The task of inducing grammar structures has received a great deal of attention. The reasons why researchers have studied are different; to use grammar induction as the first stage in building large treebanks or to make up better language models. However, grammar induction has inherent computational complexity. To overcome it, some grammar induction algorithms add new production rules incrementally. They refine the grammar while keeping their computational complexity low. In this paper, we propose a new (...) efficient grammar induction algorithm. Although our algorithm is similar to algorithms which learn a grammar incrementally, our algorithm uses the graphical EM algorithm instead of the Inside-Outside algorithm. We report results of learning experiments in terms of learning speeds. The results show that our algorithm learns a grammar in constant time regardless of the size of the grammar. Since our algorithm decreases syntactic ambiguities in each step, our algorithm reduces required time for learning. This constant-time learning considerably affects learning time for larger grammars. We also reports results of evaluation of criteria to choose nonterminals. Our algorithm refines a grammar based on a nonterminal in each step. Since there can be several criteria to decide which nonterminal is the best, we evaluate them by learning experiments. (shrink)

While Ç ´Ò¿ µ methods for parsing probabilistic context-free grammars (PCFGs) are well known, a tabular parsing framework for arbitrary PCFGs which allows for botton-up, topdown, and other parsing strategies, has not yet been provided. This paper presents such an algorithm, and shows its correctness and advantages over prior work. The paper finishes by bringing out the connections between the algorithm and work on hypergraphs, which permits us to extend the presented Viterbi (best parse) (...) class='Hi'>algorithm to an inside (total probability) algorithm. (shrink)

fundamental rule” in an order-independent manner, such that the same basic algorithm supports top-down and Most PCFG parsing work has used the bottom-up bottom-up parsing, and the parser deals correctly with CKY algorithm (Kasami, 1965; Younger, 1967) with the difficult cases of left-recursive rules, empty elements, Chomsky Normal Form Grammars (Baker, 1979; Jeand unary rules, in a natural way.

We examine the expressive power of probabilistic context free grammars (PCFGs), with a special focus on the use of probabilities as a mechanism for reducing ambiguity by filtering out unwanted parses. Probabilities in PCFGs induce an ordering relation among the set of trees that yield a given input sentence. PCFG parsers return the trees bearing the maximum probability for a given sentence, discarding all other possible trees. This mechanism is naturally viewed as a way of defining a (...) new class of tree languages. We formalize the tree language thus defined, study its expressive power, and show that the latter is beyond context freeness. While the increased expressive power offered by PCFGs helps to reduce ambiguity, we show that, in general, it cannot be decided whether a PCFG removes all ambiguities. (shrink)

We examine the expressive power of probabilistic context free grammars (PCFGs), with a special focus on the use of probabilities as a mechanism for reducing ambiguity by filtering out unwanted parses. Probabilities in PCFGs induce an ordering relation among the set of trees that yield a given input sentence. PCFG parsers return the trees bearing the maximum probability for a given sentence, discarding all other possible trees. This mechanism is naturally viewed as a way of defining a (...) new class of tree languages. We formalize the tree language thus defined, study its expressive power, and show that the latter is beyond context freeness. While the increased expressive power offered by PCFGs helps to reduce ambiguity, we show that, in general, it cannot be decided whether a PCFG removes all ambiguities. (shrink)

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase‐structure trees should be assigned to initial sentences, s/he allows (...) (implicitly) for all possible trees and lets linguistic experience decide which is the “best” tree for each sentence. The best tree is obtained by maximizing “structural analogy” between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus‐based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar‐based and rule‐based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children’s language development from item‐based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions. (shrink)

This paper presents a novel approach to the unsupervised learning of syntactic analyses of natural language text. Most previous work has focused on maximizing likelihood according to generative PCFG models. In contrast, we employ a simpler probabilistic model over trees based directly on constituent identity and linear context, and use an EM-like iterative procedure to induce structure. This method produces much higher quality analyses, giving the best published results on the ATIS dataset.

This paper presents a novel approach to the unsupervised learning of syntactic analyses of natural language text. Most previous work has focused on maximizing likelihood according to generative PCFG models. In contrast, we employ a simpler probabilistic model over trees based directly on constituent identity and linear context, and use an EM-like iterative procedure to induce structure. This method produces much higher quality analyses, giving the best published results on the ATIS dataset.

