The Logic of Categorial Grammars: Lecture Notes Christian Retoré
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A Type-Theoretical Analysis of Complex Verb Generation
A Type-theoretical Analysis of Complex Verb Generation Satoshi Tojo Mitsubishi Research Institute, Inc. 2-22 Harumi 3, Chuo-ku Tokyo 104, Japan e-mail: [email protected], [email protected] Abstract hardly find a verb element in the target language, which corresponds with the original word exactly in Tense and aspect, together with mood and modality, meaning. However we also need to admit that the usually form the entangled structure of a complex verb. problem of knowledge representation of tense and as- They are often hard to translate by machines, because pect (namely time), or that of mood and modality is of both syntactic and semantic differences between lan- not only the problem of verb translation, but that of guages. This problem seriously affects upon the gen- the whole natural language understanding. In this pa- eration process because those verb components in in- per, in order to realize a type calculus in syntax, we terlingua are hardly rearranged correctly in the target depart from a rather mundane subset of tense, aspects, language. We propose here a method in which each and modMities, which will be argued in section 2. verb element is defined as a mathematical function ac- cording to its type of type theory. This formalism gives 1.2 The difference in the structure each element its legal position in the complex verb in the target language and certifies so-called partial trans- In the Japanese translation of (1): lation. In addition, the generation algorithm is totally oyoi-de-i-ta-rashii free from the stepwise calculation, and is available on parallel architecture. -
Probabilistic Grammars and Their Applications This Discretion to Pursue Political and Economic Ends
Probabilistic Grammars and their Applications this discretion to pursue political and economic ends. and the Law; Monetary Policy; Multinational Cor- Most experiences, however, suggest the limited power porations; Regulation, Economic Theory of; Regu- of privatization in changing the modes of governance lation: Working Conditions; Smith, Adam (1723–90); which are prevalent in each country’s large private Socialism; Venture Capital companies. Further, those countries which have chosen the mass (voucher) privatization route have done so largely out of necessity and face ongoing efficiency problems as a result. In the UK, a country Bibliography whose privatization policies are often referred to as a Armijo L 1998 Balance sheet or ballot box? Incentives to benchmark, ‘control [of privatized companies] is not privatize in emerging democracies. In: Oxhorn P, Starr P exerted in the forms of threats of take-over or (eds.) The Problematic Relationship between Economic and bankruptcy; nor has it for the most part come from Political Liberalization. Lynne Rienner, Boulder, CO Bishop M, Kay J, Mayer C 1994 Introduction: privatization in direct investor intervention’ (Bishop et al. 1994, p. 11). After the steep rise experienced in the immediate performance. In: Bishop M, Kay J, Mayer C (eds.) Pri ati- zation and Economic Performance. Oxford University Press, aftermath of privatizations, the slow but constant Oxford, UK decline in the number of small shareholders highlights Boubakri N, Cosset J-C 1998 The financial and operating the difficulties in sustaining people’s capitalism in the performance of newly privatized firms: evidence from develop- longer run. In Italy, for example, privatization was ing countries. -
Grammars and Normal Forms
Grammars and Normal Forms Read K & S 3.7. Recognizing Context-Free Languages Two notions of recognition: (1) Say yes or no, just like with FSMs (2) Say yes or no, AND if yes, describe the structure a + b * c Now it's time to worry about extracting structure (and doing so efficiently). Optimizing Context-Free Languages For regular languages: Computation = operation of FSMs. So, Optimization = Operations on FSMs: Conversion to deterministic FSMs Minimization of FSMs For context-free languages: Computation = operation of parsers. So, Optimization = Operations on languages Operations on grammars Parser design Before We Start: Operations on Grammars There are lots of ways to transform grammars so that they are more useful for a particular purpose. the basic idea: 1. Apply transformation 1 to G to get of undesirable property 1. Show that the language generated by G is unchanged. 2. Apply transformation 2 to G to get rid of undesirable property 2. Show that the language generated by G is unchanged AND that undesirable property 1 has not been reintroduced. 3. Continue until the grammar is in the desired form. Examples: • Getting rid of ε rules (nullable rules) • Getting rid of sets of rules with a common initial terminal, e.g., • A → aB, A → aC become A → aD, D → B | C • Conversion to normal forms Lecture Notes 16 Grammars and Normal Forms 1 Normal Forms If you want to design algorithms, it is often useful to have a limited number of input forms that you have to deal with. Normal forms are designed to do just that. -
