A Formal Framework for Speedup Learning from Problems and Solutions

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.Comment: See http://www.jair.org/ for any accompanying file

Language as an instrument of thought

I show that there are good arguments and evidence to boot that support the language as an instrument of thought hypothesis. The underlying mechanisms of language, comprising of expressions structured hierarchically and recursively, provide a perspective (in the form of a conceptual structure) on the world, for it is only via language that certain perspectives are avail- able to us and to our thought processes. These mechanisms provide us with a uniquely human way of thinking and talking about the world that is different to the sort of thinking we share with other animals. If the primary function of language were communication then one would expect that the underlying mechanisms of language will be structured in a way that favours successful communication. I show that not only is this not the case, but that the underlying mechanisms of language are in fact structured in a way to maximise computational efficiency, even if it means causing communicative problems. Moreover, I discuss evidence from comparative, neuropatho- logical, developmental, and neuroscientific evidence that supports the claim that language is an instrument of thought

Machine learning : techniques and foundations

The field of machine learning studies computational methods for acquiring new knowledge, new skills, and new ways to organize existing knowledge. In this paper we present some of the basic techniques and principles that underlie AI research on learning, including methods for learning from examples, learning in problem solving, learning by analogy, grammar acquisition, and machine discovery. In each case, we illustrate the techniques with paradigmatic examples

Case Base Mining for Adaptation Knowledge Acquisition

In case-based reasoning, the adaptation of a source case in order to solve the target problem is at the same time crucial and difficult to implement. The reason for this difficulty is that, in general, adaptation strongly depends on domain-dependent knowledge. This fact motivates research on adaptation knowledge acquisition (AKA). This paper presents an approach to AKA based on the principles and techniques of knowledge discovery from databases and data-mining. It is implemented in CABAMAKA, a system that explores the variations within the case base to elicit adaptation knowledge. This system has been successfully tested in an application of case-based reasoning to decision support in the domain of breast cancer treatment

Recursion in cognition: a computational investigation into the representation and processing of language

La recursividad entendida como auto-referencia se puede aplicar a varios constructos de las ciencias cognitivas, como las definiciones teóricas, los procedimientos mecánicos, los procesos de cálculo (sean éstos abstractos o concretos) o las estructuras. La recursividad es una propiedad central tanto del procedimiento mecánico que subyace a la facultad del lenguaje como de las estructuras que esta facultad genera. Sin embargo, tanto las derivaciones sintácticas de la gramática, que constituyen un proceso computacional abstracto, como las estrategias de procesamiento del parser, que son un proceso en tiempo real, proceden de forma iterativa, lo cual sugiere que la especificación recursiva de un algoritmo se implementa de forma iterativa. Además, la combinación de la recursividad con las unidades léxicas y las imposiciones de los interfaces con los que la facultad del lenguaje interactúa resulta en un conjunto de estructuras sui generis que no tienen parangón en otros dominios cognitivos.Recursion qua self-reference applies to various constructs within the cognitive sciences, such as theoretical definitions, mechanical procedures (or algorithms), (abstract or real-time) computational processes and structures. Recursion is an intrinsic property of both the mechanical procedure underlying the language faculty and the structures this faculty generates. However, the recursive nature of the generated structures and the recursive character of the processes need to be kept distinct, their study meriting individual treatment. In fact, the nature of both the syntactic derivations of the grammar (an abstract computational process) and the processing strategies of the parser (a real-time process) are iterative, which suggests that recursively-defined algorithms are implemented iteratively in linguistic cognition. Furthermore, the combination of recursion, lexical items and the impositions of the interfaces the language faculty interacts with results in a sui generis set of structures with which other domains of the mind bear the most superficial of relations

