Inductive Inference

This paper presents a nonmonotonic ILP approach for the automatic revision of metabolic networks through the logical analysis of experimental data. The method extends previous work in two respects: by suggesting revisions that involve both the addition and removal of information; and by suggesting revisions that involve combinations of gene functions, enzyme inhibitions, and metabolic reactions. Our proposal is based on a new declarative model of metabolism expressed in a nonmonotonic logic programming formalism. With respect to this model, a mixture of abductive and inductive inference is used to compute a set of minimal revisions needed to make a given network consistent with some observed data. In this way, we describe how a reasoning system called XHAIL was able to correctly revise a state-of-the-art metabolic pathway in the light of real-world experimental data acquired by an autonomous laboratory platform called the Robot Scientist.

This paper presents a nonmonotonic ILP approach for the automatic revision of metabolic networks through the logical analysis of experimental data. The method extends previous work in two respects: by suggesting revisions that involve both the addition and removal of information; and by suggesting revisions that involve combinations of gene functions, enzyme inhibitions, and metabolic reactions. Our proposal is based on a new declarative model of metabolism expressed in a nonmonotonic logic programming formalism. With respect to this model, a mixture of abductive and inductive inference is used to compute a set of minimal revisions needed to make a given network consistent with some observed data. In this way, we describe how a reasoning system called XHAIL was able to correctly revise a state-of-the-art metabolic pathway in the light of real-world experimental data acquired by an autonomous laboratory platform called the Robot Scientist.

CF-induction is a sound and complete hypothesis finding procedure for full clausal logic which uses the principle of inverse entailment to compute a hypothesis that logically explains a set of examples with respect to a prior background theory. Currently, CF-induction computes hypotheses by applying combinations of several complex generalisation operators to an intermediate theory called a bridge formula. In this paper we propose an alternative approach whereby hypotheses are derived from a bridge formula using a single deductive operator and a single inductive operator. We show that our simplified procedure preserves the soundness and completeness of CF-induction.

We study consistency problems of the following form for some family (Lk) of language classes: Given a finite language F and some parameter k, is there some language L⊇ F contained in Lk? We derive non-trivial complexity results for languages of structures of categorial grammars, in terms of classical complexity, as well as in terms of parameterized complexity and approximability.

Traditional attempts to understanding inductive reasoning in science have typically involved analyzing language, focusing on statements or propositions. However, recent arguments suggest that this approach misconceives induction, prompting the need for a new perspective. This study offers a fresh view on induction by integrating William Whewell's theory of induction, which distinguishes two forms of reasoning: interpretation and representation. This perspective suggests that induction can be seen as a reasoning process based on semantic and pragmatic models rather than statements or propositions.

Conceptual understanding is essential when learning engineering. For that, the design of a case
study is considered, as well as the method of the case and two objectives: a) describe the design
process, using the SRJU model: structure, review, judges validation and user evaluation; the
dimensions of clarity, coherence, relevance, sufficiency were validated by judges; the
evaluation involved piloting of student opinions and data triangulation. b) Apply the method
with the IGAA model by activities: individual case reading; focal groups; plenary; anecdotal
logs; assessment by judges of the dimensions of understanding; diagnostic surveys and
verification of the experimental and control group. The results of the validation and evaluation
of the design showed optimal levels of relevance and sufficiency; with coincidences in
acceptable assessments that the case is not totally coherent with a linear reality but rather
complex. When implementing the method, the judges evaluated discussion in plenary, with
high levels of understanding. When evaluating logs, the results showed medium and high
levels. When implementing diagnostic surveys, similar levels of preconceptions were observed
in both groups. When comparing results of verification surveys, higher levels of understanding
were observed in the experimental group than in the control group; the method favorably
impacts understanding through dialogic socialization. However, it is rarely applied in physics
and the existence of designed cases is also limited. Both models are effective for designing and
qualifying Cases, due to their systematic processes that improve the dimensions of design and
understanding and replicated.