CS351 Pumping Lemma, Chomsky Normal Form Chomsky Normal
CS351 Pumping Lemma, Chomsky Normal Form Chomsky Normal Form When working with a context-free grammar a simple and useful form is called the Chomsky Normal Form (CNF). A CFG in CNF is one where every rule is of the form: A ! BC A ! a Where a is any terminal and A,B, and C are any variables, except that B and C may not be the start variable. Note that we have two and only two variables on the right hand side of the rule, with the exception that the rule S!ε is permitted where S is the start variable. Theorem: Any context free language may be generated by a context-free grammar in Chomsky normal form. To show how to make this conversion, we will need to do three things: 1. Eliminate all ε rules of the form A!ε 2. Eliminate all unit rules of the form A!B 3. Convert remaining rules into rules of the form A!BC Proof: 1. First add a new start symbol S0 and the rule S0 ! S, where S was the original start symbol. This guarantees that the start symbol doesn’t occur on the right hand side of a rule. 2. Remove all ε rules. Remove a rule A!ε where A is not the start symbol For each occurrence of A on the right-hand side of a rule, add a new rule with that occurrence of A deleted. Ex: R!uAv becomes R!uv This must be done for each occurrence of A, so the rule: R!uAvAw becomes R! uvAw and R! uAvw and R!uvw This step must be repeated until all ε rules are removed, not including the start. -
Development of a General-Purpose Categorial Grammar Treebank
Proceedings of the 12th Conference on Language Resources and Evaluation (LREC 2020), pages 5195–5201 Marseille, 11–16 May 2020 c European Language Resources Association (ELRA), licensed under CC-BY-NC Development of a General-Purpose Categorial Grammar Treebank Yusuke Kubota, Koji Mineshima, Noritsugu Hayashi, Shinya Okano NINJAL, Ochanomizu University, The University of Tokyo, idem. f10-2 Midori-cho, Tachikawa; 2-2-1 Otsuka, Bunkyo; 3-8-1 Komaba, Megurog, Tokyo, Japan [email protected], [email protected], fhayashi, [email protected] Abstract This paper introduces ABC Treebank, a general-purpose categorial grammar (CG) treebank for Japanese. It is ‘general-purpose’ in the sense that it is not tailored to a specific variant of CG, but rather aims to offer a theory-neutral linguistic resource (as much as possible) which can be converted to different versions of CG (specifically, CCG and Type-Logical Grammar) relatively easily. In terms of linguistic analysis, it improves over the existing Japanese CG treebank (Japanese CCGBank) on the treatment of certain linguistic phenomena (passives, causatives, and control/raising predicates) for which the lexical specification of the syntactic information reflecting local dependencies turns out to be crucial. In this paper, we describe the underlying ‘theory’ dubbed ABC Grammar that is taken as a basis for our treebank, outline the general construction of the corpus, and report on some preliminary results applying the treebank in a semantic parsing system for generating logical representations of sentences. Keywords: treebank, categorial grammar, Japanese, annotation 1. Introduction Table 1: Comparison with related work original corpus output This paper reports on the progress of the construction of a H&S Penn Treebank English CCG general-purpose categorial grammar treebank in Japanese Uematsu et al. -
Direct Compositionality and Variable-Free Semantics: the Case of “Principle B”
Direct Compositionality and Variable-Free Semantics: The Case of “Principle B” Drafty outline/handout of material to be presented at the Workshop on Direct Compositionality Pauline Jacobson Brown University 0. The big picture goals: (A) To argue that direct compositionality is a much simpler hypothesis about the organization of the grammar than the competing views It is, therefore, the view we should hope is correct. Apparent challenges to this view should perhaps lead us to rethink some of the underlying assumptions which give rise to these challenges. (B) To point out: a consequence of at least a reasonably strong version of direct compositionality is that structured representations (e.g., trees) play no actual role in the grammar: they are not something that grammatical rules/principles can “see”. They are just convenient representation for the lnguist (representing the syntactic proof system and the compositional semantics) (C) To point out the consequences of this with respect to principles regarding the distribution of pronouns (reflexives, etc.). Standard assumption: these require the grammar to include principles which are stated on non strictly-local chucks of representation Hence: the hypothesis of direct compositionality should inspire us to rethink such statements (D) To discuss a second way in which binding principles have traditionally been taken to challenge direct compositionality (at least in its strong form): • there are many cases where there are binding type effects (e.g., "binding" of pronouns, "binding" of reflexives to satisfy Principle A, Principle B violations, etc.) but where on the surface, there is no big enough chunk of representation Typical example : connectivity in specificational sentences (1) What John is is proud of himself. -
