We show that the conventional first-order algorithm of unification can be simulated by finite artificial neural networks with one layer of neurons. In these unification neural networks, the unification algorithm is performed by error-correction learning. Each time-step of adaptation of the network corresponds to a single iteration of the unification algorithm. We present this result together with the library of learning functions and examples fully formalised in MATLAB Neural Network Toolbox.

We investigate a new paradigm in the context of learning in the limit, namely, learning correction grammars for classes of computably enumerable (c.e.) languages. Knowing a language may feature a representation of it in terms of two grammars. The second grammar is used to make corrections to the first grammar. Such a pair of grammars can be seen as a single description of (or grammar for) the language. We call such grammars correction grammars. Correction grammars (...) capture the observable fact that people do correct their linguistic utterances during their usual linguistic activities. We show that learning correction grammars for classes of c.e. languages in the TxtEx-model (i.e., converging to a single correct correction grammar in the limit) is sometimes more powerful than learning ordinary grammars even in the TxtBe-model (where the learner is allowed to converge to infinitely many syntactically distinct but correct conjectures in the limit). For each n ≥ 0, there is a similar learning advantage, again in learning correction grammars for classes of c.e. languages, but where we compare learning correction grammars that make n + 1 corrections to those that make n corrections. The concept of a correction grammar can be extended into the constructive transfinite, using the idea of counting-down from notations for transfinite constructive ordinals. This transfinite extension can also be conceptualized as being about learning Ershov-descriptions for c.e. languages. For u a notation in Kleene's general system $(O,\, < _o )$ of ordinal notations for constructive ordinals, we introduce the concept of an u-correction grammar, where u is used to bound the number of corrections that the grammar is allowed to make. We prove a general hierarchy result: if u and v are notations for constructive ordinals such that $u\, < _o \,v$ , then there are classes of c.e. languages that can be TxtEx-learned by conjecturing v-correction grammars but not by conjecturing u-correction grammars. Surprisingly, we show that— above "ω-many" corrections—it is not possible to strengthen the hierarchy: TxtEx-learning u-correction grammars of classes of c.e. languages, where u is a notation in O for any ordinal, can be simulated by TxtBe-learning ω-correction grammars, where ω is any notation for the smallest infinite ordinal ω. (shrink)

When he surveyed the whole of knowledge in the first book of The Advancement of Learning, Francis Bacon identified three main diseases: firstly, an exaggerated care for form or style, which was dead learning; secondly a study of a false, not wrong, learning based on heated debates, teeming, so to speak, with the living worms of endless questions and answers. Finally, Bacon condemned not as a disease but a vice a ‘wrong’ learning based on the thriving (...) of pseudo-sciences and the comfortable connivance of masters and disciples. Altogether, after spelling out these three criticisms, he trusted that knowledge should not simply deal with correctness or exactness, but should aim at truth coupled with the welfare of mankind. He based his belief explicitly on saint Paul's view of knowledge-for-the-good-of-Christians, which to him meant potentially all men. The lesson for today's academic life, both lecturing and research, would or might be to couple the search for truth with the aim of the good of man. The academic world might then rediscover values and meaning. (shrink)

In the original publication of the article, the following paragraphs have been indented wrongly in the published article.

Grammatical error correction is an important element in language learning. In this article, based on deep learning, the application of the Transformer model in GEC was briefly introduced. Then, in order to improve the performance of the model on GEC, it was optimized by a generative adversarial network. Experiments were conducted on two data sets. It was found that the performance of the GAN-combined Transformer model was significantly improved compared to the Transformer model. The F 0.5 value (...) of the optimized model was 53.87 on CoNIL-2014, which was 2.69 larger than the Transformer model; the generalized language evaluation understanding value of the optimized model was 61.77 on JFLEG, which was 8.81 larger than that of the Transformer model. The optimized model also had a favorable correction performance in an actual English essay. The experimental results verify the reliability of the GAN-combined Transformer model on automatic English GEC, suggesting that the model can be further promoted and applied in practice. (shrink)

