The impetus for this volume developed from the 1982 University of Western Ontario Learnability Workshop, which was organized by the editors and sponsored by that University's Department of Philosophy and the Centre for Cognitive Science. The volume e~plores the import of learnability theory for contemporary linguistic theory, focusing on foundational learning-theoretic issues associated with the parametrized Government-Binding framework. Written by prominent re searchers in the field, all but two of the eight contributions are pre viously unpublished. (...) The editor's introduction provides an overview that interrelates the separate papers and elucidates the foundational issues addressed by the volume. Osherson, Stob, and Weinstein's "Learning Theory and Natural Language" first appeared in Cognition ; Matthews's "The Plausi bility of Rationalism" was published in the Journal of Philosophy. The editors would like to thank the publishers for permission to reprint these papers. Mr. Marin Marinov assisted with the preparation of the indices for the volume. VB ROBERT 1. MATTHEWS INTRODUCTION: LEARNABILITY AND LINGUISTIC THEORY 1. INTRODUCTION Formal learning theory, as the name suggests, studies the learnability of different classes of formal objects under different formal models of learning. The specification of such a model, which specifies a learning environment, a learn ing strategy, and a criterion for successful learning, determines a class of formal objects, namely, the class that can be acquired to the level of the specified success criterion by a learner implementing the specified strategy in the specified enviroment. (shrink)

In the first part of my paper I discuss eight arguments in favour of the theory-dependence of observation: realistic content, guidance function of theories, perception as cognitive construction, expectation-dependence of perception, theory-dependence of scientific data, continuity between observational and theoretical concepts, language-dependence, and meaning holism. I argue that although these arguments make correct points, they do not exclude the existence of observations that are weakly theory-neutral in the sense that they don’t depend on acquired background knowledge. In (...) the second part I suggest an experimental method, the method of ostensive learning experiments, by which the degree of theory- and language-independence of a concept can be tested. (shrink)

In his pioneering work in the field of inductive inference, Gold (Inf Control 10:447–474, 1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not identifiable in the limit (learnable in the exact sense) from complete texts. Gold’s work paved the way for computational learning theories of language and has implications for two linguistically relevant classes in the Chomsky hierarchy (cf. Chomsky in Inf Control 2:137–167, 1959, Chomsky in Knowledge (...) of language: its nature, origin, and use, Praeger, 1986; Shieber in Linguist Philos 8:333–343, 1985; Heinz in Linguist Inq 41:623–661, 2010). Within that same framework, Angluin (Inf Control 45:117–135, 1980) provided a complete characterization for the learnability of language families. Mathematically, the concept of identification in the limit from that classical setting can be seen as the use of a particular type of metric for learning in the limit (Wharton in Inf Control 26:236–255, 1974). In this research note, I use Niyogi’s extended version of a theorem by Blum and Blum (Inf Control 28:125–155, 1975) on the existence of locking data sets to prove a necessary condition for learnability in the limit of any family of languages with the Gold property in any given metric. This recovers the most general version of Gold’s Theorem as a particular case. Moreover, when the language family is further assumed to contain all finite languages, the same condition also becomes sufficient for learnability in the limit. Finally, we discuss questions that are left open and outline a research program regarding language learnability in the limit from other input types and cognitive feasibility. (shrink)

It is sometimes argued that if PDP networks can be trained to make correct judgements of grammaticality we have an existence proof that there is enough information in the stimulus to permit learning grammar by inductive means alone. This seems inconsistent superficially with Gold's theorem and at a deeper level with the fact that networks are designed on the basis of assumptions about the domain of the function to be learned. To clarify the issue I consider what we should learn (...) from Gold's theorem, then go on to inquire into what it means to say that knowledge is domain specific. I first try sharpening the intuitive notion of domain specific knowledge by reviewing the alleged difference between processing limitations due to shortage of resources vs shortages of knowledge. After rejecting different formulations of this idea, I suggest that a model is language specific if it transparently refer to entities and facts about language as opposed to entities and facts of more general mathematical domains. This is a useful but not necessary condition. I then suggest that a theory is domain specific if it belongs to a model family which is attuned in a law-like way to domain regularities. This leads to a comparison of PDP and parameter setting models of language learning. I conclude with a novel version of the poverty of stimulus argument. (shrink)

It is sometimes argued that if PDP networks can be trained to make correct judgements of grammaticality we have an existence proof that there is enough information in the stimulus to permit learning grammar by inductive means alone. This seems inconsistent superficially with Gold's theorem and at a deeper level with the fact that networks are designed on the basis of assumptions about the domain of the function to be learned. To clarify the issue I consider what we should learn (...) from Gold's theorem, then go on to inquire into what it means to say that knowledge is domain specific. I first try sharpening the intuitive notion of domain specific knowledge by reviewing the alleged difference between processing limitatons due to shartage of resources vs shortages of knowledge. After rejecting different formulations of this idea, I suggest that a model is language specific if it transparently refer to entities and facts about language as opposed to entities and facts of more general mathematical domains. This is a useful but not necessary condition. I then suggest that a theory is domain specific if it belongs to a model family which is attuned in a law-like way to domain regularities. This leads to a comparison of PDP and parameter setting models of language learning. I conclude with a novel version of the poverty of stimulus argument. (shrink)