Research advances are presented whose objective is to test and qualify the viability of
implementing Rational Thought of the ancient classical pedagogical area, in digital classrooms
of foreign languages; and answer the questions: what are the current theoretical foundations
and on which thematic digital teaching should be built in multilingual diversity classrooms?;
How does rational thought modify in students of different languages, research and
conceptualization related to linguistic, literary and cultural topics? How does classical
pedagogy help the development of didactics in the digital context, allowing the teacher to teach
and the student to build knowledge? The first stage consisted of theoretically basing classical
pedagogy, with the rational thought of ancient Greece and its derivation in scientific thought
as its guiding axis. Design that implied contrast in ways of thinking about thematic diversity.
With the following organization: methodological, theoretical and procedural foundation. For
the test design, an interaction matrix is proposed to order and interpret data that reflect the level
of conceptualization to be collected by written language; according to types of structured
thought: rational logical, methodical and narrative; For each type of thought, dimensions of
content, purpose and structure are evaluated. The methodology used for this stage is qualitative;
In the second stage, test design will be applied. As a result of the first stage, methodological,
theoretical and test design foundations were achieved, implementing the scientific method,
supported by preliminary conclusions and an annex of examples to address multiple topics.

Rūsiņš Mārtiņš Freivalds has played a key role in the development of theoretical computer science in Latvia. While also being recognised internationally and taking an active part in the computer scientists’ community, he managed to make a major contribution to the formation of the Latvian school of computer science.
In order to pay tribute to Freivalds’ scientific legacy and honour a beloved colleague, teacher, and Professor his fellow academics at the Computer Science Department of the University of Latvia, as well as some of his close Finnish, German, Japanese, and other international collaborators have contributed to this BJMC volume containing scientific papers and essays sharing personal memories of Freivalds.
This volume begins with Professor Freivalds’ academic genealogy and publications. The essay section reveals a profound sense of Freivalds’ responsibility for the future of computer science. The recollections of his lifelong scientific contributions also serve as testimony of the man’s inner freedom, and spiritual strength living under a totalitarian rule for half of his scientific career.

Presented is an algorithm (for learning a subclass of erasing regular pattern languages) which can be made to run with arbitrarily high probability of success on extended regular languages generated by patterns π of the form x 0 α 1 x 1 ...α m x m for unknown m but known c , from number of examples polynomial in m (and exponential in c ), where x 0 , . . . , x m are variables and where α 1 , ..., α m are each strings of terminals of length c . This assumes that the algorithm randomly draws samples with natural and plausible assumptions on the distribution. With the aim of finding a better algorithm, we also explore computer simulations of a heuristic.

Abstract—reasoning is an important part of many fields like logic, artificial intelligence, philosophy of science, and so on. Reasoning can either be deductive (deduction) or it can be inductive (induction). The decisions based on induction are very helpful in research but ...

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This unified framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.

& Inductive inference underlies much of human cognition. The essential component of induction is hypothesis selection based on some criterion of relevance. The purpose of this study was to determine the neural substrate of inductive inference, particularly hypothesis selection, using fMRI. Ten volunteers were shown stimuli consisting of novel animals under two task conditions, and asked to judge whether all the animals in the set were the same type of animal. In one condition, subjects were given a rule that specified the criteria for``same type of animal''. In the other condition, subjects had to infer the rule without instruction. The two conditions were further factored into easy and difficult components. Rule inference was specifically associated with bilateral hippocampal activation while the task by difficulty interaction was associated with activation in right lateral orbital prefrontal cortex. We interpret the former in terms of semantic encoding of novel stimuli, and the latter in terms of hypothesis selection. Thus, we show an anatomical dissociation between task implementation and task difficulty that may correspond to a critical psychological distinction in the processes necessary for inductive inference. &

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument: (1) If H then E; (2) E; (3) Therefore, (probably) H—here referred to as ‘hypothetico-deductive con-firmation argument’—is inductively strong. Yet this argument looks nothing like an inductive generalisation, i.e., it doesn’t seem inductive in the term's traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘in-duction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as a strong enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction.

Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1, s2, s3,. .. be the standard lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given A(s1), A(s2), A(s3),. .. , learn, in the limit, a DFA for SUBSEQ(A). We consider this model of learning and the variants of it that are usually studied in Inductive Inference: anomalies, mindchanges, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10]. S1. Introduction. Our work is based on a remarkable theorem of Higman [22], 1 given below as Theorem 1.3. Convention: Σ is a finite alphabet. Definition 1.1. Let x, y ∈ Σ *. We say that x is a subsequence of y if x = x 1 • • • x n and y ∈ Σ * x 1 Σ * x 2 • • • x n−1 Σ * x n Σ *. We denote this by x y. Notation 1.2. If A is a set of strings, then SUBSEQ(A) is the set of subsequences of strings in A. Higman [22] showed the following using well-quasi-order theory. Theorem 1.3 (Higman [22]). If A is any language over Σ * , then SUBSEQ(A) is regular. In fact, for any language A there is a unique minimum (and finite) set S of strings such that SUBSEQ(A) = {x ∈ Σ * : (∀z ∈ S)[z x]}. (1) The original proof of this theorem is nonconstructive. Nerode's Recursive Mathematics Program [27, 9] attempts to pin down what it means for a proof to be noneffective. In [11] we showed that there can be no effective proof. In particular we showed (among other things) that there is no partial computable

