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.

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.

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)

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)

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.

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)

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)

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)

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)

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)

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)

The specific mechanisms whereby Pavlovian conditioning leads to adaptive behavior need to be elaborated. There is no evidence that it is via reduction in the “destabilizing effect that time lags have on feedback control” (Domjan et al. 2000, sect. 3.3). The adaptive value of Pavlovian conditioning goes well beyond the regulation of social behavior.

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)

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.

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.

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.

. Implicit in the cognitive social learning model of personality as articulated by Walter Mischel, Albert Bandura, and others, is an epistemology which emphasizes the activity of the mind in the construction of knowledge. Using Mischel's five person variables as an outline, the epistemic implications of this model of personality are developed and then illustrated by application to William James's typology of the religious personality and to the current debate over hermeneutic and empirical approaches to studying human behavior. This (...) approach explicates the connection between personality characteristics and epistemological approaches in terms of cognitive social learning theory. (shrink)

In this thesis, we study the complexity of some mathematical problems: in particular, those arising in computable analysis and algorithmic learning theory for algebraic structures. Our study is not limited to these two areas: indeed, in both cases, the results we obtain are tightly connected to ideas and tools coming from different areas of mathematical logic, including for example descriptive set theory and reverse mathematics.After giving the necessary preliminaries, we first study the uniform computational strength of the (...) Cantor–Bendixson theorem in the Weihrauch lattice. This work falls into the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. We concentrate on problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor–Bendixson theorem, and various problems arising from them. As far as we know, this is the first systematic study of problems at the level of $\mathbf {\Pi }^1_1\mathsf {-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.We continue considering problems related to (induced) subgraphs. We provide results on the (effective) Wadge complexity of sets of graphs, that are also used to determine the Weihrauch degree of certain decision problems. The decision problems we consider are defined for a fixed graph G, and they take as input a graph H, answering whether G is an (induced) subgraph of H: we also consider the opposite problem (i.e., answering whether H is an induced subgraph of G). We conclude this part on (induced) subgraphs considering the Weihrauch degree of “search problems.”These problems are defined for a fixed graph G, and they take as input a graph H such that G is an (induced) subgraph H: the output is a copy of G in H. In both cases, we highlight differences and analogies between the subgraph and the induced subgraph relation.We then move our attention to algorithmic learning theory, and we present the framework we use to study the learnability of families of algebraic structures: here, given a countable family of pairwise nonisomorphic structures $\mathfrak {K}$, a learner receives larger and larger pieces of an arbitrary copy of a structure in $\mathfrak {K}$ and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. We say that $\mathfrak {K}$ is learnable if there exists a learner which eventually stabilizes to a correct guess. The framework was lacking a method for comparing the complexity of nonlearnable families, and so we propose a solution to this problem using tools coming from invariant descriptive set theory. To do so, we first prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation $E_0$ of eventual agreement on infinite binary sequences and then, replacing $E_0$ with Borel equivalence relations of higher complexity, we obtain a new hierarchy of learning problems. This leads to the notion of E-learnability, where a family of structures $\mathfrak {K}$ is E-learnable, for a Borel equivalence relation E, if there is a continuous reduction from the isomorphism relation associated with $\mathfrak {K}$ to E. It is then natural to ask how the notion of E-learnability interacts with “classical” learning paradigms.Finally, we study the number of mind changes that a learner needs to learn a given family, both from a topological and a combinatorial point of view, and we consider how the complexity of a learner (in terms of Turing reducibility) affects the number of mind changes for learning a given family.Abstract prepared by Vittorio Cipriani.E-mail: [email protected]: https://air.uniud.it/handle/11390/1252226. (shrink)

Virtue ethics is one of the three normative approaches to ethics. It foregrounds the virtues or moral character of the individual and can be contrasted with approaches that focus on duties or rules, as in deontological ethics, or on the consequences of actions, as in consequentialism. Virtue Ethics are different from deontological and consequentialist ethical forms. They are related to dispositions. Dispositions, as inner states, precede, condition and have some influence over actions. A disposition is a character type, an habituation, (...) a state of preparation or readiness and a tendency to act in a specified way. Two further issues are relevant to the conception of virtue ethics: notions of causality and free will. The reason why these two notions are important is that in the first case the identification and conceptualisation of the virtues requires a theory of knowledge and of being and the identification of a relationship between the two, including a notion of causation; and in the second case, any ethical theory requires a theory of intention. (shrink)