Using computer programs to correct English grammar can improve the efficiency of English grammar correction, improve the effect of error correction, and reduce the workload of manual error correction. In order to deal with and solve the problem of loss evaluation mismatch in the current mainstream machine translation, this study proposes the application of the deep learning method to propose an algorithm model with high error correction performance. Therefore, the framework of confrontation learning network (...) is introduced to continuously improve the optimization model parameters through the confrontation training of discriminator and generator. At the same time, convolutional neural network is introduced to improve the algorithm training effect, which can make the correction sentences generated by the model generator better in confrontation. In order to verify the performance of the algorithm model, P-value, R-value, F 0.5-value, and MRR-value were selected for the comprehensive evaluation of the model performance index. The simulation results of the CoNLL-2014 test set and Lang-8 test set show that the proposed algorithm model has significant performance improvement compared with the traditional transformer method and can correct the fluency of sentences. It has good application values. (shrink)

On an account of virtue as skill, virtues are acquired in the ways that skills are acquired. In this paper I focus on one implication of that account that is deserving of greater attention, which is that becoming more skillful requires learning from one’s failures, but that turns out to be especially challenging when dealing with moral failures. In skill acquisition, skills are improved by deliberate practice, where you strive to correct past mistakes and learn how to overcome your (...) current limitations. A similar story applies to virtue acquisition, as moral failures will be a part of anyone’s life, and we will all have to learn from these experiences. However, despite the importance of being able to learn from our mistakes, this is very difficult in practice, given that failure of any kind can be distressing, and especially so for moral failure. The distress created by a recognition of moral failure often prompts responses of anger, avoidance, or defensiveness; rather than attempts to make amends and when necessary to work on self-improvement. The most potentially distressing response to moral failure is shame, as it is often associated with defensiveness. It is here where emotion regulation will be important to manage that distress, and I focus on the skill of emotion differentiation. I argue that emotion differentiation is a promising strategy for distinguishing the emotions we may experience in the wake of failure, including shame, and to encourage those emotions that motivate self-improvement. Thus, emotion regulation is important for virtue acquisition. (shrink)

This paper sheds light on the shift that is taking place from the practice of ‘coding’, namely developing programs as conventional in the software community, to the practice of ‘curing’, an activity that has emerged in the last few years in Deep Learning (DL) and that amounts to curing the data regime to which a DL model is exposed during training. Initially, the curing paradigm is illustrated by means of a study-case on autonomous vehicles. Subsequently, the shift from coding (...) to curing is analysed taking into consideration the epistemological notions, central in the philosophy of computer science, of function, implementation, and correctness. First, it is illustrated how, in the curing paradigm, the functions performed by the trained model depend much more on dataset curation rather than on the model algorithms which, in contrast with the coding paradigm, do not comply with requested specifications. Second, it is highlighted how DL models cannot be considered implementations according to any of the available definitions of implementation that follow an intentional theory of functions. Finally, it is argued that DL models cannot be evaluated in terms of their correctness but rather in their experimental computational validity. (shrink)

The role of the cerebellum as a comparator of desired motor output and actual performance may be most important during learning of a novel motor task, when movement errors are common and corrective movements are produced to compensate for them. It is suggested that PET and recent fMRI data are compatible with such an interpretation. Increased activity in motor cortical areas during motor learning indicates that these areas also contribute to the learning process, [THACH].