In this work, we present the Hierarchical Grounded Truth Preservation Theorem (HGTPT), a novel framework for constructing and verifying a grounded truth predicate within axiomatic extensions of formal arithmetic. The theorem proposes a structured hierarchy of grounded truth sets, effectively avoiding inconsistencies associated with self-reference while preserving the expressive power of the truth predicate within the context of Peano Arithmetic (PA). This approach maintains logical consistency, provides a hierarchy-based semantic interpretation, and introduces new insights into the interaction of truth, provability, and conservativity in formal systems.

The main goal is to exhibit the relationship between research work on non-monotonic reasoning and recursion-theoretically based approaches to inductive learning. There are introduced the concepts of monotonic and weakly monotonic inductive inference. It is proved that these concepts are considerably distinguished from other classical concepts of inductive inference, i.e. non-monotonic reasoning is inherently required in several approaches to inductive inference.

A study investigated how young children understand natural kind terms by examining how 3-and 4-year-olds rely on category membership to draw inductive inferences about objects. One hundred four children (53 girls and 51 boys) from six preschools in California and Michigan participated in the study. The children were shown 10 sets of pictures of natural objects or creatures, told something about the items shown, and asked to draw inferences about other natural kind pictures. Two conditions were added: word only condition and picture only condition. Results suggest that even the youngest children assume that objects with the same name share underlying similarities. When given just labels, the children used them as a base for making inductions, and when labels and appearances conflicted, they relied more on labels than appearances. Even when no labels were given, the children sometimes figured out what categories the pictures belonged to and used this inference to decide about other properties. It is concluded that children are clearly sensitive to the power of language for organizing and extending language, and that words that refer, even common nouns, serve to identify objects as well as foster inductions. (MSE)

This essay examines the proposal that psychological essentialism re s u l t s f rom a history of natural selection acting on human re p resentation and inference systems. It has been argued that the features that distinguish essentialist re p resentational systems are especially well suited for re p resenting natural kinds. If the evolved function of essentialism is to exploit the rich inductive potential of such kinds, then it must be subserved by cognitive mechanisms that carry out at least three distinct functions: identifying these kinds in the environment, constructing essentialized re p resentations of them, and constraining inductive inferences about kinds. More o v e r, there are different kinds of kinds, ranging from nonliving substances to biological taxa to within-species kinds such as sex, and the causal processes that render these categories coherent for the purposes of inductive generalization vary. If the evolved function of essentialism is to support inductive generalization under ignorance of tru e causes, and if kinds of kinds vary in the implicit assumptions that support valid inductive i n f e rences about them, then we expect different, functionally incompatible modes of essentialist thinking for different kinds. In part i c u l a r, there should be differences in how biological and nonbiological substances, biological taxa, and biological and social role kinds are essentialized. The functional differences between these kinds of essentialism are discussed.

In celebration of the work of Richard Threlkeld Cox, we explore inductive logic and its role in science touching on both experimental design and analysis of experimental results. In this exploration we demonstrate that the duality between the logic of assertions and the logic of questions has important consequences. We discuss the conjecture that the relevance or bearing, b, of a question on an issue can be expressed in terms of the probabilities, p, of the assertions that answer the question via the entropy. In its application to the scientific method, the logic of questions, inductive inquiry, can be applied to design an experiment that most effectively addresses a scientific issue. This is performed by maximizing the relevance of the experimental question to the scientific issue to be resolved. It is shown that these results are related to the mutual information between the experiment and the scientific issue, and that experimental design is akin to designing a communication channel that most efficiently communicates information relevant to the scientific issue to the experimenter. Application of the logic of assertions, inductive inference (Bayesian inference) completes the experimental process by allowing the researcher to make inferences based on the information obtained from the experiment.

The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are well-suited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge. We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that incorporate additional prior information. One algorithm separates signals that are known a priori to be decorrelated and the other utilizes information about the signal propagation through the medium from the sources to the detectors.

