The question of whether grammaticality is a binary categorical or a gradient property has been the subject of ongoing debate in linguistics and psychology for many years. Linguists have tended to use constructed examples to test speakers’ judgements on specific sorts of constraint violation. We applied machine translation to randomly selected subsets of the British National Corpus (BNC) to generate a large test set which contains well-formed English source sentences, and sentences that exhibit a wide variety of grammatical infelicities. We (...) tested a large number of speakers through (filtered) crowd sourcing, with three distinct modes of classification, one binary and two ordered scales. We found a high degree of correlation in mean judgements for sentences across the three classification tasks. We also did two visual image classification tasks to obtain benchmarks for binary and gradient judgement patterns, respectively. Finally, we did a second crowd source experiment on 100 randomly selected linguistic textbook example sentences. The sentence judgement distributions for individual speakers strongly resemble the gradience benchmark pattern. This evidence suggests that speakers represent grammatical well-formedness as a gradient property. (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)

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)

Indirect negative evidence is clearly an important way for learners to constrain overgeneralisation, and yet a good learning theoretic analysis has yet to be provided for this, whether in a PAC or a probabilistic identification in the limit framework. In this paper we suggest a theoretical analysis of indirect negative evidence that allows the presence of ungrammatical strings in the input and also accounts for the relationship between grammaticality/acceptability and probability. Given independently justified assumptions about lower bounds on the probabilities (...) of grammatical strings, we establish that a limited number of membership queries of some strings can be probabilistically simulated. (shrink)

The question of whether it is possible to characterise grammatical knowledge in probabilistic terms is central to determining the relationship of linguistic representation to other cognitive domains. We present a statistical model of grammaticality which maps the probabilities of a statistical model for sentences in parts of the British National Corpus (BNC) into grammaticality scores, using various functions of the parameters of the model. We test this approach with a classifier on test sets containing different levels of syntactic infelicity. With (...) appropriate tuning, the classifiers achieve encouraging levels of accuracy. These experiments suggest that it may be possible to characterise grammaticality judgements in probabilistic terms using an enriched language model. (shrink)