El objetivo de este trabajo es medir el efecto del feedback correctivo escrito directo en el incremento del aprendizaje y el uso correcto de las preposiciones por y para en español como segunda lengua. Dichas preposiciones se consideran como unas de las más complejas durante el proceso de aprendizaje teniendo en cuenta la frecuencia de errores cometidos en sus usos y la naturaleza sintáctico-semántica. Para ello se llevó a cabo un estudio cuasiexperimental con pretest, postest inmediato, postest diferido y grupo (...) control, aplicando sistemáticamente las estrategias de FC metalingüístico directo y no metalingüístico directo a nivel escrito. Los resultados han demostrado evidencia de los efectos positivos de estos feedbacks correctivos en el incremento del aprendizaje y uso correcto de estas estructuras preposicionales. The aim of this research is to evaluate the effectiveness of written direct corrective feedback on the learning improvement of prepositions “por and para” in Spanish as second language. These grammatical structures are considered among the most complex prepositions to acquire during the learning process, considering the frequency of errors in their use and their syntactic-semantic nature. In order to achieve this aim, a quasi-experimental study with a pretest, immediate posttest, delayed posttest and control group was conducted. In this context, we have systematically applied the strategies of written metalinguistic and non-metalinguistic direct corrective feedback on these prepositions errors. The results have shown the positive effects of the written corrective feedback on the acquisition of these prepositional structures. (shrink)

Several studies highlight the importance of the order of different instructional methods when designing learning environments. Correct but also erroneous worked examples are frequently used methods to foster students’ learning performance, especially in problem-solving. However, so far no study examined how the order of these example types affects learning. While the expertise reversal effect would suggest presenting correct examples first, the productive failure approach hypothesizes the reversed order to be learning-facilitating. In addition, congruency of subsequent exemplified (...) problems was tested as a moderator of the effect of order on learning. For example, with arithmetic tasks, congruent problems target exactly the same calculation while incongruent problems refer to different calculations. Following cascade theory, a model of cognitive skill acquisition, presenting correct examples first should be more effective when the subsequent exemplified problems are different. To test the hypotheses, 83 university students were assigned to one of the four conditions in a 2 × 2 between-subject design. Learners navigated through a slideshow on the topic of Vedic mathematics consisting of explicit instruction, worked examples differing in terms of the experimental condition, and transfer problems. Although no main or interaction effects were found regarding students’ learning performance, mediational analysis offered support for the expertise reversal effect, as it indicated that there is a significant indirect effect of order via mental load on learning. Presenting correct examples first and erroneous examples second resulted in a lower mental load, which in turn was associated with better learning performance. In contrast, presenting erroneous examples first and correct examples second resulted in a more accurate self-assessment of learning performance. These findings offer first insights into the question of how the presentation order of different example types impacts learning and provide practical recommendations for the design of educational media. Results are discussed in light of the ongoing debate regarding the question if less guided instructional methods should precede or succeed more guided methods. (shrink)

This article is a brief response to Ramsey E. Ramsey’s essay ‘Letters on the hermeneutic education of dwelling’ published in Empedocles (6: 1, pp. 77–90). While it sees Ramsey’s defense of the lecture as a necessary articulation of the specificity of the work professors do in the humanities classroom, it points to the necessity of an enhanced self-awareness given the pervasive sense of crisis in the humanities, and in light of more recent developments on American and British campuses.

Learning and Teaching in Early Childhood: Pedagogies of Inquiry and Relationships is an introduction for early childhood educators beginning their studies. Reflecting the fact that there is no single correct approach to the challenges of teaching, this book explores teaching through two lenses: teaching as inquiry and teaching as relating. The first part of the book focuses on inquiry, covering early childhood learning environments, learning theories, play pedagogies, approaches to teaching and learning, documentation and assessment, and (...) the policy, curriculum and regulatory requirements in Australia. The second part explores relationships in early childhood contexts and covers topics such as fostering meaningful and respectful relationships with children, and working with families, staff and the wider community. Written by well-respected academics in the field, Learning and Teaching in Early Childhood is a vital resource for those entering the early childhood education and care profession. (shrink)

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

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)

A generator program for a computable function (by definition) generates an infinite sequence of programs all but finitely many of which compute that function. Machine learning of generator programs for computable functions is studied. To motivate these studies partially, it is shown that, in some cases, interesting global properties for computable functions can be proved from suitable generator programs which cannot be proved from any ordinary programs for them. The power (for variants of various learning criteria from the (...) literature) of learning generator programs is compared with the power of learning ordinary programs. The learning power in these cases is also compared to that of learning limiting programs, i.e., programs allowed finitely many mind changes about their correct outputs. (shrink)