This work falls into two parts. In the flrst part, we characterize the sets of all ƒ2 and all B(§1) (= boolean combinations of §1) theorems of Iƒ¡ 1 in terms of restricted exponentiation; and use these characterizations to prove that both sets are not deductively equivalent. In the second part, we investigate how these results generalize to Iƒ¡ 2 . We present a new model{theoretic approach to Iƒ ¡ 2 that allows us to obtain informative characterizations of the set of all ƒ2 and all B(§2) theorems of Iƒ¡ 2 ; and to give a model{theoretic proof of a conservation result by L. Beklemishev's stating that Iƒ¡ 2 is a B(§2) conservative extension of I§ ¡ 1 .

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the class Inf Ex-, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is Inf Ex--learnable if and only if the structures from K can be distinguished in terms of their Σ inf 2 -theories. We apply this characterization to familiar cases and we show the following: there is an infinite learnable family of distributive lattice; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable.

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions.

Quite often, heuristics and common sense suggest directions for improving well-known learning algorithms. However it seems not an easy task to verify that the modifications are indeed helpful. This is made more complicated through various additional influences inherent in different application domains. In order to obtain a faithful impression of phenomena that are intrinsic to the algorithms, the role of specific domains should be minimized. Our validation toolkit TIC allows to explore the behaviour of various algorithms for learning formal languages. This is a well-examined and standardized application domain. TIC is operated by interactive as well as automatic control. Motivation * volkerd~informatik.uni-leipzig.de *~antke~dfki.de Copyright (~2000, American Association for Artificial Intelligence (www.aaai.org). All rights reserved.

Reflection denotes someones activity of thinking about oneself as well as about one's relation to the outside world. In particular, reflecting means pondering about ones capabilities and limitations. Reasoning about ones competence is a central issue of reflective behaviour. Reflection is a key issue of recent artificial intelligence. There is investigated the problem of automated reasoning about the competence of inductive inference machines. Reflective inductive inference machines are those which are able to identify whether or not some information presented exceeds its learning capabilities. An inductive inference m~chine is self-confident, if it usually trusts in its ability to solve the learning problem on hand. It is reflecting and self-confident, if it normally believes in its power, but recognizes problems exceeding its competence. The problem is formalized and studied within the setting of inductively learning total recursive functions. There is a crucial distinction of immediately reflecting inductive inference machines and those which need an a priori unknown amount of time for reasoning about its competence.

Planning is investigated in an area where classical STRIPS-like approaches usually fail. The application domain is therapy (i.e. repair) for complex dynamic processes. The peculiarities of this domain are discussed in some detail for convincingly developing the characteristics of the inductive planning approach presented. Plans are intended to be run for process therapy. Thus, plans are programs. Because of the unavoidable vagueness and uncertainty of information about complex dynamic processes in the case of disturbance, therapy plan generation turns out to be inductive program synthesis. There is developed a graph-theoretically based approach to inductive therapy plan generation, This approach is investigated from the inductive inference perspective_ Particular emphasis is put on consistent and incremental learning of therapy plans. Basic application scenarios are developed and compared to each other, The inductive inference approach is invoked to develop and investigate a couple of planning algorithms, The core versions of these algorithms are successfully implemented in Lisp and Prolog.

People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are "theoretical cases", which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases.

We argue that a precedent is important not only because it changes the relative frequency of a certain event, making it positive rather than zero, but also because it changes the way that relative frequencies are weighed. Speci…cally, agents assess probabilities of future events based on past occurrences, where not all of these occurrences are deemed equally relevant. More similar cases are weighed more heavily than less similar ones. Importantly, the similarity function is also learnt from experience by "second-order induction". The model can explain why a single precedent a¤ects beliefs above and beyond its e¤ect on relative frequencies, as well as why it is easier to establish reputation at the outset than to re-establish it after having lost it. We also apply the model to equilibrium selection in a class of games dubbed "Statistical Games", suggesting the notion of Similarity-Nash equilibria, and illustrate the impact of precedents on the play of coordination games. Gilboa gratefully acknowledges ISF Grant 704/15 and the Investissements d'Avenir ANR-11-IDEX-0003 / Labex ECODEC No. ANR-11-LABX-0047.

The central topic of the paper is the learnability of the recursively enumerable subspaces of V∞/V , where V∞ is the standard recursive vector space over the rationals with countably infinite dimension, and V is a given recursively enumerable subspace of V∞. It is shown that certain types of vector spaces can be characterized in terms of learnability properties: V∞/V is behaviourally correct learnable from text iff V is finitely dimensional, V∞/V is behaviourally correct learnable from switching type of information iff V is finite-dimensional, 0-thin, or 1-thin. On the other hand, learnability from an informant does not correspond to similar algebraic properties of a given space. There are 0-thin spaces W1 and W2 such that W1 is not explanatorily learnable from informant and the infinite product (W1) ∞ is not behaviourally correct learnable, while W2 and the infinite product (W2) ∞ are both explanatorily learnable from informant.