We present a generative distributional model for the unsupervised induction of natural language syntax which explicitly models constituent yields and contexts. Parameter search with EM produces higher quality analyses than previously exhibited by unsupervised systems, giving the best published unsupervised parsing results on the ATIS corpus. Experiments on Penn treebank sentences of comparable length show an even higher F1 of 71% on nontrivial brackets. We compare distributionally induced and actual part-of-speech tags as input data, and examine extensions to the basic (...) model. We discuss errors made by the system, compare the system to previous models, and discuss upper bounds, lower bounds, and stability for this task. (shrink)

A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log (...) Lang Inf 14(1):49–86, 2005) procedure. Next we present a two-stage procedure for performing distributional learning by unifying the lexical types that are initially discovered. The first structural unification algorithm in essence unifies the initial family of sets of types so that the resulting grammar will generate all term-labelled trees that follow the usage patterns evident from the learning sample. Further altering the lexical categories to generate a recursively extended language can be accomplished by a second unification. The combined unification algorithm is shown to yield a new type-logical lexicon that extends the learning sample to a possibly infinite (and possibly context-sensitive) language in a principled fashion. Finally, the complete learning strategy is analyzed from the perspective of algorithmic learning theory; the range of the procedure is shown to be a class of term-labelled tree languages which is finitely learnable from good examples (Lange et al in Algorithmic learning theory, Vol 872 of lecture notes in artificial intelligence, Springer, Berlin, pp 423–437), and so is identifiable in the limit as a corollary. (shrink)

We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order (...) operation in the case of linear context-free rewriting systems. This suggest the possibility of defining an Abstract Categorial Hierarchy. (shrink)

We introduce _Interleave-Disjunction-Lock parallel multiple context-free grammars_ (IDL-PMCFG), a novel grammar formalism designed to describe the syntax of free word order languages that allow for extensive interleaving of grammatical constituents. Though interleaved constituents, and especially the so-called hyperbaton, are common in several ancient (Classical Latin and Greek, Sanskrit...) and modern (Hungarian, Finnish...) languages, these syntactic structures are often difficult to express in existing formalisms. The IDL-PMCFG formalism combines Seki et al.’s parallel multiple context-free grammars (...) (PMCFG) with Nederhof and Satta’s IDL expressions. We define the semantics of IDL-PMCFGs and study their expressivity, proving that IDL-PMCFG extends both PMCFG and IDL-CFG (context-free grammars equipped with IDL expressions) and that IDL-PMCFG parsing is \(\mathrm {NP}\) -hard. We then introduce COMPĀ, a programming language extending Ranta’s Grammatical Framework (GF) and built as a high-level front-end formalism to IDL-PMCFG for practical grammar development. We present a parsing algorithm for IDL-PMCFG inspired by earlier Earley-style PMCFG parsing algorithms and Nederhof and Satta’s IDL graphs and give a worst-case estimate of its complexity as a function of several metrics on IDL expressions, the size of the input and a new notion of the _G_-density of a language. (shrink)

The equivalence of leaf languages of tree adjoining grammars and monadic linear context-free grammars was shown about a decade ago. This paper presents a proof of the strong equivalence of these grammar formalisms. Non-strict tree adjoining grammars and monadic linear context-free grammars define the same class of tree languages. We also present a logical characterisation of this tree language class showing that a tree language is a member of this class iff it is the two-dimensional (...) yield of an MSO-definable three-dimensional tree language. (shrink)

We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order (...) operation in the case of linear context-free rewriting systems. This suggest the possibility of defining an Abstract Categorial Hierarchy. (shrink)

In this paper we prove the Chomsky Conjecture (all languages recognized by the Lambek calculus are context-free) for both the full Lambek calculus and its product-free fragment. For the latter case we present a construction of context-free grammars involving only product-free types.

This paper examines feature selection for log linear models over rich constraint-based grammar (HPSG) representations by building decision trees over features in corresponding probabilistic context free grammars (PCFGs). We show that single decision trees do not make optimal use of the available information; constructed ensembles of decision trees based on different feature subspaces show signifi- cant performance gains (14% parse selection error reduction). We compare the performance of the learned PCFG grammars and log linear models over (...) the same features. (shrink)

This paper defines the grammar class of sequentially indexed grammars. Sequentially indexed grammars are the result of a change in the index stack handling mechanism of indexed grammars [Aho68, Aho69]. Sequentially indexed grammars are different from linear indexed grammars [Gaz88]. Like indexed languages, sequentially indexed languages are a fully abstract language class. Unlike indexed languages, sequentially indexed languages allow polynomial parsing algorithms. We give a polynomial algorithm for parsing with sequentially indexed gramamrs that is an extension of the (...) Earley algorithm for parsing with context free grammars. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into (...) the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

