We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related notion of strong CPAC learning, and provide a negative answer to the COLT open problem posed by Agarwal et al. (2021) whether all decidably representable VC classes are improperly CPAC learnable. Second, we consider undecidability of (computable) PAC learnability. We give a (...) simple general argument to exhibit such ndecidability, and initiate a study of the arithmetical complexity of learnability. We briefly discuss the relation to the undecidability result of Ben-David et al. (2019), that motivated the work of Agarwal et al. (shrink)

This interdisciplinary new work explores one of the central theoretical problems in linguistics: learnability. The authors, from different backgrounds---linguistics, philosophy, computer science, psychology and cognitive science-explore the idea that language acquisition proceeds through general purpose learning mechanisms, an approach that is broadly empiricist both methodologically and psychologically. Written by four researchers in the full range of relevant fields: linguistics, psychology, computer science, and cognitive science, the book sheds light on the central problems of learnability and language, and traces (...) their implications for key questions of theoretical linguistics and the study of language acquisition. (shrink)

Feature selection is a widely studied technique whose goal is to reduce the dimensionality of the problem by removing irrelevant features. It has multiple benefits, such as improved efficacy, efficiency and interpretability of almost any type of machine learning model. Feature selection techniques may be divided into three main categories, depending on the process used to remove the features known as Filter, Wrapper and Embedded. Embedded methods are usually the preferred feature selection method that efficiently obtains a selection of (...) the most relevant features of the model. However, not all models support an embedded feature selection that forces the use of a different method, reducing the efficiency and reliability of the selection. Neural networks are an example of a model that does not support embedded feature selection. As neural networks have shown to provide remarkable results in multiple scenarios such as classification and regression, sometimes in an ensemble with a model that includes an embedded feature selection, we attempt to embed a feature selection process with a general-purpose methodology. In this work, we propose a novel general-purpose layer for neural networks that removes the influence of irrelevant features. The Feature-Aware Drop Layer is included at the top of the neural network and trained during the backpropagation process without any additional parameters. Our methodology is tested with 17 datasets for classification and regression tasks, including data from different fields such as Health, Economic and Environment, among others. The results show remarkable improvements compared to three different feature selection approaches, with reliable, efficient and effective results. (shrink)

A fundamental problem with the Clark & Thornton definition of a type-1 problem (requirement 2) is identified. An alternative classical statistical formulation is proposed where a type-1 (learnable) problem corresponds to the case where the learning machine is capable of representing its statistical environment.

This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having noisy (...) or fuzzy numerical content, it is suggested that the ANS has exquisitely precise numerical content that is subject to epistemic limitations. Similar considerations will arise for other analog representations. The chapter discusses how this new understanding of ANS representations recasts the learnability problem for number and the conceptual changes that children must accomplish in the number domain. (shrink)

An ideography is a general-purpose code made of pictures that do not encode language, which can be used autonomously – not just as a mnemonic prop – to encode information on a broad range of topics. Why are viable ideographies so hard to find? I contend that self-sufficient graphic codes need to be narrowly specialized. Writing systems are only an apparent exception: At their core, they are notations of a spoken language. Even if they also encode nonlinguistic information, they are (...) useless to someone who lacks linguistic competence in the encoded language or a related one. The versatility of writing is thus vicarious: Writing borrows it from spoken language. Why is it so difficult to build a fully generalist graphic code? The most widespread answer points to a learnability problem. We possess specialized cognitive resources for learning spoken language, but lack them for graphic codes. I argue in favor of a different account: What is difficult about graphic codes is not so much learning or teaching them as getting every user to learn and teach the same code. This standardization problem does not affect spoken or signed languages as much. Those are based on cheap and transient signals, allowing for easy online repairing of miscommunication, and require face-to-face interactions where the advantages of common ground are maximized. Graphic codes lack these advantages, which makes them smaller in size and more specialized. (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: vittorio.cipriani17@gmail.com.URL: https://air.uniud.it/handle/11390/1252226. (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)