What is the relation between humans and non-human animals? From a biological perspective, we view humans as one species among many, but in the fables and films we create for children, we often offer an anthropocentric perspective, imbuing non-human animals with human-like characteristics. What are the consequences of these distinctly different perspectives on children's reasoning about the natural world? Some have argued that children universally begin with an anthropocentric perspective and that acquiring a biological perspective requires a basic conceptual change (cf. Carey, 1985). But recent work reveals that this anthropocentric perspective, evidenced in urban 5-year-olds, is not evident in 3-year-olds (Herrmann et al., 2010). This indicates that the anthropocentric perspective is not an obligatory first step in children's reasoning about biological phenomena. In the current paper, we introduced a priming manipulation to assess whether 5-year-olds' reasoning about a novel biological property is influenced by the perspectives they encounter in children's books. Just before participating in a reasoning task, each child read a book about bears with an experimenter. What varied was whether bears were depicted from an anthropomorphic (Berenstain Bears) or biological perspective (Animal Encyclopedia). The priming had a dramatic effect. Children reading the Berenstain Bears showed the standard anthropocentric reasoning pattern, but those reading the Animal Encyclopedia adopted a biological pattern. This offers evidence that urban 5-year-olds can adopt either a biological or a human-centered stance, depending upon the context. Thus, children's books and other media are double-edged swords. Media may (inadvertently) support human-centered reasoning in young children, but may also be instrumental in redirecting children's attention to a biological model.

Adults increase the certainty of their inductive inferences by observing more diverse instances. However, most young children fail to do so. The present study tested the hypothesis that children's sensitivity to instance diversity is determined by three variables: ability to discriminate among instances (Discrimination); an intuition that large numbers of instances increase the strength of conclusion (Monotonicity); ability to detect subcategories and evaluate numerical differences between the subcategories, or Extraction. A total of 219 Chinese children aged 6 to 11 were tested for sensitivity to diversity by means of Discrimination, Monotonicity, and Extraction. The results indicated that children at all ages were able to discriminate instances and attend to set size. However, only 9-and 11-year-olds demonstrated Extraction and sensitivity to diversity. Furthermore, among all children diversity scores increased linearly with the level of Extraction. These results suggest that the law of large numbers plays a role in children's diversity-based reasoning.

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts.

The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set Γ. We make an analogous modification for interpretability logics. This is a paper from 2012. We first studied provability logics with restricted realizations, and show that for various natural candidates of theory T and restriction set Γ, where each sentence in Γ has a well understood (meta)-mathematical content in T , the result is the logic of linear frames. However, for the theory Primitive Recursive Arithmetic (PRA), we define a fragment that gives rise to a more interesting provability logic, by capitalizing on the well-studied relationship between PRA and IΣ 1. We then study interpretability logics, obtaining some upper bounds for IL(PRA), whose characterization remains a major open question in interpretability logic. Again this upper bound is closely relatively to linear frames. The technique is also applied to yield the non-trivial result that IL(PRA) ⊂ ILM. 2 Σ 1-sound is sufficient here. 3 There is a paper by de Jongh, Jumelet and Montagna [22] where an alternative proof of Solovay's theorem is given. In that proof, using the diagonal lemma, one finds some sentences with the required properties rather than defining the sentences and then proving the necessary properties.

Introduced is a new inductive inference paradigm, dynamic modeling. Within this learning paradigm, for example, function h learns function g iff, in the i-th iteration, h and g both produce output, h gets the sequence of all outputs from g in prior iterations as input, g gets all the outputs from h in prior iterations as input, and, from some iteration on, the sequence of h's outputs will be programs for the output sequence of g. Dynamic modeling provides an idealization of, for example, a social interaction in which h seeks to discover program models of g's behavior it sees in interacting with g, and h openly discloses to g its sequence of candidate program models to see what g says back. Sample results: every g can be so learned by some h; there are g that can only be learned by an h if g can also learn that h back; there are extremely secretive h which cannot be learned back by any g they learn, but which, nonetheless, succeed in learning infinitely many g; quadratic time learnability is strictly more powerful than linear time learnability. This latter result, as well as others, follows immediately from general correspondence theorems obtained from a unified approach to the paradigms within inductive inference. Many proofs, some sophisticated, employ machine self-reference, a.k.a., recursion theorems.

