Bats, balls, and substitution sensitivity: cognitive misers are no happy fools

Influential work on human thinking suggests that our judgment is often biased because we minimize cognitive effort and intuitively substitute hard questions by easier ones. A key question is whether or not people realize that they are doing this and notice their mistake. Here, we test this claim with one of the most publicized examples of the substitution bias, the bat-and-ball problem. We designed an isomorphic control version in which reasoners experience no intuitive pull to substitute. Results show that people are less confident in their substituted, erroneous bat-and-ball answer than in their answer on the control version that does not give rise to the substitution. Contrary to popular belief, this basic finding indicates that biased reasoners are not completely oblivious to the substitution and sense that their answer is questionable. This calls into question the characterization of the human reasoner as a happy fool who blindly answers erroneous questions without realizing it.     

Problem solving,recall, and isomorphic transfer among third-grade and sixth-grade children

Analogical reasoning processes were studied in third- and sixth-grade children. One group at each grade level received two analogs of the “farmer's dilemma”, a scheduling problem that requires seven moves for solution, during acquisition. Other groups received one analog or only a transfer task. On each trial the child heard a list of statements representing the exact series of moves necessary to solve the problem, was immediately asked to recall the list, materials representing the problem were then produced, and the child was asked to show how to solve it. A trial was terminated and a new one begun when an error was made on the physical task. Following criterial performance all children were transferred to an isomorphic analog and simply instructed to solve it. Third-graders in the two-analog condition required more trials in acquisition than the other groups, which did not differ from each other. Transfer was better following two analogs, but was unaffected by grade level. Grade level affected recall accuracy, but recall accuracy was not a good predictor of transfer performance. Trial-by-trial analyses suggested that propositions representing the solution are acquired piecemeal, but consolidation of the generalizable problem representation is abrupt.     

Representations and strategies for solving dynamic and static arithmetic word problems: The role of working memory capacities

This study aims at determining the structure of the representation constructed by adults to solve multiple-step arithmetic word problems. We show that this structure is isomorphic to the structure of the situation described in the text of the problem. In effect, dynamic problems, which describe sequential events, are more likely to be solved by sequential strategies than are static problems. In other words, the order of succession of subgoals reached by individuals for the resolution is determined by the order of succession of subgoals explicitly described in the text of the problem. However, an alternative mental representation is constructed by low span individuals when its cognitive cost is not too high and, therefore, certain static problems are solved by a sequential strategy as well. We conclude that the probability of the construction of an alternative representation to the one induced by the text of the problem depends on its cost and the relative amount of cognitive resources it releases.     

Selecting analogous problems: Similarity versus inclusiveness

Students were asked to select one of two analogous problems in order to solve algebra word problems. In Experiment 1, one problem was less inclusive and the other was more inclusive than a test problem. The students judged the complexity and similarity of problems, selected analogous problems, and used the solutions to solve test problems. They performed significantly better on the test problems when given the more inclusive solutions, but used perceived similarity rather than inclusiveness to select analogous problems. The same pattern of results occurred in Experiment 2, in which isomorphic problems replaced the more inclusive problems. The results show that students are deficient in selecting good analogies, both from the same category (Experiment 1) and from a different category (Experiment 2). Students who saw the analogous solutions (Experiment 3) or were majoring in mathematics (Experiment 4) were more likely to select an isomorphic problem over a less inclusive problem, but were not more likely to select a more inclusive over a less inclusive problem.     

Usefulness of Tables for Solving Word Problems

Our previous research on algebra word problems (Reed, Dempster, & Ettinger, 1985) revealed that students usually could not use one problem's solution to solve a similar problem that required a slight modification of the solution. In an attempt to improve their performance, we gave students practice on either filling in tables or using completed tables. Practice on entering values into tables usually did not improve performance on constructing equations because students often failed to enter the correct values. Students' use of completed tables resulted in improved performance when the tables were provided but did not result in transfer to isomorphic problems in which the tables were not provided. Encouraging students to use previous solutions resulted in partial success on the isomorphic problems, which was explained by using a task analysis based on Sternberg's (1977) model for four-term analogy problems.     