Natural language is full of patterns that appear to fit with general linguistic rules but are ungrammatical. There has been much debate over how children acquire these “linguistic restrictions,” and whether innate language knowledge is needed. Recently, it has been shown that restrictions in language can be learned asymptotically via probabilistic inference using the minimum description length (MDL) principle. Here, we extend the MDL approach to give a simple and practical methodology for estimating how much linguistic data are required to (...) learn a particular linguistic restriction. Our method provides a new research tool, allowing arguments about natural language learnability to be made explicit and quantified for the first time. We apply this method to a range of classic puzzles in language acquisition. We find some linguistic rules appear easily statistically learnable from language experience only, whereas others appear to require additional learning mechanisms (e.g., additional cues or innate constraints). (shrink)

Christiansen & Chater (C&C) suggest that language is an organism, like us, and that our brains were not selected for Universal Grammar (UG) capacity; rather, languages were selected for learnability with minimal trial-and-error experience by our brains. This explanation is circular: Where did our brain's selective capacity to learn all and only UG-compliant languages come from?

A word often expresses many different morphological functions. Which part of a word contributes to which part of the overall meaning is not always clear, which raises the question as to how such functions are learned. While linguistic studies tacitly assume the co-occurrence of cues and outcomes to suffice in learning these functions (Baer-Henney, Kügler, & van de Vijver, 2015; Baer-Henney & van de Vijver, 2012), error-driven learning suggests that contingency rather than contiguity is crucial (Nixon, 2020; Ramscar, Yarlett, Dye, (...) Denny, & Thorpe, 2010). In error-driven learning, cues gain association strength if they predict a certain outcome, and they lose strength if the outcome is absent. This reduction of association strength is called unlearning. So far, it is unclear if such unlearning has consequences for cue–outcome associations beyond the ones that get reduced. To test for such consequences of unlearning, we taught participants morphophonological patterns in an artificial language learning experiment. In one block, the cues to two morphological outcomes—plural and diminutive—co-occurred within the same word forms. In another block, a single cue to only one of these two outcomes was presented in a different set of word forms. We wanted to find out, if participants unlearn this cue's association with the outcome that is not predicted by the cue alone, and if this allows the absent cue to be associated with the absent outcome. Our results show that if unlearning was possible, participants learned that the absent cue predicts the absent outcome better than if no unlearning was possible. This effect was stronger if the unlearned cue was more salient. This shows that unlearning takes place even if no alternative cues to an absent outcome are provided, which highlights that learners take both positive and negative evidence into account—as predicted by domain general error-driven learning. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is (...) the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬ BOX p, read as “p is true but you do not know p.” Not (...) only is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬ BOX p, read as “p is true but you do not know p.” Not (...) only is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

We argue that the problem of ideographic codes stems from neither learnability nor standardization, but from a general issue of pragmatic interpretation. As ideographic codes increase in expressive power, in order to reduce ambiguity, they must become more detailed – such that production becomes more cumbersome, and requires greater artistry on the part of users, limiting their capacity for growth.

