An inductive reasoning model in linear and quadratic sequences

Presentamos algunos resultados de una investigación más amplia cuyo objetivo general es describir y caracterizar el razonamiento inductivo que utilizan estudiantes de tercero y cuarto de Secundaria al resolver tareas relacionadas con sucesiones lineales y cuadráticas (Cañadas, 2007). Identificamos diferencias en el empleo de algunos de los pasos considerados para la descripción del razonamiento inductivo en la resolución de dos de los seis problemas planteados a los estudiantes. Describimos estas diferencias y las analizamos en función de las características de los problemas.

A proposal of categorisation for analysing inductive reasoning

We present an analysis of the inductive reasoning of twelve Spanish secondary students in a mathematical problem-solving context. Students were interviewed while they worked on two different problems. Based on Polya´s steps and Reid’s stages for a process of inductive reasoning, we propose a more precise categorization for analyzing this kind of reasoning in our particular context. In this paper we present some results of a wider investigation (Cañadas, 2002).

Inductive reasoning in the justification of the result of adding two even numbers

In this paper we present an analysis of the inductive reasoning of twelve secondary students in a mathematical problem-solving context. Students were proposed to justify what is the result of adding two even numbers. Starting from the theoretical framework, which is based on Pólya’s stages of inductive reasoning, and our empirical work, we created a category system that allowed us to make a qualitative data analysis. We show in this paper some of the results obtained in a previous study.

Inductive reasoning and semantic cognition: More than just different names for the same thing?

We describe evidence that certain inductive phenomena are associated with IQ, that different inductive phenomena emerge at different ages, and that the effects of causal knowledge on induction are decreased under conditions of memory load. On the basis of this evidence we argue that there is more to inductive reasoning than semantic cognition.

Causal knowledge and the development of inductive reasoning

We explored the development of sensitivity to causal relations in children’s inductive reasoning. Children (5-, 8-, and 12-year-olds) and adults were given trials in which they decided whether a property known to be possessed by members of one category was also possessed by members of (a) a taxonomically related category or (b) a causally related category. The direction of the causal link was either predictive (prey → predator) or diagnostic (predator → prey), and the property that participants reasoned about established either a taxonomic or causal context. There was a causal asymmetry effect across all age groups, with more causal choices when the causal link was predictive than when it was diagnostic. Furthermore, context-sensitive causal reasoning showed a curvilinear development, with causal choices being most frequent for 8-year-olds regardless of context. Causal inductions decreased thereafter because 12-year-olds and adults made more taxonomic choices when reasoning in the taxonomic context. These findings suggest that simple causal relations may often be the default knowledge structure in young children’s inductive reasoning, that sensitivity to causal direction is present early on, and that children over-generalize their causal knowledge when reasoning.

A proposal of categorization for analysing inductive reasoning. 'Una propuesta de categorización para analizar el razonamiento inductivo'.

Investigación original con el título: 'Razonamiento inductivo puesto de manifiesto por alumnos de Secundaria' de María Consuelo Cañadas Santiago, publicada en 2002 por la Universidad de Granada

An investigation into children’s inductive reasoning strategies:What drives the development of category induction?

In a series of studies, I investigated the developmental changes in children’s inductive reasoning strategy, methodological manipulations affecting the trajectory, and driving mechanisms behind the development of category induction. I systematically controlled the nature of the stimuli used, and employed a triad paradigm in which perceptual cues were directly pitted against category membership, to explore under which circumstances children used perceptual or category induction. My induction tasks were designed for children aged 3-9 years old using biologically plausible novel items. In Study 1, I tested 264 children. Using a wide age range allowed me to systematically investigate the developmental trajectory of induction. I also created two degrees of perceptual distractor – high and low – and explored whether the degree of perceptual similarity between target and test items altered children’s strategy preference. A further 52 children were tested in Study 2, to examine whether children showing a perceptual-bias were in fact basing their choice on maturation categories. A gradual transition was observed from perceptual to category induction. However, this transition could not be due to the inability to inhibit high perceptual distractors as children of all ages were equally distracted. Children were also not basing their strategy choices on maturation categories. In Study 3, I investigated category structure (featural vs. relational category rules) and domain (natural vs. artefact) on inductive preference. I tested 403 children. Each child was assigned to either the featural or relational condition, and completed both a natural kind and an artefact task. A further 98 children were tested in Study 4, on the effect of using stimuli labels during the tasks. I observed the same gradual transition from perceptual to category induction preference in Studies 3 and 4. This pattern was stable across domains, but children developed a category-bias one year later for relational categories, arguably due to the greater demands on executive function (EF) posed by these stimuli. Children who received labels during the task made significantly more category choices than those who did not receive labels, possibly due to priming effects. Having investigated influences affecting the developmental trajectory, I continued by exploring the driving mechanism behind the development of category induction. In Study 5, I tested 60 children on a battery of EF tasks as well as my induction task. None of the EF tasks were able to predict inductive variance, therefore EF development is unlikely to be the driving factor behind the transition. Finally in Study 6, I divided 252 children into either a comparison group or an intervention group. The intervention group took part in an interactive educational session at Twycross Zoo about animal adaptations. Both groups took part in four induction tasks, two before and two a week after the zoo visits. There was a significant increase in the number of category choices made in the intervention condition after the zoo visit, a result not observed in the comparison condition. This highlights the role of knowledge in supporting the transition from perceptual to category induction. I suggest that EF development may support induction development, but the driving mechanism behind the transition is an accumulation of knowledge, and an appreciation for the importance of category membership.