This paper discusses recent improvements and extensions in Synapse system for inductive inference of context free grammars from sample strings. Synapse uses incremental learning, rule generation based on bottom-up parsing, and the search for rule sets. The form of production rules in the previous system is extended from Revised Chomsky Normal Form A →βγ to Extended Chomsky Normal Form, which also includes A → B, where each of β and γ is either a terminal or nonterminal symbol. From (...) the result of bottom-up parsing, a rule generation mechanism synthesizes minimum production rules required for parsing positive samples. Instead of inductive CYK algorithm in the previous version of Synapse, the improved version uses a novel rule generation method, called ``bridging,'' which bridges the lacked part of the derivation tree for the positive string. The improved version also employs a novel search strategy, called serial search in addition to minimum rule set search. The synthesis of grammars by the serial search is faster than the minimum set search in most cases. On the other hand, the size of the generated CFGs is generally larger than that by the minimum set search, and the system can find no appropriate grammar for some CFL by the serial search. The paper shows experimental results of incremental learning of several fundamental CFGs and compares the methods of rule generation and search strategies. (shrink)

Notice that this paper has not claimed that all natural languages are CFL's. What it has shown is that every published argument purporting to demonstrate the non-context-freeness of some natural language is invalid, either formally or empirically or both.18 Whether non-context-free characteristics can be found in the stringset of some natural language remains an open question, just as it was a quarter century ago.Whether the question is ultimately answered in the negative or the affirmative, there will be (...) interesting further questions to ask. If it turns out that natural languages are indeed always CFL's, it will be reasonable to ask whether this helps to explain why speakers apparently recognize so quickly whether a presented utterance corresponds to a grammatical sentence or not, and to associate structural and semantic details with it. It might also be reasonable to speculate about the explanation for the universally context-free character of the languages used by humans, and to wonder whether evolutionary biological factors are implicated in some way (Sampson (1979) could be read in this light). And naturally, it will be reasonable to pursue the program put forward by Gazdar (1981, in press) to see to what extent CFL-inducing grammatical devices can be exploited to yield insightful descriptions of natural languages that capture generalizations in revealing ways.If a human language that is not a CFL is proved to exist, on the other hand, a different question will be raised: give the non-context-free character of human languages in general, why has this property been so hard to demonstrate that it has taken over twenty-five years to bring it to light since the issue was first explicitly posed? If human languages do not have to be CFL's, why do so many (most?) of them come so close to having the property of context-freeness? And, since the CFL's certainly constitute a very broad class of mathematically natural and computationally tractable languages, what property of human beings or their communicative or cognitive needs is it that has caused some linguistic communities to reach beyond the boundaries of this class in the course of evolving a linguistic system?Either way, we shall be interested to see our initial question resolved, and further questions raised. One cautionary word should be said, however, about the implications (or lack of them) that the answer will have for grammatical studies. Chomsky has repeatedly stated that he does not see weak generative capacity as a theme of central importance in the theory of grammar, and we agree. It is very far from being the case that the recent resurgence of interest in exploring the potential of CF-PSG or equivalent systems will, or should, be halted dead in its tracks by the discovery (if it is ever forthcoming) that some natural language is not a CFL. In the area of parsing, for instance, it seems possible that natural languages are not only parsed on the basis of constituent structure such as a CF-PSG would assign, but are parsed as if they were finite state languages (see Langendoen (1975) and Church (1980) for discussion along these lines). That is, precisely those construction-types that figure in the various proofs that English is not an FSL appear to cause massive difficulty in the human processing system; the sentences crucial to the proofs are for the most part unprocessable unless they are extremely short (yet the arguments for English not being and FSL only go through if length is not an issue). This means that in practice properties of finite state grammars are still of great potential importance to linguistic theory despite the fact that they do not provide the framework for defining the total class of grammatical sentences. The same would almost certannly be true of CF-PSG's if they were shown to be inadequate in a similar sense. It is highly unlikely that the advances made so far in far in phrase structure description could be nullified by a discovery about weak generative capacity. Moreover, there are known to be numerous ways in which the power of CF-PSG's can be marginally enhanced to permit, for example, xx languages to be generated without allowing anything like the full class of recursively enumerable or even context-sensitive languages (see Hopcroft and Ullmann (1979), Chapter 14) for an introduction to this topic, noting especially Figure 14.7 on p. 393. The obvious thing to do if natural languages were ever shown not to be CFL's in the general case would be to start exploring such minimal enhancements of expressive power to determine exactly what natural languages call for in this regard and how it could be effectively but parsimoniously provided in a way that closely modelled human linguistic capacities.In the meantime, it seems reasonable to assume that the natural languages are a proper subset of the infinite-cardinality CFL's until such time as they are validly shown not to be. (shrink)