PREFACE PART I METAPHYSICS Review of John McDowell’s Mind and World Special Sciences: Still Autonomous after All These Years Conclusion Acknowledgment Notes PART II CONCEPTS Review of Christopher Peacocke’s A Study of Concepts Notes There Are No Recognitional Concepts--Not Even RED Introduction Compositionality Why Premise P is Plausible Objections Conclusion Afterword Acknowledgment Notes There Are No Recognitional Concepts--Not Even RED, Part 2: The Plot Thickens Introduction: The Story ’til Now Compositonality and Learnability Notes Do We Think in Mentalese? Remarks (...) on Some Arguments of Peter Carruthers Appendix: Higher-Order Thoughts Notes Review of A. W. Moore’s Points of View PART III COGNITIVE ARCHITECTURE Review of Paul Churchland’s The Engine of Reason, The Seat of the Soul Connectionism and the Problem of Systematicity: Why Smolensky’s Solution Doesn’t Work Introduction I The Systematicity Problem and Its Classical Solution II Weak Compositionality III Strong Compositional Structure Conclusion Notes Connectionism and the Problem of Systematicity : Why Smolensky’s Solution Still Doesn’t Work Stage 1: Classical Theories The Connection with The Connection with Stage 2: Smolenksy Architectures Stage 3: Why Smolensky’s Solution Still Doesn’t Work Digression on singing and sailing Acknowledgment Notes There and Back Again: A Review of Annette Karmiloff-Smith’s Beyond Modularity 1. Encapsulation 2. Inaccessibility 3. Domain specificity 4. Innateness Conclusion Notes Review of Jeff Elman et al., Rethinking Innateness Brainlikeness Interactions Representational Nativism Empiricism Review of Steven Mithen’s The Prehistory of the Mind PART IV PHILOSOPHICAL DARWINISM Review of Richard Dawkins’s Climbing Mount Improbable Deconstructing Dennett’s Darwin Introduction Adaptation Adaptation and Teleology Deconstruction Notes Is Science Biologically Possible? Comments on Some Arguments of Patricia Churchland and of Alvin Plantinga Acknowledgment Notes Review of Steven Pinker’s How the Mind Works and Henry Plotkin’s Evolution in Mind Computation Massive modularity Innateness Psychological Darwinism. (shrink)

The seeming absence of negative evidence in the input that children receive during language acquisition has long been regarded as a serious problem for non-nativist linguistic theories. Among the solutions that have been suggested for this problem, preemption by competing structures is doubtless the most intensively researched and widely accepted. However, while preemption works well in the domain of morphology, it cannot apply categorically in the domain of syntax, as this would preclude the existence of semantically overlapping constructions, (...) such as the ditransitive and the prepositional dative, which can be used alternatively with many, but not all, verbs of literal or metaphorical transfer. This paper investigates one specific version of preemption briefly entertained by Pinker (Language learnability and language development, Harvard University Pressm, 1984), which would account both for the existence of semantically overlapping constructions and for the fact that these constructions may preempt each other in the case of individual verbs. Typically, such pairs of grammatical constructions differ in their information-structural restrictions and speakers tend to choose the construction that best fits a given discourse context; when speakers use a construction even though there is an alternative that fits the discourse context better, children may take this as evidence that the alternative is not available for the specific verb in question. Two corpus studies are presented, comparing the information-structural profile of prepositional dative constructions containing verbs that may alternate between the dative and the ditransitive with the information structural profile of verbs that are restricted to the prepositional dative. For Pinker's preemptive mechanism to be feasible, there should be a clear and systematic difference in the information-structural profile of these two classes of verbs. However, no such difference can be found in actual usage. (shrink)

Clark & Thornton's type-1/-2 distinction is not well-defined. The classes of type-1 and type-2 problems are too broad: many nocomputable functions are type-1 and type-2 learnable. They are also too narrow: trivial functions, such as identity, are neither type-1 nor type-2 learnable. Moreover, the scope of type-1 and type-2 problems appears to be equivalent. Overall, this distinction does not appear useful for machine learning or cognitive science.

Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes be corrected. Such learning from “positive evidence” has been viewed as raising “logical” problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this “logical problem” can be dissolved. In this study, we (...) review recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input. Results include the learnability of linguistic prediction, grammaticality judgments, language production, and form-meaning mappings. The simplicity approach can also be “scaled down” to analyze the learnability of specific linguistic constructions, and it is amenable to empirical testing as a framework for describing human language acquisition. (shrink)

Learning theory has frequently been applied to language acquisition, but discussion has largely focused on information theoretic problems—in particular on the absence of direct negative evidence. Such arguments typically neglect the probabilistic nature of cognition and learning in general. We argue first that these arguments, and analyses based on them, suffer from a major flaw: they systematically conflate the hypothesis class and the learnable concept class. As a result, they do not allow one to draw significant conclusions about the learner. (...) Second, we claim that the real problem for language learning is the computational complexity of constructing a hypothesis from input data. Studying this problem allows for a more direct approach to the object of study—the language acquisition device—rather than the learnable class of languages, which is epiphenomenal and possibly hard to characterize. The learnability results informed by complexity studies are much more insightful. They strongly suggest that target grammars need to be objective, in the sense that the primitive elements of these grammars are based on objectively definable properties of the language itself. These considerations support the view that language acquisition proceeds primarily through data-driven learning of some form. (shrink)

We investigate how Reinforcement Learning methods can be used to solve the production selection and production ordering problem in ACT‐R. We focus on four algorithms from the Q learning family, tabular Q and three versions of Deep Q Networks, as well as the ACT‐R utility learning algorithm, which provides a baseline for the Q algorithms. We compare the performance of these five algorithms in a range of lexical decision tasks framed as sequential decision problems.

