Computational learning theory explores the limits of learnability. Studying language acquisition from this perspective involves identifying classes of languages that are learnable from the available data, within the limits of time and computational resources available to the learner. Different models of learning can yield radically different learnability results, where these depend on the assumptions of the model about the nature of the learning process, and the data, time, and resources that learners have access to. To the (...) extent that such assumptions accurately reflect human language learning, a model that invokes them can offer important insights into the formal properties of natural languages, and the way in which their representations might be efficiently acquired. In this chapter we consider several computational learning models that have been applied to the language learning task. Some of these have yielded results that suggest that the class of natural languages cannot be efficiently learned from the primary linguistic data (PLD) available to children, through.. (shrink)

In this paper, we explore the possibility that machine learning approaches to naturallanguage processing being developed in engineering-oriented computational linguistics may be able to provide specific scientific insights into the nature of human language. We argue that, in principle, machine learning results could inform basic debates about language, in one area at least, and that in practice, existing results may offer initial tentative support for this prospect. Further, results from computational learning theory can inform arguments carried (...) on within linguistic theory as well. (shrink)

In this paper, we explore the possibility that machine learning approaches to naturallanguage processing being developed in engineering-oriented computational linguistics may be able to provide specific scientific insights into the nature of human language. We argue that, in principle, machine learning results could inform basic debates about language, in one area at least, and that in practice, existing results may offer initial tentative support for this prospect. Further, results from computational learning theory can inform arguments carried (...) on within linguistic theory as well. (shrink)

Formal learning theory is an approach to the study of inductive inference that has been developed by computer scientists. In this paper, I discuss the relevance of formal learning theory to such standard topics in the philosophy of science as underdetermination, realism, scientific progress, methodology, bounded rationality, the problem of induction, the logic of discovery, the theory of knowledge, the philosophy of artificial intelligence, and the philosophy of psychology.

An important question for a naturalized philosophical psychology is what constitutes moral agency (MA). The two prominent scientific theories to which such a philosophical approach might appeal, those of cognitive developmental theory (CDT) and social learning theory (SLT), currently face an investigative dilemma: The better theories of the acquisition of beliefs and the performance of action based on them, the SLTs, seem to be irrelevant to the phenomenon of MA and the theories that seem to be relevant, (...) the CDTs, are unsatisfactory in their accounts of acquisition and action. In this paper I take up the cause of SLT accounts of MA. Critics of SLT accounts of MA can be interpreted as arguing that they are irrelevant to MA because they lack one or more of five functional criteria that require MA to be integral morally motivated cognitive agency. I argue that SLT accounts of MA, and specifically Bandura's social cognitive theory, (SCT), when applied to issues of MA, meet these criteria. Assuming the merits of SLT explanations of both the acquisition of beliefs and the performance of actions based on them, I conclude that SLTs generally, and specifically Bandura's SCT, are promising candidates for explaining MA. If so, they merit the attention of naturalistic philosophical psychologists. (shrink)

Artificial intelligence research connected with learning theory ("deep learning," “machine learning,” analysis of the quality of learning, etc.) has existed for many years; however, there have been few investigations in that area conducted from a robust philosophical methodological basis.

then essentially characterized the hypotheses that mechanical scientists can successfully decide in the limit in terms of arithmetic complexity. These ideas were developed still further by Peter Kugel [4]. In this paper, I extend this approach to obtain characterizations of identification in the limit, identification with bounded mind-changes, and identification in the short run, both for computers and for ideal agents with unbounded computational abilities. The characterization of identification with n mind-changes entails, as a corollary, an exact arithmetic characterization of (...) Putnam's n-trial predicates, which closes a gap of a factor of two in Putnam's original characterization [12]. (shrink)

In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture many of the interesting aspects that are present in the cases of more than two classes and in the problem of estimation, and many of the (...) results can be extended to these cases. Focusing on two-class pattern classification simplifies our discussion, and yet it is directly applicable to a wide range of practical settings. (shrink)

Go beyond reading about early learning theories and see what they look like in action in modern programs and teacher practices. With classroom vignettes and colorful photographs, this book makes the works of Jean Piaget, Erik Erikson, Lev Vygotsky, Abraham Maslow, John Dewey, Howard Gardner, and Louise Derman-Sparks visible, accessible, and easier to understand. Each theory is defined-through engaging stories and rich visuals-in relation to cognitive, social-emotional, and physical developmental domains. Use this book to build a stronger comprehension (...) of the foundations of early learning theories and become more reflective and intentional in your work with young children. (shrink)

One version of the problem of induction is how to justify hypotheses in the face of data. Why advance hypothesis A rather than B — or in a probabilistic context, why attach greater probability to A than B? If the data arrive as a stream of observations (distributed through time) then the problem is to justify the associated stream of hypotheses. Several perspectives on this problem have been developed including Bayesianism (Howson and Urbach, 1993) and belief-updating (Hansson, 1999). These are (...) broad families of approaches; the citations are meant just as portals. (shrink)

Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.