Numerical data (e.g., DNA micro-array data, sensor data) pose a challenging problem to existing frequent pattern mining methods which hardly handle them. In this framework, gradual patterns have been recently proposed to extract covariations of attributes, such as: "When X increases, Y decreases". There exist some algorithms for mining frequent gradual patterns, but they cannot scale to real-world databases. We present in this paper GLCM, the first algorithm for mining closed frequent gradual patterns, which proposes strong complexity guarantees: the mining time is linear with the number of closed frequent gradual itemsets. Our experimental study shows that GLCM is two orders of magnitude faster than the state of the art, with a constant low memory usage. We also present PGLCM, a parallelization of GLCM capable of exploiting multicore processors, with good scale-up properties on complex datasets. These algorithms are the first algorithms capable of mining large real world datasets to discover gradual patterns.

Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively.

In this paper, we review our novel information geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it could provide an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.

A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed f...

Los programas de enseñanza estratégica y mediada de la lectura basados en procesos cognitivos permiten el dominio eficaz de esta habilidad específica, así como la mejora de los procesos cognitivos. Estudiantes de 2º, 5º y 6º curso de la etapa de Educación Primaria, con y sin riesgo de dificultad lectora, participaron en la implementación de este tipo de programas. A los estudiantes de 2º curso, en riesgo de dificultad lectora, se les aplicó un programa de refuerzo en habilidades lectoras con una metodología diseñada para que el aprendizaje de la lectura tuviese lugar de manera espontánea a través de la interiorización de principios y estrategias. Los estudiantes de 5º y 6º curso, sin riesgo de dificultad lectora, participaron de un programa de comprensión lectora basado en la instrucción estratégica y metacognitiva de dicha habilidad. En 2º curso los resultados indicaron una mejora significativa del proceso cognitivo sucesivo, asociado al dominio de la conciencia fonológica. En 5º y 6º se obtuvieron mejoras significativas en compresión lectora y en el proceso cognitivo de planificación, vinculado al uso de estrategias y a la supervisión y regulación del aprendizaje. Para los estudiantes de 2º curso, el uso de este tipo de programas de intervención constituye la mejor prevención de la dificultad de aprendizaje como evidencia en la mejora significativa de sus puntuaciones en procesamiento sucesivo. Los resultados obtenidos en 5º y 6º amplían el conocimiento existente sobre la eficacia de los programas de instrucción en comprensión lectora al incluir, en el contexto de aprendizaje, el apoyo mediante preguntas para hacer conscientes a los estudiantes de las estrategias cognitivas más eficientes para el desarrollo de la competencia lectora. Palabras clave: Lectura, prevención, intervención, aprendizaje mediado, instrucción estratégica y metacognitiva.

The initial questions of 180 males and females between the ages of 12 and 26 years were classified as they participated in a 20-questions problem-solving procedure. Three levels of questions (superordinate, basic, and subordinate) were observed for an array of conceptually organized exemplars. No age or gender differences were found but preference for superordinate-level initial questions was significant.

In order to faithfully describe real-life applications, knowledge bases have to manage general integrity constraints. In this article, we analyse methods for an efficient verification of integrity constraints in updated knowledge bases. These methods rely on the satisfaction of the integrity constraints before the update for sim plifying their evaluation in the updated knowledge base. During the last few years, an increasing amount of publications has been devoted to various aspects of this prob lem. Since they use distinct formalisms and different terminologies, they are difficult to compare. Moreover, it is often complex to recognize commonalities and to find out whether techniques described in different articles are in principle different. A first part of this report aims at giving a comprehensive state-of-the-art in integrity verification. It describes integrity constraint verification techniques in a common formalism. A sec ond part of this report is devoted to comparing several proposals. The differences and similarities between various methods are investigated.

A considerable amount of work has focused on the processes that underlie children's inductive reasoning. For instance, numerous studies explored the role of linguistic labels, perceptual similarity, and children's beliefs in generalization of properties to novel cases. The present studies investigated an aspect of induction that has received considerably less attention in prior developmental research, namely-the effect of the statistical properties of evidence on inductive reasoning. Studies presented below were motivated by the hypothesis that induction involves an evaluation of the statistical properties available in the evidence. From this perspective, sample size, or the amount of available evidence, should influence inductive reasoning. Sample size effects were investigated in three experiments with 90 5-year-olds and 90 adults. Results indicated that children made higher rate of projections for larger than smaller samples, particularly when samples were represented by ...