What does it mean to be a rational language user? What is it to obey linguistic rules? What is the proper account of linguistic competence? A Fregean answer to these questions would make essential appeal to the notion of sense: we are masters of a language to the extent that we are able to recognise the cognitive value of its expressions; we are rational judges regarding truth-value assignments to the extent that we are sensitive to the ways in which the (...) sense of an expression guides us in the semantic evaluation process; and as for obeying rules, it is our ability to respond to how sense directs us, for a particular assertion of a sentence, towards the determination of its truth-value that best exemplifies what it is like to follow a linguistic rule. My thesis explores a cluster of closely interrelated issues arising from these questions. Accordingly, in tracing the routes of sense my dissertation places itself at the intersection of the philosophy of language, linguistics, philosophy of logic, and meta-ethics—and indeed, I end up agreeing with Allan Gibbard that the theory of meaning really belongs to meta-ethical reflection. Chapter 1 introduces some of the main research questions that I try to address in the rest of the thesis. In chapter 2 I state a number of theses which I take to be the defining ones for semanticism. I show that they form a class of jointly incompatible commitments. I choose nonsense as a problem case for compositionality and I argue that it forces the semanticist to abandon either the learnability or the compositionality constraint. The escape route I adopt, going radically minimalist about content, is incompatible with another key semanticist thesis, namely, that grasp of meaning is grasp of truth-conditions. In chapter 3, I consider the account of atomic meanings given by both the semanticist and the pragmaticist and I conclude that on neither account does interpretation come out as a process of rational choice between candidate bearers of content. Again, I suggest the lesson from indeterminacy is that we ought to embrace an ineradicably minimal conception of content. In chapter 4 I turn my attention to the meaning of the logical constants and I argue that indeterminacy worries extend to the very heart of the compositional machinery. Chapter 5 examines the view that logic is the science of reasoning. Unsurprisingly, I conclude that a defence of this claim requires endorsing content-minimalism. In chapter 6 I conclude my dissertation by sketching a radical view of content minimalism and I try to show how it can solve the puzzles I had been considering over the course of the previous chapters. (shrink)

We argue that number principles may be learnable instead of innate, by suggesting that children acquire probabilistically true number concepts rather than algorithms. We also suggest that non-propositional representational formats (e.g., mental models) may implicitly provide information that supports the induction of numerical principles. Given probabilistically true number concepts, the problem of the acquisition of mathematical principles is eliminated.

Reporting systems based on mobile technologies and feedback from regular citizens are becoming increasingly popular, especially as far as protection of environmental and cultural heritage is concerned. Reporting life-threatening situations, such as sudden natural disasters or traffic accidents, belongs to the same class of problems and could be aided by IT systems of a similar architecture. Designing and developing systems for reporting life-threatening situations is not a trivial task, requiring close cooperation between software developers and experts in different domains, who (...) could possibly find industrially recognized languages and notations difficult. Thus, the question is whether using simplified graphical domain-specific languages (SGDSLs) could help in creating a common communication platform. It has been revealed that domain experts have a preference for such languages as they offer good learnability, readability and ability to focus on the idea of application. The perspective of developers (technical persons) is introduced on the basis of feedback obtained from 84 students of Computer Science at the Lublin University of Technology, who attended comprehensive workshops followed by an anonymous survey. All participants received theoretical and practical training in modeling mobile software using the same set of languages as domain experts. An analysis of the results revealed that opinions expressed by technical and nontechnical persons concerning SGDSLs oriented on defining a flow of actions is consistent. Most respondents claimed that such languages might be valuable as tools for creating a common communication platform. (shrink)

