Between reasoning

In two experiments we investigated three-term reasoning with spatial relational assertions using the preposition between as compared to projective prepositions (such as to the left of). For each kind of assertion we distinguish the referent expression (i.e., the grammatical subject) from the relatum expression (i.e., the internal argument of the preposition; e.g., [The hedgehog]_{referent_expression} is to the left of [the frog]_{relatum_expression}; [the snake]_{referent_expression} is between [the donkey and the deer]_{relatum_expression}). Previous research has shown that integrating premises with projective prepositions is easier (a) when the relatum expression of the second premise denotes an element already given by the first premise (relatum = given), and (b) when the term denoting a given element precedes the term denoting a new element (given–new). Experiment 1 extended this finding to second premises with the preposition between. In Experiment 2, between figured in the first premise. In this case, participants built an initial preferred model already from the first premise, although such a premise is indeterminate with respect to the array that it describes. Since there is no need left for integrating the second premise, this premise is instead used to verify the initial model and to modify it when necessary. A further investigation of conclusion evaluation times showed that conclusions were evaluated faster when they first mentioned the element that was included most recently into the mental model of the premises. The use of premises with between permitted the separation of recency of model inclusion from recency of appearance of an element in a premise.     

Causal reasoning

The main focus of this paper is the question as to what it is for an individual to think of her environment in terms of a concept of causation, or causal concepts, in contrast to some more primitive ways in which an individual might pick out or register what are in fact causal phenomena. I show how versions of this question arise in the context of two strands of work on causation, represented by Elizabeth Anscombe and Christopher Hitchcock, respectively. I then describe a central type of reasoning that, I suggest, a subject has to be able to engage in, if we are to credit her with causal concepts. I also point out that this type of reasoning turns on the idea of a physical connection between cause and effect, as articulated in recent singularist approaches of causation.     

Unless reasoning

We report the results of two experiments investigating conditional inferences from conditional unless assertions, such as Juan is not in León unless Nuria is in Madrid. Experiments 1 and 2 check Fillenbaum's hypothesis about the semantic similarity of unless with if not and only if assertions; both also examine inferential endorsements (Experiment 1) and endorsements and latencies (Experiment 2) of the four logically equivalent conditional formulations: if A then B, if not-B then not-A, A only if B and notA unless B. The results of these experiments show the similarity of unless and only if confirming that the representation of both conditionals from the outset probably include two possibilities directionally oriented from B to A; results also confirm the especial difficulty of unless assertions. The implications of the results are discussed in the context of recent psychological and linguistic theories of the meaning of unless.     

Circular reasoning

Good informal arguments offer justification for their conclusions. They go wrong if the justifications double back, rendering the arguments circular. Circularity, however, is not necessarily a single property of an argument, but may depend on (a) whether the argument repeats an earlier claim, (b) whether the repetition occurs within the same line of justification, and (c) whether the claim is properly grounded in agreed‐upon information. The experiments reported here examine whether people take these factors into account in their judgments of whether arguments are circular and whether they are reasonable. The results suggest that direct judgments of circularity depend heavily on repetition and structural role of claims, but only minimally on grounding. Judgments of reasonableness take repetition and grounding into account, but are relatively insensitive to structural role.     

Between reasoning

In two experiments we investigated three-term reasoning with spatial relational assertions using the preposition between as compared to projective prepositions (such as to the left of). For each kind of assertion we distinguish the referent expression (i.e., the grammatical subject) from the relatum expression (i.e., the internal argument of the preposition; e.g., [The hedgehog]_{referent_expression} is to the left of [the frog]_{relatum_expression}; [the snake]_{referent_expression} is between [the donkey and the deer]_{relatum_expression}). Previous research has shown that integrating premises with projective prepositions is easier (a) when the relatum expression of the second premise denotes an element already given by the first premise (relatum = given), and (b) when the term denoting a given element precedes the term denoting a new element (given-new). Experiment 1 extended this finding to second premises with the preposition between. In Experiment 2, between figured in the first premise. In this case, participants built an initial preferred model already from the first premise, although such a premise is indeterminate with respect to the array that it describes. Since there is no need left for integrating the second premise, this premise is instead used to verify the initial model and to modify it when necessary. A further investigation of conclusion evaluation times showed that conclusions were evaluated faster when they first mentioned the element that was included most recently into the mental model of the premises. The use of premises with between permitted the separation of recency of model inclusion from recency of appearance of an element in a premise.     