Modelling recursion

The purpose of my research is to examine and explore the ways that undergraduate students understand the concept of recursion. In order to do this, I have designed computer-based software, which provides students with a virtual and interactive environment where they can explore the concept of recursion, and demonstrate and develop their knowledge of recursion through active engagement. I have designed this computer-based software environment with the aim of investigating how students think about recursion. My approach is to design digital tools to facilitate students' understanding of recursion and to expose that thinking. My research investigates students' understanding of the hidden layers and inherent complexity of recursion, including how they apply it within relevant contexts. The software design embedded the idea of functional abstraction around two basic principles of: 'functioning' and 'functionality'. The functionality principle focuses on what recursion achieve, and the functioning dimension concerns how recursion is operationalised. I wanted to answer the following crucial question: How does the recursive thinking of university students evolve through using carefully designed digital tools? In the process of exploring this main question, other questions emerged: 1. Do students understand the difference between recursion and iteration? 2. How is tail and embedded recursion understood by the students? 3. To what extent does prior knowledge of the concept of iteration influence students' understanding of tail and embedded recursion? 4. Why is it important to have a clear understanding of the control passing mechanisms in order to understand recursion? 5. What is the role of functional abstraction in both, the design of computer-based tools and the students' understanding of recursion? 6. How are students' mental models of recursion shaped by their engagement with computer-based tools? From a functional abstraction point of view almost all previous research into the concept of recursion has focused on the functionality dimension. Typically, it has focused on procedures for the calculation of the factorial of a natural number, and students were tested to see if they are able to work out the values of the a function recursively (Wiedenbeck, 1988; Anazi and Uesato, 1982) or if they are able to recognize a recursive structure (Sooriamurthi, 2001; Kurland and Pea, 1985). Also, I invented the Animative Visualisation in the Domain of Abstraction (AVDA) which combines the functioning and functionality principles regarding the concept of recursion. In the AVDA environment, students are given the opportunity to explore the hidden layers and the complicated behaviour of the control passing mechanisms of the concept of recursion. In addition, most of the textbooks in mathematics and computer sciences usually fail to explain how to use recursion to solve a problem. Although it is also true that text books do not typically explain how to use iteration to solve problems, students are able to draw on to facilitate solving iterative problems (Pirolli et al, 1988). My approach is inspired by how recursion can be found in everyday life and in real world phenomena, such as fractal-shaped objects like trees and spirals. This research strictly adheres to a Design Based Research methodology (DBR), which is founded on the principle of the cycle of designing, testing (observing the students' experiments with the design), analysing, and modifying (Barab and Squire, 2004; Cobb and diSessa, 2003). My study was implemented throughout three iterations. The results showed that in the AVDA (Animative Visualisation in the Domain of Abstraction) environment students' thinking about the concept of recursion changed significantly. In the AVDA environment they were able to see and experience the complicated control passing mechanism of the tail and embedded recursion, referred to a delegatory control passing. This complicated control passing mechanism is a kind of generalization of flow in the iterative procedures, which is discussed later in the thesis. My results show that, to model a spiral, students prefer to use iterative techniques, rather than tail recursion. The AVDA environment helped students to appreciate the delegatory control passing for tail recursive procedures. However, they still demonstrated difficulties in understanding embedded recursive procedures in modelling binary and ternary trees, particularly regarding the transition of flow between recursive calls. Based on the results of my research, I have devised a model of the evolution of students' mental model of recursion which I have called – the quasi-pyramid model. This model was derived from applying functional abstraction including both functionality and functioning principles. Pedagogic implications are discussed. For example, the teaching of recursion might adopt 'animative' visualization, which is of vitally important for students' understanding of latent layers of recursion

About the relations between Management Accounting Systems, Intellectual Capital and Performance

The present study is focused on the contribution of management accounting systems (MAS) in the development of intellectual capital (IC). Based on empirical evidence that supports the proposition that the value creation process is strongly associated to the level of IC, the study also examines the mediating effect of MAS on performance through their positive direct effect on IC. These relationships were consolidated into a model and empirically tested with data from 281 Portuguese firms using the Structural Equation Modeling (SEM). The findings show that six out of nine hypothesized relationships were supported by data with positive and significant causal links between MAS and the human and structural dimensions of IC. Results confirmed the conceptual validity of the circular model for the interactions among the three IC dimensions. Results also showed a positive and significant direct effect of structural capital on performance. Overall, the results confirmed the validity of the proposed model and contributed to the literature on the role of MAS in supporting the development of the I

Not All Numbers Were Created Equal: Evidence the Number One is Unique

Universally across modern cultures children acquire the meaning of the words one, two, and three in order. While much research has focused on how children acquire this knowledge and what this knowledge represents, the question of why children learn numbers in order has been comparatively neglected. To address this question, a non-verbal anticipatory looking task was implemented. In this task, 35 14- to 23-month-old infants were assessed on their ability to form implicit category structures for the numbers one, two, and three. We hypothesized that children would be able to form the implicit category structure for the number one but not for two or three because sets of two and three objects would exceed the working memory capacities of infants. We found results consistent with this hypothesis; infants (regardless of age) were able form a category for sets with one object, as evidenced by their looking behavior while the looking behavior for the numbers two and three did not demonstrate a statistically significant pattern. We interpret our results as consistent with our hypothesis and discuss implications for parallel individuation, number acquisition theories, and the development of working memory resources