Inductive reasoning is the development of a theory or a conclusion
after consideration of several empirical observations.
Inductive means leading on to an action, or inducing.
Inductive reasoning is based on, or characterized by induction;
using a method of induction.
Deductive means of or pertaining to deduction; of the nature of
or characterized by deduction; reasoning from the general to the particular.
Deductivism is the belief in the superiority of, or preference
for, deductive over inductive methods of reasoning.
Deductive versus Inductive Reasoning
Noah D. Alper - cooperativeindividualism.org
In his History of Civilization in England, Henry Thomas Buckle makes some interesting
observations on the respective merits of the deductive and inductive methods of
propagating thought in the development of civilization. In the deductive method we begin
with a general conclusion and then attempt to point out the facts which support it. In the
inductive method we first select our facts and then seek to lead to the acceptance of the
general conclusions or principles.
The Development of Inductive Reasoning: Cross-sectional
Assessments in an Educational Context
Beno Csapó, Attila József University, Szeged, Hungary
This paper links two research paradigms, one that studies attributes and mechanisms of
inductive reasoning and one that tries to make school learning more meaningful and
knowledge better understood and more easily applied, by examining how inductive reasoning
develops during a significant age range of schooling and how it relates to certain other
cognitive functions. Six tests of inductive reasoning (number analogies, verbal analogies,
number series, verbal series, coding, exclusion) were devised and administered to 3rd,
5th, 7th, 9th, and 11th grade students (N 2000). Data were also collected on
students’ school achievement, and a test of applied science knowledge was
administered to the two oldest samples. The comparison of age groups indicated that the
fastest development of inductive reasoning took place between the 5th and 9th grades; a
major development was detected before the 5th grade, and only modest changes were found
after the 9th grade. Regression analysis models indicated that inductive reasoning
accounted for around twice as large a proportion of the results of the test that measured
the applied science knowledge in everyday situations as did school knowledge (represented
by school grades). - jbd.sagepub.com/cgi/content/abstract/20/4/609
The seats of reason? An imaging study of deductive and inductive reasoning.Goel V,
Gold B, Kapur S, Houle S.
Department of Psychology, York University, North York, Ontario, Canada.
We carried out a neuroimaging study to test the neurophysiological predictions made by
different cognitive models of reasoning. Ten normal volunteers performed deductive and
inductive reasoning tasks while their regional cerebral blood flow pattern was recorded
using [15O]H2O PET imaging. In the control condition subjects semantically comprehended
sets of three sentences. In the deductive reasoning condition subjects determined whether
the third sentence was entailed by the first two sentences. In the inductive reasoning
condition subjects reported whether the third sentence was plausible given the first two
sentences. The deduction condition resulted in activation of the left inferior frontal
gyrus (Brodmann areas 45, 47). The induction condition resulted in activation of a large
area comprised of the left medial frontal gyrus, the left cingulate gyrus, and the left
superior frontal gyrus (Brodmann areas 8, 9, 24, 32). Induction was distinguished from
deduction by the involvement of the medial aspect of the left superior frontal gyrus
(Brodmann areas 8, 9). These results are consistent with cognitive models of reasoning
that postulate different mechanisms for inductive and deductive reasoning and view
deduction as a formal rule-based process. - ncbi.nlm.nih.gov
Supporting Inductive Reasoning in Adaptive Virtual Learning Environment
T. Lin, Kinshuk, and P. McNab (New Zealand)
Abstract: Inductive reasoning ability is one of most important mental abilities that give
rise to human intelligence and is regarded as the best predictor for academic performance.
