The wording of conclusions in relational reasoning

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of "mental models" compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms that people use in drawing conclusions from spatial relation problems (A is to the left of B, B is to the left C, D is in front of A, E is in front C, What is the relation between D and E?). We observed a general preference for expressing conclusions with 'left' rather than conclusions with 'right'. We also found that three factors had an influence on the wording of the conclusions: the linguistic form of premises, the question type and the presentation format. On the other hand, the number of models and premise order did not affect the wording of conclusions. Our study shows that the type of conclusion produced provides a new key to identifying the mental processes involved in spatial reasoning. Implications for the two main approaches to reasoning processes (i.e. the analogical and the propositional approaches) are discussed.     

Reasoning with contrary-to-fact propositions

In the initial study, the ability of subjects at four age levels (10, 13, 15, 18 years) (1) to accept if-then premises as a basis for reasoning and (2) to reason correctly with if-then premises was examined. Half the subjects were assessed with four reasoning problems involving factually accurate premises. The other half received factually inaccurate premises which were derived from the preceding ones by altering a single term. Both tests included an abstract problem which preceded the concrete propositions. Results indicate that the 10 year olds, and to a lesser extent the 13 year olds, did have difficulty in accepting contrary-to-fact premises as a basis for reasoning. The 15 and 18 year olds did not, but did find reasoning correctly more difficult with contrary-to-fact premises. The second study examined the ability of 5 and 7 year olds to accept contrary-to-fact premises. Subjects were given factually false premises either alone or within a fantasy context. Results indicate that the fantasy context decreases the extent to which empirical knowledge interferes with accepting contrary-to-fact premises. This result supports the notion that a representational process may be involved in accepting contrary-to-fact premises.     

Figural effects in a syllogistic evaluation paradigm: an inspection-time analysis

Robust biases have been found in syllogistic reasoning that relate to the figure of premises and to the directionality of terms in given conclusions. Mental models theorists (e.g., Johnson-Laird & Byrne, 1991) have explained figural bias by assuming that reasoners can more readily form integrated models of premises when their middle terms are contiguous than when they are not. Biases associated with the direction of conclusion terms have been interpreted as reflecting a natural mode of reading off conclusions from models according to a "first-in, first-out principle." We report an experiment investigating the impact of systematic figural and conclusion-direction manipulations on the processing effort directed at syllogistic components, as indexed through a novel inspection-time method. The study yielded reliable support for mental-models predictions concerning the nature and locus of figural and directionality effects in syllogistic reasoning. We argue that other accounts of syllogistic reasoning seem less able to accommodate the full breadth of inspection-time findings observed.     

Collective rationality in interactive decisions: evidence for team reasoning

Decision theory and game theory rest on a fundamental assumption that players seek to maximize their individual utilities, but in some interactive decisions it seems intuitively reasonable to aim to maximize the utility of the group of players as a whole. Such team reasoning requires collective preferences and a distinctive mode of reasoning from preferences to decisions. Findings from two experiments provide evidence for collective preferences and team reasoning. In lifelike vignettes (Experiment 1) and abstract games (Experiment 2) with certain structural properties, most players preferred team-reasoning strategies to strategies supporting unique Nash equilibria, although individually rational players should choose equilibrium strategies. These findings suggest that team reasoning predicts strategy choices more powerfully than orthodox game theory in some games.     

Supposition and representation in human reasoning

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.     

Representing Meta-Knowledge in Poole-Systems

We show how Poole-systems, a simple approach to nonmonotonic reasoning, can be extended to take meta-information into account adequately. The meta-information is used to guide the choice of formulas accepted by the reasoner as premises. Existence of a consistent set of conclusions is guaranteed by a least fixpoint construction. The proposed formalism has useful applications in defeasible reasoning, knowledge base fusion and belief revision.     

Computers for cognitive research: A HyperCard adventure game

For researchers interested in exploring the cognitive and metacognitive processes involved in problem-solving, one obstacle has been the difficulty of creating engaging and ecologically valid situations in which to observe these skills in practice. Computer games can provide a rich environment for research on such skills. I present a HyperCard example of an adventure game that serves as an environment for research on analogy in problem-solving. The design of the game and interface is detailed, and initial results of and suggestions for extensions to this work are presented.     