平面几何解题过程中加工水平对迁移的影响

通过实验研究,平面几何靶题难度以及解题者对靶题与源题之间存在着共性关系的加工水平对解题迁移的影响得到了验证。结果表明,解题者对具有内在联系的先后问题之间共性关系的加工水平是影响解题迁移的因素之一;靶题的难度太大或太小,将导致解题者对先后问题之间共性关系的加工作用失败而出现地板效应和天花板效应,且靶题难度与加工水平在影响解题迁移时有交互作用。     

Social laws in alternating time: effectiveness,feasibility, and synthesis

Since it was first proposed by Moses, Shoham, and Tennenholtz, the social laws paradigm has proved to be one of the most compelling approaches to the offline coordination of multiagent systems. In this paper, we make four key contributions to the theory and practice of social laws in multiagent systems. First, we show that the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman provides an elegant and powerful framework within which to express and understand social laws for multiagent systems. Second, we show that the effectiveness, feasibility, and synthesis problems for social laws may naturally be framed as atl model checking problems, and that as a consequence, existing atl model checkers may be applied to these problems. Third, we show that the complexity of the feasibility problem in our framework is no more complex in the general case than that of the corresponding problem in the Shoham–Tennenholtz framework (it is np-complete). Finally, we show how our basic framework can easily be extended to permit social laws in which constraints on the legality or otherwise of some action may be explicitly required. We illustrate the concepts and techniques developed by means of a running example. This paper was presented at the Social Software conference in May 2004, Copenhagen, organised by PHILOG. We thank the organisers for providing the opportunity, and the participants for their useful feedback.     

Assessing Students' Misclassifications of Physics Concepts: An Ontological Basis for Conceptual Change

Physics novices and experts solved conceptual physics problems involving light, heat, and electric current and then explained their answers. Novices were ninth-grade students with no background in physics; experts were two postgraduates in physics and two advanced physics graduate students. Problems were multiple choice, with one correct response and three alternative responses representing possible misconceptions. For each conceptual physics problem, an isomorphic material-substance problem was constructed by imagining a materialistic conception of the physics topic and creating the resulting version of the problem. In each physics problem, one of the incorrect choices corresponded to the correct choice in the isomorphic material-substance problem. The empirical question was whether novices would reason about the physics problem as if it were conceptually similar to the substance isomorph. This question was addressed by comparing subjects' responses in the problem pairs, as well as by examining their explanations concerning all problems. A content analysis of subjects' explanations revealed that physics novices were strongly inclined to conceptualize physics concepts as material substances, whereas expert protocols revealed distinctly nonmaterialistic representations. A theory of conceptual change involving ontologically distinct categories is substantiated by these findings.     

Judging a book by its cover: Interpretative effects of content on problem-solving transfer

We examine how cover stories of isomorphic problems affect transfer. Existing models posit that people retain content in problem representations and that similarities and differences between the “undeleted” cover stories might interfere with recognition of structural similarities.We propose that cover stories can affect transfer in another way—by inducing semantic knowledge that modifies problem structures. Two experiments examined how people represent and solve permutation problems dealing with random assignment of elements from one set to elements from another set. Although the problems were structurally isomorphic, cover stories involving different pairs of element sets led subjects to abstract different “interpreted structures.” Problems involving objects and people (e.g., prizes and students) led subjects to abstract an asymmetric structure (“get”) and problems involving similar sets of people (e.g., doctors and doctors) led subjects to abstract a symmetric structure (“pair”). Transfer was mediated by similarities and differences between the interpreted structures of the learned and the novel problems.     

Basic emotions,rationality, and folk theory

Abstract

Answering the question of whether there are basic emotions requires considering the functions of emotions. We propose that just a few emotions are basic and that they have functions in managing action. When no fully rational solution is available for a problem of action, a basic emotion functions to prompt us in a direction that is better than a random choice. We contrast this kind of theory with a componential approach which we argue is either a version of the theory of basic emotions or else leads to the doctrine that emotions are mistaken tenets of folk psychology. We defend the psychological reality of the folk theory of emotions, and we argue that universal basic emotions make it possible to understand people from distant cultures, and to translate emotional terminology from one language to another. Finally, we show how theories of basic emotions can be tested, and indicate the kinds of empirical result that can bear on the issue.     

Temperament and adolescent substance use: an epigenetic approach to risk and protection

We outline an epigenetic approach to understanding the relation between simple dispositional characteristics and complex problem behaviors, with a focus on adolescent substance use. Epigenetic theory predicts that effects of temperament are mediated through self-control and risk-taking tendency, isomorphic attributes that are based in temperament but represent developmental elaborations of these characteristics. We describe how the research program has confirmed predictions from epigenetic theory, addressed additional questions embodied in the theory, and clarified the multiple pathways from temperament characteristics to life stress, social relationships, and motives for substance use. In a final section, we discuss implications for the study of problem behavior and psychopathology.     