LAS is a program that acquires augmented transition network (ATN) grammars. It requires as data sentences of the language and semantic network representatives of their meaning. In acquiring the ATN grammars, it induces the word classes of the language, the rules of formation for sentences, and the rules mapping sentences onto meaning. The induced ATN grammar can be used both for sentence generation and sentence comprehension. Critical to the performance of the program are assumptions that it makes about the (...) relation between sentence structure and surface structure (the graph deformation condition), about when word classes may be formed and when ATN networks may be merged, and about the structure of noun phrases. These assumptions seem to be good heuristics which are largely true for natural languages although they would not be true for many nonnatural languages. Provided these assumptions are satisfied LAS seems capable of learning any context‐free language. (shrink)

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context- (...) class='Hi'>free language theory is of fundamental importance in the analysis, design, and implementation of computer programming languages. This work describes a formalization effort, using the Coq proof assistant, of fundamental results of the classical theory of contextfree grammars and languages. These include closure properties (union, concatenation, and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules, and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. As it turns out, this is a comprehensive formalization of the classical context-free language theory in the Coq proof assistant and includes the formalization of the Pumping Lemma for context-free languages. The perspectives for the further development of this work are diverse and can be grouped in three different areas: inclusion of new devices and results, code extraction, and general enhancements of its libraries. (shrink)

This paper extends the Earley parsing algorithm for context free languages [3] to the case of sequentially indexed languages. Sequentially indexed languages are related to indexed languages [1, 2]. The difference is that parallel processing of index stacks is replaced by sequential processing [4].

In this chapter we consider unsupervised learning from two perspectives. First, we briefly look at its advantages and disadvantages as an engineering technique applied to large corpora in natural language processing. While supervised learning generally achieves greater accuracy with less data, unsupervised learning offers significant savings in the intensive labour required for annotating text. Second, we discuss the possible relevance of unsupervised learning to debates on the cognitive basis of human language acquisition. In this context we explore the implications (...) of recent work on grammar induction for poverty of stimulus arguments that purport to motivate a strong bias model of language learning, commonly formulated as a theory of Universal Grammar (UG). We examine the second issue both as a problem in computational learning theory, and with reference to empirical work on unsupervised Machine Learning (ML) of syntactic structure. We compare two models of learning theory and the place of unsupervised learning within each of them. Looking at recent work on part of speech tagging and the recognition of syntactic structure, we see how far unsupervised ML methods have come in acquiring different kinds of grammatical knowledge from raw text. (shrink)

This paper classifies a family of grammar formalisms that extendcontext-free grammar by talking about tuples of terminal strings, ratherthan independently combining single terminal words into larger singlephrases. These include a number of well-known formalisms, such as headgrammar and linear context-free rewriting systems, but also a new formalism,(simple) literal movement grammar, which strictly extends the previouslyknown formalisms, while preserving polynomial time recognizability.The descriptive capacity of simple literal movement grammars isillustrated both formally through a weak generative (...) capacity argument and ina more practical sense by the description of conjunctive cross-serialrelative clauses in Dutch. After sketching a complexity result and drawing anumber of conclusions from the illustrations, it is then suggested that thenotion of mild context-sensitivity currently in use, that depends on therather loosely defined concept of constant growth, needs a modification toapply sensibly to the illustrated facts; an attempt at such a revision isproposed. (shrink)

We present a new axiomatization of the non-associative Lambek calculus. We prove that it takes polynomial time to reduce any non-associative Lambek categorial grammar to an equivalent context-free grammar. Since it is possible to recognize a sentence generated by a context-free grammar in polynomial time, this proves that a sentence generated by any non-associative Lambek categorial grammar can be recognized in polynomial time.