However, most of the adaptive virtual learning environments tailor the learning material
adaptively according to only learners' domain performance thus leaving learner's cognitive
capacity, such as inductive reasoning ability, unsupported. As part of a series of
research on cognitive trait model that aim to allow virtual learning environments to
provide adaptive support for the learner's cognitive capacity, this paper presents the
finding on the particular issue of how individual's inductive reasoning capability can be
supported using adaptive techniques for improved learning performance. -
actapress.com/PaperInfo.aspx?PaperID=19753
Fuzzy Measures in Inductive Reasoning
Donghui Li, Physical Design (CAD), LSI Logic Corporation
François E. Cellier, Institute of Computational Science, ETH Zürich
Abstract: Inductive Reasoning is a technique which allows us to reason about a finite
state representation of a system on the basis of available data. If the data stem from a
continuous system, they are first discretized (recoded) into a finite set of discrete
values. Recently, optimal recoding techniques have been devised which are presented in
this paper. The forecasting power of the Inductive Reasoning approach has been shown to be
dramatic in a number of examples. Yet, the forecast was always expressed in terms of the
recoded, i.e. the discrete, variables, and not in terms of the original continuous
variables. Recently, we have been working on a modification of the technique which allows
us to reconstruct the continuous signals from the forecast discrete signals with very good
accuracy. For this purpose, we exchanged the previously used probabilistic quality
measures for fuzzy quality measures, and we predict, together with the discrete states
also new fuzzy membership functions of the forecast signals. From these membership
functions, we can then regenerate the continuous signals. The technique has been tested by
means of a third order continuous-time linear system and has given promising results. -
inf.ethz.ch/personal/fcellier/Pubs/FIR/wsc_90_li.html
Inductive Reasoning, Bounded Rationality and the Bar Problem
W. Brian Arthur
Abstract: This paper draws on modern psychology to argue that as humans, in economic
decision contexts that are complicated or ill-defined, we use not deductive, but inductive
reasoning. That is, in such contexts we induce a variety of working hypotheses or mental
models, act upon the most credible, and replace hypotheses with new ones if they cease to
work. Inductive reasoning leads to a rich psychological world in which an agent’s
hypotheses or mental models compete for survival against each other, in an environment
formed by other agents’ hypotheses or mental models--a world that is both
evolutionary and complex. Inductive reasoning can be modeled in a variety of ways. The
main body of the paper introduces and models a coordination problem--“the bar
problem”--in which agents’ expectations are forced to be subjective and to
differ. It shows that while agents’ beliefs never settle down, collectively they form
and “ecology” that does converge to an equilibrium pattern. -
santafe.edu/research/publications/wpabstract/199403014
Inductive Reasoning and Judgment Interference: Experiments on Simpson’s
Paradox
Klaus Fiedler, Eva Walther, Peter Freytag, Stefanie Nickel, University of
Heidelberg
In a series of experiments on inductive reasoning, participants assessed the relationship
between gender, success, and a covariate in a situation akin to Simpson’s paradox:
Although women were less successful then men according to overall statistics, they
actually fared better then men at either of two universities. Understanding trivariate
relationships of this kind requires cognitive routines similar to analysis of covariance.
Across the first five experiments, however, participants generalized the disadvantage of
women at the aggregate level to judgments referring to the different levels of the
covariate, even when motivation was high and appropriate mental models were activated. The
remaining three experiments demonstrated that Simpson’s paradox could be mastered
when the salience of the covariate was increased and when the salience of gender was
decreased by the inclusion of temporal cues that disambiguate the causal status of the
covariate. - psp.sagepub.com/cgi/content/abstract/29/1/14
Time Series Prediction Using Inductive Reasoning Techniques
Josefina López Herrera, Professora Associada, Llenguatges i Sistemes
Informŕtics
Universitat Politčcnica de Catalunya
Abstract: In this dissertation, new elements are described that have been added to the
methodology of Fuzzy Inductive Reasoning (FIR), elements that allow the prediction of the
future behavior of time series. In the identification of systems, very good results of
using this methodology had been reported earlier. Therefore, it was decided to evaluate
the methodology also in the context of predicting time series, a more complex undertaking,
because of the impossibility of exerting the systems that generate these time series
through their inputs.
In order to determine whether the methodology could be used in the analysis of time
series, a comparative study of different methodologies was made, including connectionist
methods, as well as linear and non-linear predictors. This study allowed to characterize
the types of time series that FIR predicts well. It turns out that FIR exploits all the
information that is contained in the available training data of time series that are
quasi-stationary with deterministic elements.
Due to the qualitative nature of the methodology, predictions were initially obtained that
were ambiguous. In order to overcome these difficulties, new elements of prediction were
introduced. The formula used for calculating the relative distances and the absolute
weights of the five nearest neighbors was modified, and new confidence measures (based on
similarity and proximity) were incorporated, measures that allow to estimate the
prediction error without necessity of knowing the true value of the series. The proximity
measure is based on a distance function, whereas the similarity measure is based on the
similarity between fuzzy sets. A generalization of the classical equivalence function is
used that is based on definitions of cardinality and difference of the theory of fuzzy
sets, originally proposed by Dubois and Pradé.
Two new techniques of prediction were developed that make use of these confidence
measures. These methods allow to select, at every time instant, the best qualitative
prediction model. These new techniques allow to improve the prediction of a
quasi-stationary time series. By dynamically changing the qualitative model, the
prediction error can be reduced considerably in non-stationary time series that operate in
multiple regimes.
The relation between the degree of deterioration of the accumulated confidence measure and
the horizon of predictability of a signal was evaluated in a quantitative fashion. It was
shown that the similarity measure is more sensitive to the prediction error than the
proximity measure.
Also presented are first results obtained when applying the methodology to the problems of
the design of intelligent sensors and predictive controllers.
This thesis is structured into eight chapters and two appendices.
In Chapter 1, the principal focus of the investigation is described as well as its
antecedents.