It is increasingly argued that polymathy—vocational and avocational pursuits in multiple domains—is deeply associated with creativity and innovation, and that its development enables the creation of important bridges between otherwise fragmented, dispersed sets of knowledge. Nevertheless, the dominant culture in both industry and academia is still that of narrow specialization. In this paper, we argue that in the context of COVID-19 crisis, with its wicked and transdisciplinary nature, the disciplinary approach of specialization is ill-suited to solve our increasingly complex problems, (...) and that polymathic thinking can be a crucial asset in this regard. Drawing on different literature strands, we first examine the interplay between polymathy and other well-developed constructs in personality and temperament research. We then advance theoretical predictions regarding the relationship between trait polymathy and resilience in the COVID-19 crisis. After that, we discuss learnable strategies that can be used in complex, uncertain and adverse situations, which are associated with development of a more polymathic set of knowledge. Later, we discuss how it may be possible to better capitalize on the key features of polymathic thinking at the societal level. Finally, we conclude with a reflection on the adequacy of our current institutions for dealing with complex problems, and we underscore the crucial role of polymathic thinking in an increasingly complex and interrelated world. (shrink)

The chapters in this volume address a variety of issues surrounding quotation, such as whether it is a pragmatic or semantic phenomenon, what varieties of quotation exist, and what speech acts are involved in quoting. Quotation poses problems for many prevailing theories of language. One fundamental principle is that for a language to be learnable, speakers must be able to derive the truth-conditions of sentences from the meanings of their parts. Another popular view is that indexical expressions like "I" display (...) a certain fixity -- that they always refer to the speaker using them. Both of these tenets appear to be violated by quotation. This volume is suitable for scholars in philosophy of language, semantics, and pragmatics, and for graduate students in philosophy and linguistics. The book will also be useful for researchers in other fields that study quotation, including psychology and computer science. (shrink)

It is now a common belief that the truths of our lives are hidden in the databases streamed from our interactions in smart environments. In this current hype of big data, the Internet of Things has been suggested as the idea to embed small sensors and actuators everywhere to unfold the truths beneath the surfaces of everything. However, remaining the technology that promises more than it can provide thus far, more important for the IoT’s actual expansion to various social domains (...) than the actual discovery of hidden truths has been people’s speculations about the unknown problems, such as hidden security issues or lifestyle concerns, beyond the narrow human knowability but assumed to leave their traces in the IoT-collected big data. This paper discuss this speculation as the concealed cognitive labor of IoT users that projects some fictitious values to the big data IoT companies accumulate. By the term pan-kinetics, the systemic operation of smart actuators is analyzed as the process through which fictitious values of data are converted to the real values as these actuators draw some profitable correlations from physical domains of the IoT. Analyzing smart electroencephalogram headsets as the unique IoT devices operating on human brains, it argues how the IoT translates this speculative realism of unknown problems into its big data, which the IoT developers believe to be full of machine-learnable correlations that would lead to the smart solutions of the problems. (shrink)

The main task is to discuss the issue in belief dynamics in which philosophical beliefs and rational introspective agents incorporate Moorean type new information. First, a brief survey is conducted on Moore’s Paradox, and one of its solutions is introduced with the help of Update Semantics. Then, we present a Dynamic Doxastic Logic (DDL) which revises the belief of introspective agents put forward by Lindström & Rabinowicz. Next, we attempt to incorporate Moorean type new information within the DEL (DDL) framework, (...) as advised by van Benthem, Segerberg et al. Though we maintain the principle of “the primacy of new information” from the literature on traditional belief revision theory, several unsuccessful ways are also presented. We then conclude that some special kind of success (weak success) can still be found in those revision processes although absolute success does not hold. At last, the relevant problem of “learnability” is re-considered through weak success. (shrink)