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods —have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other methods in their predictive success. In this article this conflict is analyzed and dissolved, by means (...) of probabilistic analysis and computer simulation. (shrink)

It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) (...) class='Hi'>algorithm for determining categorial grammars from input consisting of functor-argument structures. (shrink)

A recent hypothesis in empirical brain research on language is that the fundamental difference between animal and human communication systems is captured by the distinction between finite-state and more complex phrase-structure grammars, such as context-free and context-sensitive grammars. However, the relevance of this distinction for the study of language as a neurobiological system has been questioned and it has been suggested that a more relevant and partly analogous distinction is that between non-adjacent and adjacent dependencies. Online memory (...) resources are central to the processing of non-adjacent dependencies as information has to be maintained across intervening material. One proposal is that an external memory device in the form of a limited push-down stack is used to process non-adjacent dependencies. We tested this hypothesis in an artificial grammar learning paradigm where subjects acquired non-adjacent dependencies implicitly. Generally, we found no qualitative differences between the acquisition of non-adjacent dependencies and adjacent dependencies. This suggests that although the acquisition of non-adjacent dependencies requires more exposure to the acquisition material, it utilizes the same mechanisms used for acquiring adjacent dependencies. We challenge the push-down stack model further by testing its processing predictions for nested and crossed multiple non-adjacent dependencies. The push-down stack model is partly supported by the results, and we suggest that stack-like properties are some among many natural properties characterizing the underlying neurophysiological mechanisms that implement the online memory resources used in language and structured sequence processing. (shrink)

A number of criticisms of a recent paper byare made. (1) In attempting to assess the observational adequacy of story grammars, they state that a context‐free grammar cannot handle discontinuous elements; however, they do not show that such elements occur in the domain to which the grammars apply. Further, they do not present adequate evidence for their claim that there are acceptable stories not accounted for by existing grammars and that the grammars will accept nonstories such as (...) procedures. (2) They state that it has been proven that under natural conditions children cannot learn transformational grammars, which is a misrepresentation of the learnability proofs which have been offered. (3) Most important, they take an unduly narrow approach to story understanding by claiming that people only understand story content and do not have knowledge of story structure which is useful in comprehension or memory. Counterevidence from the literature is cited which indicates that such knowledge is both useful and used, and a number of methods for assessing the psychological adequacy of structural models are discussed. (shrink)

Natural languages are riddled with context-sensitivity. One and the same string of words can express many different meanings on occasion of use, and yet we understand one another effortlessly, on the fly. How do we do so? What fixes the meaning of context-sensitive expressions, and how are we able to recover the meaning so effortlessly? -/- This book offers a novel response: we can do so because we draw on a broad array of subtle linguistic conventions that determine (...) the interpretation of context-sensitive items. Contrary to the dominant tradition, which maintains that the meaning of context-sensitive language is underspecified by grammar and that interpretation relies on non-linguistic cues and speakers' intentions, this book argues that meaning is determined entirely by discourse conventions, rules of language that have largely been missed and the effects of which have been mistaken for extra-linguistic effects of an utterance situation on meaning. The linguistic account of context developed here sheds new light on the nature of linguistic content and the interaction between content and context. At the same time, it provides a novel model of context that should constrain and help evaluate debates across many subfields of philosophy where appeal to context has been common, often leading to surprising conclusions such as epistemology, ethics, value theory, metaphysics, metaethics, and logic. (shrink)

Since a human language consists of an infinite number of sentences, it cannot be adequately described by enumeration. Hence, as Chomsky wrote in the first paragraph of his first book, Syntactic Structures, an adequate description of a language is approached through the specification of a generative device that will generate and structurally describe all the sentences of a language. And since generative devices form a hierarchy in terms of descriptive power, the basic question of grammar is what is the (...) minimum of power needed to generate human languages. What this book does is describe the Chomsky hierarchy in a very clear and accessible way. Finite state grammars are shown to be equivalent in generative power to regular phrase structure grammars. After context free, and context sensitive phrase structure grammars, one finds at the top of the hierarchy transformational grammars, which Kimball has shown to be weakly equivalent to a universal phrase structure grammar, i.e., one in which rules can delete items. This last equivalence allows one to appreciate the central problem in current grammatical theory: that the "standard theory" of Aspects of the Theory of Syntax allows so much power for the construction of grammars that solutions become arbitrary and non-empirical, and hence the problem is to find a principled minimization of the power of transformational grammars. This is a clear, up-to-date, and elegant little book. One admirably suitable as a comparatively undemanding introduction to the abstract theory of grammar, or as a way of brushing-up on the subject.—J.L. (shrink)