In Chapter 2, the parameters are established that allow to classify the time series that
are analyzed in this investigation. The chapter also offers a brief review of the
methodologies that are being used in time series analysis.
In Chapter 3, the state of the art of the Fuzzy Inductive Reasoning methodology is
presented.
A study comparing the performance of FIR with that of the best known time-series
prediction methods is presented in Chapter 4.
Two new measures of the prediction quality are introduced in the FIR methodology. The
results of this investigation are presented in Chapter 5. The theoretical foundations of
these measures are described, and their application to different types of time series is
shown.
In Chapter 6, the results of applying the prediction quality measures, introduced in the
previous chapter, to the problem of improving the prediction capability of FIR in the case
of non-stationary time series are presented.
In order to evaluate up to which point a prediction is reliable, Chapter 7 introduces
measures of accumulated prediction quality that can be used to estimate the horizon of
predictability in quasi-stationary time series.
In Chapter 8, the contributions obtained in this dissertation related to the FIR
methodology are summarized.
Its applications as a methodology for designing intelligent sensors and predictive
controllers are presented in Appendices A and B. -
inf.ethz.ch/personal/fcellier/PhD/fina_phd.html
Unities in Inductive Reasoning
Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF PSYCHOLOGY
Personal Author(s) : Sternberg,Robert J. ; Gardner,Michael K.
Abstract : Two experiments sought to discover sources of communalities in performance on
three inductive reasoning tasks: analogies, series completions, and classifications. In
Experiment 1, 30 subjects completed an untimed pencil-and-paper test in which they were
asked to solve 90 induction items, equally divided among the three kinds of induction
items noted above. The subjects' task was to rank-order four response options in terms of
their goodness of fit as completions for each particular item. Data sets for the three
tasks were highly intercorrelated, suggesting the possibility of a common model of
response choice across tasks. Moreover, a single exponential model of response choice
provided a good fit to each data set. The single parameter estimate for this model was
roughly comparable across tasks. In Experiment 2, 36 subjects completed a timed
tachistoscopic test in which they, too, were asked to solve 90 induction items, equally
divided among the three kinds of induction items noted above. The subjects' task was to
choose the better of two response options as a completion for each particular item. Data
sets for the three tasks were again highly intercorrelated, suggesting the possibility of
a common model of real-time information processing across tasks. Moreover, a single linear
model of response times provided a good fit to each data set. Three of four parameter
estimates for this model were roughly comparable across tasks. - stinet.dtic.mil
Inductive Reasoning - mindtools.com/pages/article/newTMC_96.htm
Drawing good generalized conclusions from a necessarily limited number of observations
Why use the tool?
Inductive reasoning involves making useful generalizations about the environment as a
whole, based on a necessarily limited number of observations. As such, it is an important
tool that people use to build the models of reality they need to function
effectively.
While conclusions can be wrong if observations are faulty or are drawn from an
unrepresentative sample, if properly used, inductive reasoning can be incredibly powerful.
Indeed, it lies at the root of the scientific method that has done so much to advance
humanity in the last 500 years. Properly-applied scientific method is inductive reasoning
in its purest form.
At the core of inductive reasoning is the ability to look at outcomes, events, ideas and
observations, and draw these together to reach a unified conclusion. Considering this, an
experienced business person can use his or her own experiences to draw conclusions about
current situations and solve problems based on what he or she has known to work in the
past in similar situations.
By accepting conclusions derived from inductive reasoning as “true” (in a
practical sense), good managers can build on these conclusions and move forward
effectively and successfully.
How to use the tool: Much inductive reasoning happens ...
The geometry of inductive reasoning in games
Diana Richards
Abstract: Summary. This paper contributes to the recent focus on dynamics in
noncooperative games when players use inductive learning. The most well-known inductive
learning rule, Brown's fictitious play, is known to converge for 2 ×2 games, yet many
examples exist where fictitious play reasoning fails to converge to a Nash equilibrium.
Building on ideas from chaotic dynamics, this paper develops a geometric conceptualization
of instability in games, allowing for a reinterpretation of existing results and
suggesting avenues for new results. - springerlink.com/content/0wyuk7t77aw2cx04/
Developing Measures of Inductive Reasoning Using Logic-Based Measurement -Tutorial
- ipmaac.org/conf/06/simpson.pdf
How is Inductive Reasoning Different from Deductive Reasoning?
Inductive reasoning
•The evidence does not guarantee the truth of the conclusion, but it gives us a good
reason to believe in the truth of the conclusion. The premises support the conclusion.
Deductive reasoning
•The truth of the evidence makes the truth of the conclusion certain.
Arthur, W. B., 1994. Inductive reasoning and bounded rationality. American Economic Review
84 (2), 406-11. |