Chapter 1 Negation in a Cross-Linguistic Perspective
Chapter 1 Negation in a cross-linguistic perspective 0. Chapter summary This chapter introduces the empirical scope of our study on the expression and interpretation of negation in natural language. We start with some background notions on negation in logic and language, and continue with a discussion of more linguistic issues concerning negation at the syntax-semantics interface. We zoom in on cross- linguistic variation, both in a synchronic perspective (typology) and in a diachronic perspective (language change). Besides expressions of propositional negation, this book analyzes the form and interpretation of indefinites in the scope of negation. This raises the issue of negative polarity and its relation to negative concord. We present the main facts, criteria, and proposals developed in the literature on this topic. The chapter closes with an overview of the book. We use Optimality Theory to account for the syntax and semantics of negation in a cross-linguistic perspective. This theoretical framework is introduced in Chapter 2. 1 Negation in logic and language The main aim of this book is to provide an account of the patterns of negation we find in natural language. The expression and interpretation of negation in natural language has long fascinated philosophers, logicians, and linguists. Horn’s (1989) Natural history of negation opens with the following statement: “All human systems of communication contain a representation of negation. No animal communication system includes negative utterances, and consequently, none possesses a means for assigning truth value, for lying, for irony, or for coping with false or contradictory statements.” A bit further on the first page, Horn states: “Despite the simplicity of the one-place connective of propositional logic ( ¬p is true if and only if p is not true) and of the laws of inference in which it participate (e.g. -
1 English Subjectless Tagged Sentences Paul Kay Department Of
1 English subjectless tagged sentences Paul Kay Department of Linguistics University of California Berkeley, CA 94720 [email protected] 2 Abstract A colloquial English sentence like Fooled us, didn't they? contains a finite main verb but no expressed subject. The identity of the missing subject of fooled is recovered from the tag subject they: compare Fooled us, didn't she?, Fooled us, didn't you? This paper argues (1) that such subjectless tagged sentences (STSs) pose a problem for grammatical approaches based on movement and empty categories and (2) that STSs receive a revealing analysis as part of a finely articulated family of tagged sentence constructions when viewed within a non-derivational, constructional, multiple-inheritance-based approach.* *I would like to thank Peter Culicover, Liliane Haegeman, Charles Fillmore Andreas Kathol and Richard Oehrle for comments on previous versions of this paper, as well as an anonymous reviewer for Language. They have doubtless offered more good advice than I have accepted. 3 0. Introduction. It has been argued from several points of view that whatever can be done with empty categories (ecs) can be done without them (Ades and Steedman 1982, Gazdar et al. 1984, Kaplan and Zaenen 1989, Pollard and Sag 1994 chapter 9, Sag and Fodor 1994, Kay and Fillmore 1999, Sag 1999). It has also been argued that, because there is no hard evidence for their existence, linguistic theory would be better off dispensing with these unobservable entities (Pickering and Barry 1991, Sag and Fodor 1994, Sag 1999).1 The present paper purports to take the argument one step further by showing that there are things that can be done without empty categories that cannot be done with them, at least not with any of the ecs currently available. -
LING83600: Context-Free Grammars
LING83600: Context-free grammars Kyle Gorman 1 Introduction Context-free grammars (or CFGs) are a formalization of what linguists call “phrase structure gram- mars”. The formalism is originally due to Chomsky (1956) though it has been independently discovered several times. The insight underlying CFGs is the notion of constituency. Most linguists believe that human languages cannot be even weakly described by CFGs (e.g., Schieber 1985). And in formal work, context-free grammars have long been superseded by “trans- formational” approaches which introduce movement operations (in some camps), or by “general- ized phrase structure” approaches which add more complex phrase-building operations (in other camps). However, unlike more expressive formalisms, there exist relatively-efficient cubic-time parsing algorithms for CFGs. Nearly all programming languages are described by—and parsed using—a CFG,1 and CFG grammars of human languages are widely used as a model of syntactic structure in natural language processing and understanding tasks. Bibliographic note This handout covers the formal definition of context-free grammars; the Cocke-Younger-Kasami (CYK) parsing algorithm will be covered in a separate assignment. The definitions here are loosely based on chapter 11 of Jurafsky & Martin, who in turn draw from Hopcroft and Ullman 1979. 2 Definitions 2.1 Context-free grammars A context-free grammar G is a four-tuple N; Σ; R; S such that: • N is a set of non-terminal symbols, corresponding to phrase markers in a syntactic tree. • Σ is a set of terminal symbols, corresponding to words (i.e., X0s) in a syntactic tree. • R is a set of production rules. -