不同认知风格学生的问题共性意识水平对解题迁移的影响

 本文通过实验,对初中生的平面几何成绩与其认知风格之间的关系、解题者对迁移题与源题之间共性关系的意识水平对解题迁移的影响进行了研究。结果表明:(1)初中生的平面几何成绩与认知风格有显著的正相关;(2)在平面几何解题过程中,当迁移题与源题之间具有结构共同性,且表面相似性和条件隐蔽性为中等程度时,解题者对先后问题之间共性关系的意识水平对解题迁移有显著影响。     

W-algebras which are Boolean products of members of SR[1] and CW-algebras

We show that the class of all isomorphic images of Boolean Products of members of SR [1] is the class of all archimedean W-algebras. We obtain this result from the characterization of W-algebras which are isomorphic images of Boolean Products of CW-algebras.     

ANALYSIS,ABSTRACTION PRINCIPLES,AND SLINGSHOT ARGUMENTS

Frege's views regarding analysis and synomymy have long been the subject of critical discussion. Some commentators, led by Dummett, have argued that Frege was committed to the view that each thought admits of a unique ultimate analysis. However, this interpretation is in apparent conflict with Frege's criterion of synonymy, according to which two sentence express the same thought if one cannot understand them without regarding them as having the same truth–value. In a recent article in this journal, Drai attempts to reconcile Frege's criterion of synonymy with unique ultimate analysis by holding that, for Frege, if two sentences satisfy the criterion without being intensionally isomorphic, at most one of them is a privileged representation of the thought expressed. I argue that this proposal fails, because it conflicts not only with Frege's views of abstraction principles but also with slingshot arguments (including one presented by Drai herself) that accurately reflect Frege's commitment to the view that sentences alike in truth–value have the same Bedeutung. While Drai helpfully connects Frege's views of abstraction principles with such slingshot arguments, this connection cannot become fully clear until we recognise that Frege rejects unique ultimate analysis.     

Color,context, and compositionality

Color adjectives have played a central role in work on language typology and variation, but there has been relatively little investigation of their meanings by researchers in formal semantics. This is surprising given the fact that color terms have been at the center of debates in the philosophy of language over foundational questions, in particular whether the idea of a compositional, truth-conditional theory of natural language semantics is even coherent. The challenge presented by color terms is articulated in detail in the work of Charles Travis. Travis argues that structurally isomorphic sentences containing color adjectives can shift truth value from context to context depending on how they are used and in the absence of effects of vagueness or ambiguity/polysemy, and concludes that a deterministic mapping from structures to truth conditions is impossible. The goal of this paper is to provide a linguistic perspective on this issue, which we believe defuses Travis’ challenge. We provide empirical arguments that color adjectives are in fact ambiguous between gradable and nongradable interpretations, and that this simple ambiguity, together with independently motivated options concerning scalar dimension within the gradable reading accounts for the Travis facts in a simpler, more constrained, and thus ultimately more successful fashion than recent contextualist analyses such as those in Szabó (Perspectives on semantics, pragmatics and discourse: A festschrift for Ferenc Kiefer, 2001) or Rothschild and Segal (Mind Lang, 2009).     

The role of sound intensity and stop-consonant voicing on McGurk fusions and combinations

The present paper argues that generalisation is conservative. Our goal was to experimentally study the links between knowledge generalisation and the storage of contextual elements. The knowledge domain, very simple chess configurations, allowed subjects, novices in chess, to acquire micro-expertise based on the analysis of a single source problem. In the first experimental phase, subjects had to analyse a source problem. We induced two modes of source-problem encoding: In the first group, subjects were given explanations focused on the sequence of elementary solving steps; in the other group they were given the general principle relevant to the category of problems in question. Subjects had then to solve different tests (solving isomorphic problems, recall tests, similarity tests) designed to answer two questions: The first question was to test whether the experimental manipulation in the two groups had in fact generated knowledge that varied in abstractness; the second question was to determine whether generalisation is accompanied by storage of surface features of the source problem. Results show that the knowledge generalisation is conservative. Subjects who generalise their knowledge have a better memory retention of context-dependent elements than the other subjects.     

Reductio ad contradictionem: An Algebraic Perspective

We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms.     

Arbitrary reference,numbers, and propositions

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended.     

Multi-Modal CTL: Completeness,Complexity, and an Application

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E ^δ and A ^δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic. Presented by Jacek Malinowski