Speed of reasoning and its relation to reasoning ability

The study investigates empirical properties of reasoning speed which is conceived as the fluency of solving reasoning problems. Responses and response times in reasoning tasks are modeled jointly to clarify the covariance structure of reasoning speed and reasoning ability. To determine underlying abilities, the predictive validities of two cognitive covariates, namely perceptual and executive attention, are investigated. A sample of N = 230 test takers completed a reasoning test, Advanced Progressive Matrices (APM), and attention tests indicating perceptual and executive attention. For modeling responses the two-parameter normal ogive model, and for modeling response times the two-parameter lognormal model was applied. Results suggest that reasoning speed is a unidimensional construct representing significant individual differences, and that reasoning speed and ability are negatively correlated but clearly distinguishable constructs. Perceptual and executive attention showed differential effects on reasoning speed and reasoning ability, i.e., reasoning speed is explained by executive attention only, while reasoning ability is explained by both covariates. Implications for the assessment of reasoning are discussed.     

Co-reference and reasoning

Memory &; Cognition - Co-reference occurs when two or more noun phrases refer to the same individual, as in the following inferential problem: Mark is kneeling by the fire or he is looking at...     

Training propositional reasoning

Two experiments compared the effects of four training conditions on propositional reasoning. A syntactic training demonstrated formal derivations, in an abstract semantic training the standard truth-table definitions of logical connectives were explained, and a domain-specific semantic training provided thematic contexts for the premises of the reasoning task. In a control training, an inductive reasoning task was practised. In line with the account by mental models, both kinds of semantic training were significantly more effective than the control and the syntactic training, whereas there were no significant differences between the control and the syntactic training, nor between the two kinds of semantic training. Experiment 2 replicated this pattern of effects using a different set of syntactic and domain-specific training conditions.     

Conditionals in reasoning

The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given a non-bivalent semantics and epistemic states are represented via preferential models.     

Enhancing geometric reasoning

Geometry is an important part of the mathematics curriculum. However, students are not demonstrating strong conceptual knowledge of this subject. The research of Van Hiele and Van Hiele-Geldof has focused on the concept of thinking levels in geometry and the role of instruction in raising levels of thinking. This paper describes a field trial of a supplemental geometry unit intended to raise Van Hiele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels and attitudes toward geometry, as well as field-tested activities yielding the most positive results, are presented. Educators can benefit from this application of the Van Hiele model of geometric thinking, since the thought processes involved in learning geometry are explained, along with teaching techniques and tools for assessment. By having teachers become more aware of their students' cognitive skills, attitudes, and misconceptions, teaching practices and student achievement can be enhanced.     

Pragmatic reasoning schemas

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.     

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.     

Belief in reasoning

Reasoning has three types, deduction, induction, and abduction, of which we perceive deduction to be necessarily true, induction plausibly true, and abduction only hypothetically true. Syllogistic is a theory of deductive reasoning, introducing three figures of inferencing, of which figure-1 is obviously true, figure-3 and figure-2 are increasingly less transparent. We argue that the three figures of syllogistic and the three types of reasoning are related and their truth perceptions can be explained as different degrees of belief. We suggest that the source of this difference can be found in the conversion of a premise required by syllogistic processing. Experimental results illustrating our theory are included.     

The influence of complexity and reasoning direction on children's causal reasoning

Causal reasoning is the core and basis of cognition about the objective world. This experiment studied the development of causal reasoning in 86 3.5–4.5-year-olds using a ramp apparatus with two input holes and two output holes [Frye, D., Zelazo, P. D., & Palfai, T. (1995). Theory of mind and rule-based reasoning. Cognitive Development 10, 483–527]. Results revealed that: (1) children performed better on cause–effect inferences than on effect–cause inferences; (2) there was an effect of rule complexity such that uni-dimensional causal inferences were easier than bi-dimensional inferences which, in turn, were easier than tri-dimensional causal inferences; and (3) children's causal reasoning develops rapidly between the ages of age of 3.5 and 4 years.     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

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.