Categorial Grammar and Lexical-Functional Grammar∗
Categorial Grammar and Lexical-Functional Grammar¤ Reinhard Muskens Department of Linguistics Tilburg University The Netherlands Proceedings of the LFG01 Conference University of Hong Kong, Hong Kong Miriam Butt and Tracy Holloway King (Editors) 2001 CSLI Publications http://csli-publications.stanford.edu/ ¤I wish to thank the participants of LFG2001, especially Mary Dalrymple and Ron Kaplan, for valuable feedback. All comments are very welcome. Abstract This paper introduces ¸-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, ¸-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representa- tions are combined with the help of linear combinators, closed pure ¸-terms in which each abstractor binds exactly one variable. Mathe- matically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable. While ¸-grammars could be used to formalize many approaches to grammatical theory, they are certainly natural as a basis for the formalization of LFG. This leads to a theory I would like to call ¸- LFG. In this paper it will be shown how the standard components of LFG can be set up in the framework. We will have descriptions of c-structure, descriptions of f-structure, and semantics. The di®erence between de¯ning and constraining information will be explained in terms of entailment, and requirements on long-distance paths in f- structure will be explained in terms of entailment in the presence of a simple set of axioms. 1 Introduction In this paper I want to discuss a version of Lexical-Functional Grammar (LFG) that is also a version of Categorial Grammar (CG). -
The Categorial Fine-Structure of Natural Language
1 The categorial fine-structure of natural language Johan van Benthem, Amsterdam & Stanford, March 2003 Abstract Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/ argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light example-based manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characte- ristic semantic structures in natural language, (b) coexistence of the original type-theoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the total architecture of natural language, which involves mixtures of interpretation and inference. 1 From Montague Grammar to Categorial Grammar Logic and linguistics have had lively connections from Antiquity right until today (GAMUT 1991). A recurrent theme in this history is the categorial structure of language and ontology, from Aristotle's grammatical categories to Russell's theory of types in the foundations of mathematics. Further bridges were thrown as logic and linguistics developed, with Lambek 1958 as a major advance in sophistication, many years ahead of its time. Large-scale logical analysis of natural language really took off around 1970, thanks to Montague's work (Montague 1975, Partee 1997). This system connects linguistic structure and logical semantics in the following architecture. The pivotal deep structure are syntax trees formed by grammatical construction rules. -
Chapter 3 Language Analysis and Understanding
Chapter 3 Language Analysis and Understanding 3.1 Overview a b Annie Zaenen & Hans Uszkoreit a Rank Xerox ResearchCentre, Grenoble, France b Deutsches Forschungszentrum fur Kunstlic he Intelligenz and Universitat des Saarlandes, Saarbruc ken, Germany We understand larger textual units bycombining our understanding of smaller ones. The main aim of linguistic theory is to showhow these larger units of meaning arise out of the combination of the smaller ones. This is mo deled by means of a grammar. Computational linguistics then tries to implement this pro cess in an ecientway.Itis traditional to sub divide the task into syntax and semantics, where syntax describ es how the di erent formal elements of a textual unit, most often the sentence, can b e combined and semantics describ es how the interpretation is calculated. In most language technology applications the enco ded linguistic knowledge, i.e., the grammar, is separated from the pro cessing comp onents. The grammar consists of a lexicon, and rules that syntactically and semantically combine words and phrases into larger phrases and sentences. A variety of representation languages have b een develop ed for the enco ding of linguistic knowledge. Some of these languages are more geared towards conformity with formal linguistic theories, others are designed to facilitate certain pro cessing mo dels or sp ecialized applications. Several language technology pro ducts that are on the market to day employ annotated 109 110 Chapter 3: Language Analysis and Understanding phrase-structure grammars, grammars with several hundreds or thousands of rules describing di erent phrase typ es. Each of these rules is annotated by features and sometimes also by expressions in a programming language.