The methodology implicit in empirically grounded social scientific studies of religion naturally allies with forms of semantic holism. However, a well known argument which questions whether holism in general is consistent with the fact that languages are learnable can be extended into an epistemological one which questions whether holism is consistent with an empirical methodology. In other words, there is question whether holism, in fact, makes social science possible. I diagnose the assumptions on which that objection rests, pointing out that (...) they are not necessary for semantic holism per se. I argue that a form of semantic holism along the lines advocated by W. V. O. Quine and Donald Davidson can avoid the objection. Moreover, when seen in this light, it has the resources to withstand an even deeper methodological problem. In so doing, though, several important but overlooked implications for the study of religion emerge. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC (...) reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: senadheerad@winthrop.eduURL: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

"Critique is a form of thinking and acting. It is determined by its objects, yet never accesses them immediately but is always mediated through its own forms of (re)presentation. Since the end of the 18th century, there has been a dynamization and fluidization of the understanding of form, as topoi such as the break, the marginalization, the tearing and opening indicate. However, these multifarious attempts to "build on the structure through demolition" (Benjamin) testify to the dependence of all articulation on (...) the forms of (re)presentation ["Darstellung"]. As a philosophical problem, the question of form arises in critical theory from Marx to Adorno. Since the 1960s, literary practices have proliferated which generate their critical statements less argumentatively than through the programmatic use of formal means. At the same time, the writing self, along with its attitudes, reflections, affects and instruments, visibly enters the critical scene - whereas the theatrical scene as a stage of critique has been contested intensively during the 20th century. This volume examines how the interdependence of critique, object, and form translates into critical stances, understood as learnable, reproducible gestures, which bear witness to changing conditions and media of critical practice. With contributions by Maria Fusco, Eva Geulen, Thomas Glaser, Birgit M. Kaiser, Sami Khatib, Sebastian Kirsch, Chris Kraus, Holger Kuhn, Oona Lochner, Isabel Mehl, Bettine Menke, Beate Söntgen, Heiko Stubenrauch, Kathrin Thiele, Lynne Tillman, Masha Tupitsyn, Mimmi Woisnitza."-Publisher's website. (shrink)

In his book Scientific Realism and the Plasticity of Mind, Paul Churchland suggests that the singular terms for prepositional attitude predicates serve an adverbial function as elements of complex predicates. This view, called monadic adverbialism, has three problems. First the monadic predicates cannot be semantic primitives because this would compromise the learnability of the language containing them. Second, the account has no way to analyze general de dicto beliefs that does not compromise the language being learnable. Third, the account (...) requires that de re behefs be treated as instances of general de dicto beliefs, which leads back to the second problem. The conclusion is that monadic adverbialism ought to be rejected. (shrink)

In his book Scientific Realism and the Plasticity of Mind, Paul Churchland suggests that the singular terms for prepositional attitude predicates serve an adverbial function as elements of complex predicates. This view, called monadic adverbialism, has three problems. First the monadic predicates cannot be semantic primitives because this would compromise the learnability of the language containing them. Second, the account has no way to analyze general de dicto beliefs that does not compromise the language being learnable. Third, the account (...) requires that de re behefs be treated as instances of general de dicto beliefs, which leads back to the second problem. The conclusion is that monadic adverbialism ought to be rejected. (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)

Limiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to (...) compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)

The deep formal and conceptual link existing between artificial life and artificial intelligence can be highlighted using conceptual tools derived by Karl Popper's evolutionary epistemology.Starting from the observation that the structure itself of an organism embodies knowledge about the environment which it is adapted to, it is possible to regard evolution as a learning process. This process is subject to the same rules indicated by Popper for the growth of scientific knowledge: causal conjectures (mutations) and successive refutations (extinction). In the (...) field of machine learning such a paradigm is represented by genetic algorithms that, simulating biological processes, emulate cognitive processes. From a practical viewpoint, that perspective allows to identify the two different kinds of learning considered by artificial intelligence, knowledge acquisition and skill improvement, and to get a different view of the problem of heuristic knowledge in learning systems. From a theoretical point of view, these considerations can shade a new light on an old epistemological problem: why do we live in a learnable world? (shrink)