Robot Control Using Inductive, Deductive and Case Based Reasoning

The paper deals with a problem of intelligent system’s design for complex environments. There is discussed a possibility to integrate several technologies into one basic structure that could form a kernel of an autonomous intelligent robotic system. One alternative structure is proposed in order to form a basis of an intelligent system that would be able to operate in complex environments. The proposed structure is very flexible because of features that allow adapting via learning and adjustment of the used knowledge. Therefore, the proposed structure may be used in environments with stochastic features such as hardly predictable events or elements. The basic elements of the proposed structure have found their implementation in software system and experimental robotic system. The software system as well as the robotic system has been used for experimentation in order to validate the proposed structure - its functionality, flexibility and reliability. Both of them are presented in the paper. The basic features of each system are presented as well. The most important results of experiments are outlined and discussed at the end of the paper. Some possible directions of further research are also sketched at the end of the paper.

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.

Probabilistic Inductive Querying Using ProbLog

We study how probabilistic reasoning and inductive querying can be combined within ProbLog, a recent probabilistic extension of Prolog. ProbLog can be regarded as a database system that supports both probabilistic and inductive reasoning through a variety of querying mechanisms. After a short introduction to ProbLog, we provide a survey of the different types of inductive queries that ProbLog supports, and show how it can be applied to the mining of large biological networks.

Relations between premise similarity and inductive strength

According to the diversity principle, diverse evidence is strong evidence. There has been considerable evidence that people respect this principle in inductive reasoning. However, exceptions may be particularly informative. Medin, Coley, Storms, and Hayes (2003) introduced a relevance theory of inductive reasoning and used this theory to predict exceptions, including the nondiversity-by-property-reinforcement effect. A new experiment in which this phenomenon was investigated is reported here. Subjects made inductive strength judgments and similarity judgments for stimuli from Medin et al. (2003). The inductive strength judgments showed the same pattern as that in Medin et al. (2003); however, the similarity judgments suggested that the pattern should be interpreted as a diversity effect, rather than as a nondiversity effect. It is concluded that the evidence regarding the predicted nondiversity-by-property-reinforcement effect does not give distinctive support for relevance theory, although this theory does address other results.

The Engine of Thought Is a Hybrid: Roles of Associative and Structured Knowledge in Reasoning

Across a range of domains in psychology different theories assume different mental representations of knowledge. For example, in the literature on category-based inductive reasoning, certain theories (e.g., Rogers & McClelland, 2004; Sloutsky & Fisher, 2008) assume that the knowledge upon which inductive inferences are based is associative, whereas others (e.g., Heit & Rubinstein, 1994; Kemp & Tenenbaum, 2009; Osherson, Smith, Wilkie, López, & Shafir, 1990) assume that knowledge is structured. In this article we investigate whether associative and structured knowledge underlie inductive reasoning to different degrees under different processing conditions. We develop a measure of knowledge about the degree of association between categories and show that it dissociates from measures of structured knowledge. In Experiment 1 participants rated the strength of inductive arguments whose categories were either taxonomically or causally related. A measure of associative strength predicted reasoning when people had to respond fast, whereas causal and taxonomic knowledge explained inference strength when people responded slowly. In Experiment 2, we also manipulated whether the causal link between the categories was predictive or diagnostic. Participants preferred predictive to diagnostic arguments except when they responded under cognitive load. In Experiment 3, using an open-ended induction paradigm, people generated and evaluated their own conclusion categories. Inductive strength was predicted by associative strength under heavy cognitive load, whereas an index of structured knowledge was more predictive of inductive strength under minimal cognitive load. Together these results suggest that associative and structured models of reasoning apply best under different processing conditions and that the application of structured knowledge in reasoning is often effortful.