This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the law-of-excluded-middle, one can extract functionals , where L is a learning procedure for a rate of convergence which succeeds after at most B-many mind changes. This -learnability provides quantitative information strictly in between a full rate of convergence and a rate of metastability in the sense of (...) Tao . In fact, it corresponds to rates of metastability of a particular simple form. Moreover, if a certain gap condition is satisfied, then B and L yield a bound on the number of possible fluctuations. We explain recent applications of proof mining to ergodic theory in terms of these results. (shrink)

Theories of relational concept acquisition based on structured intersection discovery predict that relational concepts with a probabilistic structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate the learning of such categories. Experiment 1 showed that changing the task from a category-learning task to choosing the “winning” object in each stimulus greatly facilitated participants' ability to learn probabilistic relational categories. Experiments 2 and 3 further investigated the mechanisms underlying this (...) “who's winning” effect. Experiment 4 replicated and generalized the “who's winning” effect with more natural stimuli. Together, our findings suggest that people learn relational concepts by a process of intersection discovery akin to schema induction, and that any task that encourages people to discover a higher order relation that remains invariant over members of a category will facilitate the learning of putatively probabilistic relational concepts. (shrink)

It is argued that donald davidson has not succeeded in showing that we need a constructive theory of meaning--A theory for a natural language which davidson considers to have as its base a finite number of semantic primitives--In order to explain language learning and, In particular, Linguistic productivity. This linguistic productivity is the ability of a speaker who has mastered the meaning of a finite stock of words and a finite number of grammatical rules, To produce and understand (...) sentences which he has not constructed or encountered before. (shrink)

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is (...) equivalent to finite View the MathML sourceΔ20-piecewise computability, and learnability is equivalent to countable View the MathML sourceΠ10-piecewise computability . Second, we introduce disjunction-like operations such as the coproduct based on BHK-like interpretations, and then, we see that these operations induce Galois connections between the Medvedev degree structure and associated Medvedev/ Muchnik-like degree structures. Finally, we interpret these results in the context of the Weihrauch degrees and Wadge-like games. (shrink)

We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results:1. The class of unions of rectangles is polynomial time learnable for constant dimension d.2. The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable.3. The class (...) of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses. (shrink)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in (...) the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in (...) the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Metaphor, I argue, is a type of expression that is used to communicate information beyond that communicated by its literal meaning. I argue that the literal meaning of metaphors are essential. I attempt to account for metaphor in such a way as to retain the literal meaning, while also accounting for what is called the "metaphorical meaning" of metaphors. Secondly, I am concerned with the mechanisms in virtue of which we are able to distinguish the metaphorical from the literal. ;Chapter (...) I is a discussion of the problems that I will consider in the dissertation. These include distinguishing metaphorical from literal expressions, Donald Davidson's learnability and scrutability criteria, the exclusionary criteria, conversion and constancy theories of metaphor, and truth-values of metaphors. ;Chapter II critically examines Aristotle's, Max Black's, and Monroe C. Beardsley's intensional conversion theories. Here I argue that conversion theories are inadequate and unnecessary to account for metaphorical attributions. ;Chapter III critically examines extensional conversion theories of metaphor including Nelson Goodman's version. I discuss the difficulties that arise in postulating such reference conversions. I argue that this type of conversion theory is also unsuccessful and unnecessary. ;Chapter IV is a critical examination of four types of emotive theory of metaphor, one of which is Max Rieser's. These theories maintain, and I deny, that metaphors have an "emotive meaning" in addition to or instead of their literal meaning. I consider the shortcomings and consequences of emotive views, and argue that the postulation of emotive meanings is also misguided and unnecessary. ;Chapter V offers an alternative to conversion theories. Here I argue for a theory requiring no meaning or reference conversions. My view involves H. P. Grice's notions of conversational maxims and implicatures. I conclude that metaphors retain their literal meaning, partly in virtue of which they generate implicatures. I also conclude that our recognition of, and ability to distinguish, metaphors from literal expressions involves the violations of conversational maxims. (shrink)

About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, (...) this gives many new examples of mathematically interesting classes which are learnable in the online setting. (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)

The present work determines the arithmetic complexity of the index sets of u.c.e. families which are learnable according to various criteria of algorithmic learning. Specifically, we prove that the index set of codes for families that are TxtFex\-learnable is \-complete and that the index set of TxtFex\-learnable and the index set of TxtFext\-learnable families are both \-complete.