According to a recent proposal, natural concepts are represented in an optimally designed similarity space, adhering to principles a skilled engineer would use for creatures with our perceptual and cognitive capacities. One key principle is that natural concepts should be easily learnable. While evidence exists for parts of this optimal design proposal, there has been no direct evidence linking naturalness to learning until now. This article presents results from a computational study on perceptual color space, demonstrating that naturalness indeed facilitates (...) learning. (shrink)

One of the great successes of the application of generalized quantifiers to natural language has been the ability to formulate robust semantic universals. When such a universal is attested, the question arises as to the source of the universal. In this paper, we explore the hypothesis that many semantic universals arise because expressions satisfying the universal are easier to learn than those that do not. While the idea that learnability explains universals is not new, explicit accounts of learning that (...) can make good on this hypothesis are few and far between. We propose a model of learning — back-propagation through a recurrent neural network — which can make good on this promise. In particular, we discuss the universals of monotonicity, quantity, and conservativity and perform computational experiments of training such a network to learn to verify quantifiers. Our results are able to explain monotonicity and quantity quite well. We suggest that conservativity may have a different source than the other universals. (shrink)

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)

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact (...) that finiteness of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory. (shrink)

No natural language has contrafactive attitude verbs. Because factives are universal across natural languages, this means that there is a major asymmetry between contrafactives and factives. We previously hypothesised that this asymmetry arises partly because the meaning of contrafactives is significantly harder to learn than that of factives. Here we test this hypothesis by using a production-oriented computational experiment that overcomes two limitations of our previous experiments. We find that our results do not support our previous hypothesis.

The ability to process center‐embedded structures has been claimed to represent a core function of the language faculty. Recently, several studies have investigated the learning of center‐embedded dependencies in artificial grammar settings. Yet some of the results seem to question the learnability of these structures in artificial grammar tasks. Here, we tested under which exposure conditions learning of center‐embedded structures in an artificial grammar is possible. We used naturally spoken syllable sequences and varied the presence of prosodic cues. The (...) results suggest that mere distributional information does not suffice for successful learning. Prosodic cues marking the boundaries of the major relevant units, however, can lead to learning success. Thus, our data are consistent with the hypothesis that center‐embedded syntactic structures can be learned in artificial grammar tasks if language‐like acoustic cues are provided. (shrink)

In recent articles Fodor and Lepore have argued that not only do considerations of learnability dictate that meaning must be compositional in the wellknown sense that the meanings of all sentences are determined by the meanings of a finite number of primitive expressions and a finite number of operations on them, but also that meaning must be 'reverse compositional' as well, in the sense that the meanings of the primitive expressions of which a complex expression is composed must be (...) determined by the meaning of that complex expression plus the manner of its composition. I argue against the requirement of reverse compositionality and against the claim that learnability requires it. I consider some objections and close the paper by arguing against the related claim that concepts are reverse compositional. (shrink)

This paper investigates the learnability by positive examples in the sense of Gold of Pregroup Grammars. In a first part, Pregroup Grammars are presented and a new parsing strategy is proposed. Then, theoretical learnability and non-learnability results for subclasses of Pregroup Grammars are proved. In the last two parts, we focus on learning Pregroup Grammars from a special kind of input called feature-tagged examples. A learning algorithm based on the parsing strategy presented in the first part is (...) given. Its validity is proved and its properties are examplified. (shrink)

Richard Holton has drawn attention to a new semantic universal, according to which (almost) no natural language has contrafactive attitude verbs. This semantic universal is part of an asymmetry between factive and contrafactive attitude verbs. Whilst factives are abundant, contrafactives are scarce. We propose that this asymmetry is partly due to a difference in learnability. The meaning of contrafactives is significantly harder to learn than that of factives. We tested our hypothesis by conducting a computational experiment using an artificial (...) neural network. The results of this experiment support our hypothesis. (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)

In this paper we present learning algorithms for classes of categorial grammars restricted by negative constraints. We modify learning functions of Kanazawa [10] and apply them to these classes of grammars. We also prove the learnability of intersection of the class of minimal grammars with the class of k-valued grammars.

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)