The article addresses the question of how should scientific peers revise their beliefs (if at all) upon recognized disagreement. After presenting the basics of peer disagreement in sections 1 and 2, we focus, in section 3, on a concrete case of scientific disagreement, to wit, the dispute over the evidential status of randomized control trials in medical practice. The examination of this case motivates the idea that some scientific disagreements permit a steadfast reaction. In section 4, we support this conclusion (...) by providing a normative argument in the same direction; if we are correct, typical reasons for conciliation are absent in this kind of scientific disagreements. (shrink)

Does life have meaning? What is flourishing? How do we attain the good life? Philosophers, and many others of us, have explored these questions for centuries. As Eva Feder Kittay points out, however, there is a flaw in the essential premise of these questions: they seem oblivious to the very nature of the ways in which humans live, omitting a world of co-dependency, and of the fact that we live in and through our bodies, whether they are fully abled or (...) disabled. Our dependent, vulnerable, messy, changeable, and embodied experience colors everything about our lives both on the surface and when it comes to deeper concepts, but we tend to leave aside the body for the mind when it comes to philosophical matters. Disability offers a powerful challenge to long-held philosophical views about the nature of the good life, what provides meaning in our lives, and the centrality of reason, as well as questions of justice, dignity, and personhood. These concepts need not be distant and idealized; the answers are right before us, in the way humans interact with one another, care for one another, and need one another--whether they possess full mental capacities or have cognitive limitations. We need to revise our concepts of things like dignity and personhood in light of this important correction, Kittay argues. This is the first of two books in which Kittay will grapple with just how we need to revisit core philosophical ideas in light of disabled people's experience and way of being in the world. Kittay, an award-winning philosopher who is also the mother to a multiply-disabled daughter, interweaves the personal voice with the philosophical as a critical method of philosophical investigation. Here, she addresses why cognitive disability can reorient us to what truly matters, and questions the centrality of normalcy as part of a good life. With profound sensitivity and insight, Kittay examines other difficult topics: How can we look at the ethical questions regarding prenatal testing in light of a new appreciation of the personhood of disabled people? What do new possibilities in genetic testing imply for understanding disability, the family, and bioethics? How can we reconsider the importance of care, and how does it work best? In the process of pursuing these questions, Kittay articulates an ethic of care, which is the ethical theory most useful for claiming full rights for disabled people and providing the opportunities for everyone to live joyful and fulfilling lives. She applies the lessons of care to the controversial alteration of severely cognitively disabled children known as the Ashley Treatment, whereby a child's growth is halted with extensive estrogen treatment and related bodily interventions are justified. This book both imparts lessons that advocate on behalf of those with significant disabilities, and constructs a moral theory grounded on our ability to give, receive, and share care and love. Above all, it aims to adjust social attitudes and misconceptions about life with disability. (shrink)

This paper presents an experimental study investigating artificial grammar learning (AGL) in monolingual and bilingual children, with and without dyslexia, using an original methodology. We administered a serial reaction time (SRT) task, in the form of a modified Simon task, in which the sequence of the stimuli was manipulated according to the rules of a simple Lindenmayer grammar (more specifically, a Fibonacci grammar). By ensuring that the subjects focused on the correct response execution at the motor stage in presence (...) of congruent or incongruent visual stimuli, we could meet the two fundamental criteria for implicit learning: the absence of an intention to learn and the lack of awareness at the level of resulting knowledge. The participants of our studies were four groups of 10-year-old children: 30 Italian monolingual typically developing children, 30 bilingual typically developing children with Italian L2, 24 Italian monolingual dyslexic children and 24 bilingual dyslexic children with Italian L2. Participants were administered the modified Simon task developed according to the rules of the Fibonacci grammar and tested with respect to the implicit learning of three regularities: (i) a red is followed by a blue; (ii) a sequence of two blues is followed by a red and (iii) a blue can be followed either by a red or by a blue. Results clearly support the hypothesis that implicit learning took place, since participants of all groups became increasingly sensitive to the structure of the input, implicitly learning the sequence of the trials and thus appropriately predicting the occurrence of the relevant items, as manifested by faster reaction times in predictable trials. Moreover, group differences were found, with bilinguals being overall faster than monolinguals and dyslexics less accurate than controls. Finally, an advantage of bilingualism in dyslexia was found, with bilingual dyslexics performing consistently better than monolingual dyslexics and, in some conditions, at the level of the two control groups. These results are taken to suggest that bilingualism should be supported also among linguistically impaired individuals. (shrink)