This chapter introduces values-based practice as a resource for working with individually diverse values in health and social care, and describes its origins in an on-going development through the resources of philosophy. The chapter is in two main sections. Section I, Values-Based Practice, builds on two brief interactive exercises to introduce and explain the key features of values-based practice. As a relatively recent addition to the range of resources for working with values in health and social care, values-based practice is (...) distinctive in focussing on the diversity of values comprising individual lived experience. Like evidence-based practice, values-based practice is a process-driven rather than an outcome-driven methodology. That is to say, rather than offering prescribed answers, both approaches offer processes that support decision-makers in coming to answers for themselves based on the particular circumstances presented by the situation in question. Although entirely complementary, the processes involved are of course different. Where evidence-based practice relies on meta-analyses of the results of high-quality clinical trials to inform a consensual model of decision-making, values-based practice builds on learnable clinical skills and other process elements to inform a dissensual model of decision-making rather than seeking to overcome value-conflicts in reaching consensus. Working within a premise of mutual respect for differences of values, and guided by three key principles linking values and evidence, values-based practice, as described in the chapter, supports dissensual decision-making, balanced according to the circumstances presented by the decision in question, within frameworks of locally-set frameworks of shared values. Section II, The Theory-Practice Dynamic, then outlines the theory-practice dynamic on which values-based practice is based. The origins of values-based practice in mid-twentieth century ordinary language philosophy of the Oxford School are outlined. As the chapter illustrates, although a limited area of analytic philosophy, many aspects of values-based practice are informed by ordinary language philosophy, ranging from its premise, through the training exercises and other process elements described in Section I, to its role in hybrid empirical studies supporting its model of service delivery. The development of values-based practice, furthermore, as section II goes on to describe, is ongoing, with key initiatives drawing not only on both analytic and Continental traditions of European philosophy, but also on non-European philosophies such as those of Africa and the Caribbean. (shrink)

Jablonka & Lamb's (J&L's) extended evolutionary theory is more amenable to being applied to human cultural change than standard neo-Darwinian evolutionary theory. However, the authors are too quick to dismiss past evolutionary approaches to human culture. They also overlook a potential parallel between evolved genetic mechanisms that enhance evolvability and learned cognitive mechanisms that enhance learnability.

The second volume in the Vancouver Studies in Cognitive Science series, this collection presents recent work in the fields of phonology, morphology, semantics, and neurolinguistics. Its overall theme is the relationship between the contents of grammatical formalisms and their real-time realizations in machine or biological systems. Individual essays address such topics as learnability, implementability, computational issues, parameter setting, and neurolinguistic issues. Contributors include Janet Dean Fodor, Richard T. Oehrle, Bob Carpenter, Edward P. Stabler, Elan Dresher, Arnold Zwicky, Mary-Louis Kean, (...) and Lewis P. Shapiro. (shrink)

Focusing on the tendency of terrorist organizations to explosive attack, this article applied the institutional theory as the basis to explain the inherent logic of attack type similarity from the perspective of mimetic, coercive, and normative isomorphism. Subsequently, the study conducted an empirical analysis of the data onto 1825 terrorist organizations recorded in the Global Terrorism Database with the logistic regression method. The results show that: Terrorist organizations will learn from pre-existing terrorist organizations' experiences, and mimetic isomorphism will promote (...) explosive tendency; Due to the normative isomorphism effect, terrorist groups' tendency to explosive attacks is weakened by their increased duration; If terrorist organizations are hostile to a strong government, coercive isomorphism positively moderates the negative effects of increasing duration. The study suggests that counter-terrorism approaches such as destroying the learnable experience of attacks, addressing the root causes of terrorism, and maintaining a strong government may be helpful in stopping increasing terrorist activities, which is essential for reducing terrorist organizations' vivosphere, blocking the inter-flow and imitation between terrorist organizations, and ultimately interrupting the terrorist propagation chain. (shrink)

How do minds emerge from developing brains? According to the representational features of cortex are built from the dynamic interaction between neural growth mechanisms and environmentally derived neural activity. Contrary to popular selectionist models that emphasize regressive mechanisms, the neurobiological evidence suggests that this growth is a progressive increase in the representational properties of cortex. The interaction between the environment and neural growth results in a flexible type of learning: minimizes the need for prespecification in accordance with recent neurobiological evidence (...) that the developing cerebral cortex is largely free of domain-specific structure. Instead, the representational properties of cortex are built by the nature of the problem domain confronting it. This uniquely powerful and general learning strategy undermines the central assumption of classical learnability theory, that the learning properties of a system can be deduced from a fixed computational architecture. Neural constructivism suggests that the evolutionary emergence of neocortex in mammals is a progression toward more flexible representational structures, in contrast to the popular view of cortical evolution as an increase in innate, specialized circuits. Human cortical postnatal development is also more extensive and protracted than generally supposed, suggesting that cortex has evolved so as to maximize the capacity of environmental structure to shape its structure and function through constructive learning. (shrink)

"An important contribution to contemporary jurisprudential debate and to legal thought more generally, Just Interpretations is far ahead of currently available work."--Peter Goodrich, author of Oedipus Lex "I was struck repeatedly by the clarity of expression throughout the book. Rosenfeld's description and criticism of the recent work of leading thinkers distinguishes his work within the legal theory genre. Furthermore, his own theory is quite original and provocative."--Aviam Soifer, author of Law and the Company We Keep.