Is behavioral pro-sociality game-specific? Pro-social preference and expectations of pro-sociality

We observed the behaviors of the same people across five games – two prisoner’s dilemma games, a trust game (in which the subject took on the role of both truster and trustee), a dictator game, and a faith game – any pair of which was separated by an interval of several months to reduce potential carry-over effects, and found strong consistency in behaviors among these games. We also found consistency between the expectations of other players’ behaviors and the player’s own behavior across games. We further found that the consistent behavioral pro-sociality observed across different games was related to the general measures of pro-social value orientation and perceiving the game situations. These findings suggest that individual and cultural differences in game behaviors can reflect both the ways in which people perceive game situations and their general social preferences.     

Evaluating Practical Reasoning

In this paper, the defeasible argumentation scheme for practical reasoning (Walton 1990) is revised. To replace the old scheme, two new schemes are presented, each with a matching set of critical questions. One is a purely instrumental scheme, while the other is a more complex scheme that takes values into account. It is argued that a given instance of practical reasoning can be evaluated, using schemes and sets of critical questions, in three ways: by attacking one or more premises of the argument, by attacking the inferential link between the premises and conclusion, or by mounting a counter-argument. It is argued that such an evaluation can be carried out in many cases using an argument diagram structure in which all components of the practical reasoning in the case are represented as premises, conclusions, and inferential links between them that can be labeled as argumentation schemes. This system works if every critical question can be classified as a assumption of or an exception to the original argument. However, it is also argued that this system does not work in all cases, namely those where epistemic closure is problematic because of intractable disputes about burden of proof.     

Levels of theory‐of‐mind reasoning in competitive games

The literature on recursive theory of mind (TOM) reasoning in interactive decision making (reasoning of the type “I think that you think that I think…”) has been pessimistic, suggesting that adults attribute to others levels of reasoning that are low and slow to increase with learning. In four experiments with college‐age adults playing sequential games, we examined whether choices and predictions were consistent with believing that others pursue their immediate self‐interest, or with believing that others reason through their own decision making, with fixed‐sum games that were simpler and more competitive. This manipulation led to higher‐level default TOM reasoning; indeed, reasoning against a lower‐level opponent was frequently consistent with assuming the opponent's reasoning to be higher‐level, leading to sub‐optimal choices. We conclude that TOM reasoning is not of a low level in all game settings; rather, individuals may display effective TOM reasoning, reflecting realistic assumptions about their opponents, in competitive and relatively simple games. Copyright © 2010 John Wiley & Sons, Ltd.     

ERP characteristics of sentential inductive reasoning in time and frequency domains

Earlier studies have examined the issues of brain spatial localization in human sentential inductive reasoning using PET/fMRI. However, the temporal characteristics of such reasoning remain unclear. In our present study, we have used ERP (Event-related Potential) to further study human inductive reasoning involving sentential tasks. For congruent induction tasks, in which premises and conclusions are related, participants need to synthesize semantic information from the premises, conclusions, as well as background knowledge, while for incongruent induction tasks (baseline), in which premises and conclusions are unrelated, participants can respond “no” immediately. Behavioral data have been obtained that is consistent with expectations. ERPs imply that participants may integrate semantic information within the time window of 350–650 ms. Statistical analysis in the frequency domain has revealed a significant increase in the power of the gamma band (30–50 Hz) for congruent induction tasks in contrast to incongruent induction tasks.     

Strategies in Syllogistic Reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.     

Common reasoning about admissibility

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction.     

Classical Game Theory, Socialization and the Rationalization of Conventions

The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game theory readily explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products.     