A theory of learning for the future advocates the teaching of a preparedness to respond in a creative way to difference and otherness. This includes an ability to act imaginatively in situations of uncertainties. John Dewey’s pragmatism holds the key to such a learning theory his view of the continuous meetings of individuals and environments as experimental and playful. That pragmatism has not yet been acknowledged as a relevant learning theory for the future may (...) be due to the immediate connotation and the many interpretations associated with the term ‘experience’, which is at the heart of Dewey’s educational thinking. Dewey defi ned experience in a way that is not well understood within educational research, and in a way that is easily confused with the term ‘experiential learning’. The latter refers to the importance of participants’ ‘experiences’ derived from bodily actions and stored in memory as more or less tacit knowledge. (shrink)

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

Statistical Learning Theory (e.g., Hastie et al., 2001; Vapnik, 1998, 2000, 2006) is the basic theory behind contemporary machine learning and data-mining. We suggest that the theory provides an excellent framework for philosophical thinking about inductive inference.

Statistical learning theory is often associated with the principle of Occam’s razor, which recommends a simplicity preference in inductive inference. This paper distills the core argument for simplicity obtainable from statistical learning theory, built on the theory’s central learning guarantee for the method of empirical risk minimization. This core “means-ends” argument is that a simpler hypothesis class or inductive model is better because it has better learning guarantees; however, these guarantees are model-relative and (...) so the theoretical push towards simplicity is checked by our prior knowledge. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and (...) iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

This article reviews a number of different areas in the foundations of formal learning theory. After outlining the general framework for formal models of learning, the Bayesian approach to learning is summarized. This leads to a discussion of Solomonoff's Universal Prior Distribution for Bayesian learning. Gold's model of identification in the limit is also outlined. We next discuss a number of aspects of learning theory raised in contributed papers, related to both computational and (...) representational complexity. The article concludes with a description of how semi-supervised learning can be applied to the study of cognitive learning models. Throughout this overview, the specific points raised by our contributing authors are connected to the models and methods under review. (shrink)

Context: It is beyond doubt that RC has received a great deal of attention in educational studies and learning theory. But overall, the current situation seems to be rather ambivalent in view of the blurring of the various strands in constructivist discourses and the different ways of distinguishing and foregrounding constructivist positions. Correspondingly, there is a wide range of claims, from the claim that (radical) constructivism represents a mainstream endeavor to attributions of its being outdated, self-refuting or irrelevant. (...) Purpose: The paper seeks to sound out the ambivalent situation of (radical) constructivism between “all” and “nothing” by examples of attributions of meaning to constructivist positions in academic everyday life and by challenging both prevalent criticisms of systemic-constructivist pedagogy and widespread broad classifications in learning theory. Method: The article critically reflects on (1) one-sentence “destructions” of constructivist positions, (2) Pongratz’s criticism of systemic-constructivist pedagogy, and (3) the threefold classification of the world of learning, i.e., behaviorism, cognitivism, and constructivism. Results: Both the current criticism of constructivism as a mainstream endeavor and evolutionary suggestions provided by the threefold classification are criticized. Although some constructivist concepts and distinctions are widely accepted today, often these achievements are not recognized as being rooted in constructivist discourses. Implications: As far as mainstreaming constructivism might be related to power politics, selling the “real thing,” and joining the ranks of truth-oriented Isms, it would not appear to be a desirable endeavor for those who rely on viability, circular foundations, relativist philosophy, and relationalist approaches. Nevertheless, clarifications of power relations and the interplay between constructivist analyses of politics and the politics of constructivism might contribute to overcoming the diffuse popularity of constructivist thought towards a better understanding of constructivist contributions to solution oriented, meaningful ways of dealing with urgent problems. (shrink)

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: The value of Cifarelli & Sevim’s target article lies in the analysis of how reflective abstraction contributes to the description of mathematical learning through problem solving. The additional value of the article lies in its emphasis of some aspects of the learning process that goes beyond radical constructivist (...) learning theory. I will look for common ground between the humanist philosophy of mathematics and radical constructivism. By doing so, I want to stress two converging elements: (i) the move away from traditionalist ontological positions and (ii) the central role of the students’ activity in the learning process. (shrink)