Two great problems of learning confront humanity: learning about the nature of the universe and our place in it, and learning how to become civilized. The first problem was solved, in essence, in the 17th century, with the creation of modern science. But the second problem has not yet been solved. Solving the first problem without also solving the second puts us in a situation of great danger. All our current global problems have arisen as a result. (...) What we need to do, in response to this unprecedented crisis, is learn from our solution to the first problem how to solve the second. This was the basic idea of the 18th century Enlightenment. Unfortunately, in carrying out this programme, the Enlightenment made three blunders, and it is this defective version of the Enlightenment programme that we have institutionalized in 20th century academic inquiry. In order to solve the second great problem of learning we need to correct the three blunders of the traditional Enlightenment. This involves changing the nature of social inquiry, so that social science becomes social methodology or social philosophy, concerned to help us build into social life the progress-achieving methods of aim-oriented rationality, arrived at by generalizing the progress-achieving methods of science. It also involves, more generally, bringing about a revolution in the nature of academic inquiry as a whole, so that it takes up its proper task of helping humanity learn how to become wiser by increasingly cooperatively rational means. The scientific task of improving knowledge and understanding of nature becomes a part of the broader task of improving global wisdom. (shrink)

Aesthetic non-cognitivists deny that aesthetic statements express genuinely aesthetic beliefs and instead hold that they work primarily to express something non-cognitive, such as attitudes of approval or disapproval, or desire. Non-cognitivists deny that aesthetic statements express aesthetic beliefs because they deny that there are aesthetic features in the world for aesthetic beliefs to represent. Their assumption, shared by scientists and theorists of mind alike, was that language-users possess cognitive mechanisms with which to objectively grasp abstract rules fixed independently of human (...) responses, and that cognizers are thereby capable of grasping rules for the correct application of aesthetic concepts without relying on evaluation or enculturation. However, in this article I use Wittgenstein’s rule-following considerations to argue that psychological theories grounded upon this so-called objective model of rule-following fail to adequately account for concept acquisition and mastery. I argue that this is because linguistic enculturation, and the perceptual learning that’s often involved, influences and enables the mastery of aesthetic concepts. I argue that part of what’s involved in speaking aesthetically is to belong to a cultural practice of making sense of things aesthetically, and that it’s within a socio-linguistic community, and that community’s practices, that such aesthetic sense can be made intelligible. (shrink)

How people learn chunks or associations between adjacent items in sequences was modelled. Two previously successful models of how people learn artificial grammars were contrasted: the CCN, a network version of the competitive chunker of Servan‐Schreiber and Anderson [J. Exp. Psychol.: Learn. Mem. Cogn. 16 (1990) 592], which produces local and compositionally‐structured chunk representations acquired incrementally; and the simple recurrent network (SRN) of Elman [Cogn. Sci. 14 (1990) 179], which acquires distributed representations through error correction. The models' susceptibility to (...) two types of interference was determined: prediction conflicts, in which a given letter can predict two other letters that appear next with an unequal frequency; and retroactive interference, in which the prediction made by a letter changes in the second half of training. The predictions of the models were determined by exploring parameter space and seeing howdensely different regions of the space of possible experimental outcomes were populated by model outcomes. For both types of interference, human data fell squarely in regions characteristic of CCN performance but not characteristic of SRN performance. (shrink)