is believed to involve the application of (...) second-order ToM is the comprehension of sentences that the hearer can only understand by considering the speaker’s alternatives. In this study we tested 40 children between 8 and 10 years old and 27 adult controls on (adaptations of) the three tasks mentioned above: the false belief task, a strategic game, and a sentence comprehension task. The results show interesting differences between adults and children, between the three tasks, and between this study and previous research. (shrink)

This article describes the Adaptive Control of Thought–Rational (ACT–R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children learn to solve linear equations and perfect their skills over a 6‐day period. Functional MRI data show that: (a) a motor region tracks the output of equation solutions, (b) (...) a prefrontal region tracks the retrieval of declarative information, (c) a parietal region tracks the transformation of mental representations of the equation, (d) an anterior cingulate region tracks the setting of goal information to control the information flow, and (e) a caudate region tracks the firing of productions in the ACT–R model. The article concludes with an architectural comparison of the competence children display in this task and the competence that monkeys have shown in tasks that require manipulations of sequences of elements. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (shrink)

Reasoning that compares two objects or situations to draw conclusions about previously unknown properties of one of them has traditionally been taken to be ampliative and probabilistic. I propose that it is apodeictic reasoning from a premise about isomorphic structures that is often uncertain, but which we may have good reasons to believe. I characterize the structures and their isomorphism, describe patterns of reasoning appropriate to them, and discuss some complications not immediately obvious.

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as (...) the result of a joint act of learning that the node is reached. We then use the notion of "stable belief, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to believe in a player's rationality after updating with his irrationality. (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (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)

Most accounts of the Stroop effect (Stroop, 1935) emphasize its negative aspect, namely, that in particular situations, processing of an irrelevant stimulus dimension interferes with participants' performance of the instructed task. In contrast, this paper emphasizes the fact that, even with that interference, participants actually can (and usually do) exert enough control to perform the instructed task. An Adaptive Control of Thought–Rational (ACT–R) model of the Stroop task interprets this as a kind of learned strategic control. Specifically, the concept of (...) utility is applied to the two processes that compete in the Stroop task, and a utility‐learning mechanism serves to update the corresponding utility values according to experience and hence influence the competition. This model both accounts for various extant Stroop results and makes novel predictions about when people can reduce their susceptibility to Stroop interference. These predictions are tested in three experiments that involve a double‐response variant of the Stroop task. (shrink)

The paper is concerned with the psychological relevance of a logical model for deductive reasoning. We propose a new way to analyze logical reasoning in a deductive version of the Mastermind game implemented within a popular Dutch online educational learning system (Math Garden). Our main goal is to derive predictions about the difficulty of Deductive Mastermind tasks. By means of a logical analysis we derive the number of steps needed for solving these tasks (a proxy for working memory load). Our (...) model is based on the analytic tableaux method, known from proof theory. We associate the difficulty of Deductive Mastermind game-items with the size of the corresponding logical trees obtained by the tableaux method. We derive empirical hypotheses from this model. A large group of students (over 37 thousand children, 5–12 years of age) played the Deductive Mastermind game, which gave empirical difficulty ratings of all 321 game-items. The results show that our logical approach predicts these item ratings well, which supports the psychological relevance of our model. (shrink)

Strategic games require reasoning about other people’s and one’s own beliefs or intentions. Although they have clear commonalities with psychological tests of theory of mind, they are not clearly related to theory of mind tests for children between 9 and 10 years of age “Flobbe et al. J Logic Language Inform 17(4):417–442 (2008)”. We studied children’s (5–12 years of age) individual differences in how they played a strategic game by analyzing the strategies that they applied in a zero, first, and (...) second-order reasoning task. For the zero-order task, we found two subgroups with different accuracy levels. For the first-order task, subgroups of children applied different suboptimal strategies or an optimal strategy. For the second-order task only suboptimal strategies were present. Strategy use for all tasks was related to age. The 5- and 6-year old children were additionally tested on theory of mind understanding and executive functioning. Strategy-use in these children was related to working memory, but not to theory of mind after correction for age, verbal ability and general IQ. (shrink)

is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [ 4 , 5 ]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.

Strategic games require reasoning about other people’s and one’s own beliefs or intentions. Although they have clear commonalities with psychological tests of theory of mind, they are not clearly related to theory of mind tests for children between 9 and 10 years of age “Flobbe et al. J Logic Language Inform 17(4):417–442 (2008)”. We studied children’s (5–12 years of age) individual differences in how they played a strategic game by analyzing the strategies that they applied in a zero, first, and (...) second-order reasoning task. For the zero-order task, we found two subgroups with different accuracy levels. For the first-order task, subgroups of children applied different suboptimal strategies or an optimal strategy. For the second-order task only suboptimal strategies were present. Strategy use for all tasks was related to age. The 5- and 6-year old children were additionally tested on theory of mind understanding and executive functioning. Strategy-use in these children was related to working memory, but not to theory of mind after correction for age, verbal ability and general IQ. (shrink)

Complex problem solving is often an integration of perceptual processing and deliberate planning. But what balances these two processes, and how do novices differ from experts? We investigate the interplay between these two in the game of SET. This article investigates how people combine bottom-up visual processes and top-down planning to succeed in this game. Using combinatorial and mixed-effect regression analysis of eye-movement protocols and a cognitive model of a human player, we show that SET players deploy both bottom-up and (...) top-down processes in parallel to accomplish the same task. The combination of competition and cooperation of both types of processes is a major factor of success in the game. Finally, we explore strategies players use during the game. Our findings suggest that within-trial strategy shifts can occur without the need of explicit meta-cognitive control, but rather implicitly as a result of evolving memory activations. (shrink)

Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views.

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we (...) do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

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)