What do you think I think you think?: Strategic reasoning in matrix games

In reasoning about strategic interpersonal situations, such as in playing games, an individual's representation of the situation often includes not only information about the goals and rules of the game, but also a mental model of other minds. Often such mental models involve a hierarchy of reflexive reasoning commonly employed in social situations ("What do you think I think you think..."), and may be related to the developmental notion of 'theory of mind'. In two experiments, the authors formally investigate such interpersonal recursive reasoning in college-age adults within the context of matrix games. Participants are asked to predict the moves of another player (experimenter's confederate) in a two-choice, sequential-move game that may terminate at various stages with different payoffs for each player. Participants are also asked to decide optimally on their own moves based on the prediction made. Errors concerning the prediction, or translation of those predictions into decisions about one's action, were recorded. Results demonstrate the existence of a "default" mental model about the other player in the game context that is dynamically modified as new evidence is accumulated. Predictions about this other player's behavior are, in general, used consistently in decision-making, though the opponent tends to be modeled, by default, to behave in a myopic fashion not anticipating the participant's own action.     

视频游戏对认知能力的影响及其神经基础

视频游戏是一类需要借助视听设备并基于一定剧情进行操作的游戏。先前研究大多关注暴力视频游戏对攻击等负面行为的影响,但本文着重探讨视频游戏对个体认知能力的积极影响及内在神经基础,以辩证看待视频游戏对个体心理和行为的作用。本文对前人研究归纳梳理发现,视频游戏训练能使个体认知能力得到持久改善,同时论述了视频游戏中脑神经基础和奖赏预期对认知能力的调控作用。未来研究应在规范视频游戏训练技术的基础上,用其干预靶脑区以提升个体特定脑功能。     

The effects of belief on the spontaneous production of syllogistic conclusions

Two experiments examined the effects of subjects' beliefs on syllogistic inference. The first experiment showed that beliefs biased the spontaneous conclusions that subjects drew for themselves. These effects were more marked for indeterminate premises (which yield no non-trivial valid conclusions) than for determinate premises (which yield valid conclusions). There was also an effect of the nature of the beliefs: conclusions that were false by definition had a bigger effect on deductions than those that were false as a matter of fact. The second experiment replicated the finding for determinate syllogisms, using problems in moods in which the status of the valid conclusion could not be altered by conversion of the premises. Beliefs accordingly appear to affect the process of reasoning rather than the interpretation of premises.     

Believability and syllogistic reasoning

In this paper we investigate the locus of believability effects in syllogistic reasoning. We identify three points in the reasoning process at which such effects could occur: the initial interpretation of premises, the examination of alternative representations of them (in all of which any valid conclusion must be true), and the "filtering" of putative conclusions. The effect of beliefs at the first of these loci is well established. In this paper we report three experiments that examine whether beliefs have an effect at the other two loci. In experiments 1 and 2 subjects drew their own conclusions from syllogisms that suggested believable or unbelievable ones. In the third experiment they evaluated conclusions that were presented to them. The data show that beliefs both affect the examination of alternative models and act as a filter on putative conclusions. We conclude by showing how some types of problem and some problem contents make the existence of alternative models more obvious than others.     

Content and strategy in syllogistic reasoning.

Syllogistic reasoning has been investigated as a general deductive process (Johnson-Laird & Byrne, 1991; Revlis, 1975; Rips, 1994). However, several studies have demonstrated the role of cognitive strategies in this type of reasoning. These strategies focus on the method used by the participants (Ford, 1995; Gilhooly, Logie, Wetherick, & Wynn, 1993) and strategies related to different interpretations of the quantified premises (Roberts, Newstead, & Griggs, 2001). In this paper, we propose that content (as well as individual cognitive differences) is an important factor in inducing a certain strategy or method for syllogistic resolution. Specifically, we suggest that syllogisms with a causal conditional premise that can be extended by an agency premise induce the use of a conditional method. To demonstrate this, we carried out two experiments. Experiment 1 provided evidence that this type of syllogism leads participants to draw the predicted conditional conclusions, in contrast with control content syllogisms. In Experiment 2, we demonstrated that the drawing of conditional conclusions is based on a causal conditional to an agent representation of the syllogism premises. These results support the role of content as inducing a particular strategy for syllogistic resolution. The implications of these results are discussed.