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show (...) that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages. (shrink)

English grammar error correction algorithm refers to the use of computer programming technology to automatically recognize and correct the grammar errors contained in English text written by nonnative language learners. Classification model is the core of machine learning and data mining, which can be applied to extracting information from English text data and constructing a reliable grammar correction method. On the basis of summarizing and analyzing previous research works, this paper expounded the research status and significance (...) of English grammar error correction algorithm, elaborated the development background, current status, and future challenges of the classification model, introduced the methods and principles of feature extraction method and dynamic residual structure, constructed a basic model for English grammar error correction based on the classification model, analyzed the classification model and translation model of English grammar error correction, proposed the English grammar error correction algorithm based on the classification model, performed the analyses of the model architecture and model optimizer of the grammar error correction algorithm, and finally conducted a simulation experiment and its result analysis. The study results show that, with the continuous increase of training samples and the continuous progress of learning process, the proposed English grammar error correction algorithm based on the classification model will continue to increase its classification accuracy, further refine its recognition rules, and gradually improve correction efficiency, thereby reducing processing time, saving storage space, and streamlining processing flow. The study results of this paper provide a certain reference for the further research on English grammar error correction algorithm based on the classification model. (shrink)

The computation of scalar implicatures is sometimes costly relative to basic meanings. Among the costly computations are those that involve strengthening `some' to `not all' and strengthening inclusive disjunction to exclusive disjunction. The opposite is true for some other cases of strengthening, where the strengthened meaning is less costly than its corresponding basic meaning. These include conjunctive strengthenings of disjunctive sentences (e.g., free-choice inferences) and exactly-readings of numerals. Assuming that these are indeed all instances of strengthening via implicature/exhaustification, the (...) puzzle is to explain why strengthening sometimes increases costs while at other times it decreases costs. I develop a theory of processing costs that makes no reference to the strengthening mechanism or to other aspects of the derivation of the sentence's form/meaning. Instead, costs are determined by domain-general considerations of the grammar's output, and in particular by aspects of the meanings of ambiguous sentences and particular ways they update the context. Specifically, I propose that when the hearer has to disambiguate between a sentence's basic and strengthened meaning, the processing cost of any particular choice is a function of (i) a measure of the semantic complexity of the chosen meaning and (ii) a measure of how much relevant uncertainty it leaves behind in the context. I measure semantic complexity with Boolean Complexity in the propositional case and with semantic automata in the quantificational case, both of which give a domain-general measure of the minimal representational complexity needed to express the given meaning. I measure relevant uncertainty with the information-theoretic notion of entropy; this domain-general measure formalizes how `far' the meaning is from giving a complete answer to the question under discussion, and hence gives an indication of how much representational complexity is yet to come. Processing costs thus follow from domain-general considerations of current and anticipated representational complexity. The results might also speak to functional motivations for having strengthening mechanisms in the first place. Specifically, exhaustification allows language users to use simpler forms than would be available without it to both resolve relevant uncertainties and convey complex meanings. (shrink)

Lambek categorial grammars is a class of formal grammars based on the Lambek calculus. Pentus proved in 1993 that they generate exactly the class of context-free languages without the empty word. In this paper, we study categorial grammars based on the Lambek calculus with the permutation rule LP. Of particular interest is the product-free fragment of LP called the Lambek-van Benthem calculus LBC. Buszkowski in his 1984 paper conjectured that grammars based on the Lambek-van Benthem calculus (LBC-grammars (...) for short) generate exactly permutation closures of context-free languages. In this paper, we disprove this conjecture by presenting a language generated by an LBC-grammar that is not a permutation closure of any context-free language. Firstly, we introduce an ad-hoc modification of vector addition systems called linearly-restricted branching vector addition systems with states and additional memory (LRBVASSAMs for short) and prove that the latter are equivalent to LBC-grammars. Then we construct an LRBVASSAM that generates a non-semilinear set and thus disprove Buszkowski’s conjecture. Since Buszkowski’s conjecture is false, not so much is known about the languages generated by LBC-grammars or by LP-grammars. The equivalence of LRBVASSAMs and LBC-grammars allows us to establish a number of their properties. We show that LP-grammars generate the same class of languages as LBC-grammars; that is, removing product from LP does not decrease expressive power of corresponding categorial grammars. We also prove that this class of languages is closed under union, intersection, concatenation, and Kleene plus. (shrink)