Showing papers in "Grammars in 2000"

Context-Free Recognition with Weighted Automata

Abstract: We introduce the definition of language recognition with weighted automata, a generalization of the classical definition of recognition with unweighted acceptors. We show that, with our definition of recognition, weighted automata can be used to recognize a class of languages that strictly includes regular languages. The class of languages accepted depends on the weight set which has the algebraic structure of a semiring. We give a generic linear time algorithm for recognition with weighted automata and describe examples with various weight sets illustrating the recognition of several classes of context-free languages. We prove, in particular, that the class of languages equivalent to the language of palindromes can be recognized by weighted automata over the (+,ċ)-semiring, and that the class of languages equivalent to the Dyck language of first order D 1 '*can be recognized by weighted automata over the real tropical semiring. We also prove that weighted automata over the real tropical semiring can be used to recognize regular expressions.

A Cubic Time Extension of Context-Free Grammars

Abstract: Context-free grammars and cubic parse time are so related in people's minds that they often think that parsing any extension of context-free grammars must need some extra time. Of course, this is not necessarily true and this paper presents a generalization of context-free grammars which nonetheless still has a cubic parse time complexity. This extension, which defines a subclass of context-sensitive languages, has both a theoretical and a practical interest. The class of languages defined by these grammars is closed under both intersection and complement (in fact this class contains both the intersection and the complement of context-free languages). Moreover, these languages belong to an extension of mildly context-sensitive languages in which the constant growth property is relaxed and which can thus potentially be used in natural language processing.

Descriptions of Cross-Serial Dependencies

Abstract: The main result of this paper is a description of cross-serial dependencies equivalently in terms of (a) regular tree languages (to express the recursive properties) and regular string languages (to establish the intended linguistic relations) and (b) transductions definable in monadic second-order (MSO) logic which are defined on a domain of finite trees that is characterized as the model set of a closed MSO formula. In fact, we shall not deal directly with the two types of regular language families and MSO definable structures, but shall instead consider implementation in the form of finite-state (tree) automata to emphasize the effective nature of our approach.

Relaxing Underspecified Semantic Representations for Reinterpretation

Abstract: Type and sort conflicts in semantics are usually resolved by a process of reinterpretation, which introduces an operator into the semantic representation. We elaborate on the foundations of a recent approach to reinterpretation within a framework for semantic underspecification. In this approach, relaxed underspecified semantic representations are inferred from the syntactic structure, leaving space for subsequent addition of reinterpretation operators. Unfortunately, a structural danger of overgeneration is inherent to the relaxation of underspecified semantic representations. We identify the problem and distinguish structural properties that avoid it. We furthermore develop techniques for proving these properties and apply them to prove the safety of relaxation in a prototypical syntax/semantics interface. In doing so, we present some novel properties of tree descriptions in the constraint language over lambda structures (CLLS).

Regulated Grammars under Leftmost Derivation

Abstract: In this paper, we investigate various concepts of leftmost derivation in grammars controlled by bicoloured digraphs, paying specific attention to their descriptive capacity. This approach allows us to unify the presentation of known results regarding especially programmed and matrix grammars, and to obtain new results concerning grammars with regular control, and periodically time-variant grammars. Moreover, we consider leftmost derivations in grammars with (regular) context conditions.

Monotonic C-Command: A New Perspective on Tree Adjoining Grammar

Abstract: In this paper we argue for a reconceptualization of the Tree Adjoining Grammar (TAG) formalism, in which the elementary structures are collections of c-command relations, and the combinatory operation is substitution. We show how the formalism we sketch resolves a number of problems for TAG that have been identified in the literature. Additionally, we demonstrate that our proposal is preferable to other previously proposed extensions to TAG, for example D-tree grammars (Rambow et al., 1995), in that it preserves many of the linguistically desirable aspects of TAG's restrictiveness, specifically concerning the derivation of locality constraints on unbounded dependencies.

On the Power of Reading the Whole Infinite Input Tape

Abstract: Finite devices accepting infinite strings are the topic of several papers (see the recent surveys [4], [8] or [10], [11]). Most of these papers deal with finite automata. Thus finite automata as devices accepting infinite strings are wellunderstood. The situation is a little bit more involved if one considers more complicated accepting devices like, e.g., pushdown automata or Turing machines.

Tabulation of Automata for Tree-Adjoining Languages

Abstract: We propose a modular design of tabular parsing algorithms for tree- adjoining languages. The modularity is made possible by a separation of the parsing strategy from the mechanism of tabulation. The parsing strategy is expressed in terms of the construction of a nondeterministic automaton from a grammar; three distinct types of automaton will be discussed. The mechanism of tabulation leads to the simulation of these nondeterministic automata in polynomial time, independent of the parsing strategy. The proposed application of this work is the design of efficient parsing algorithms for tree-adjoining grammars and related formalisms.

The Algebraic Semantics of Interrogative NPs

Abstract: We suggest a new semantic interpretation of interrogative NPs, based on a novel algebraic theory of the semantics of questions. We discuss the role of interrogative NPs in compositionally deriving the semantics of wh-questions, examine the coordination of interrogative NPs, and apply notions from generalized quantifier theory to their interpretation.

Combining Contextual Grammars and Tree Adjoining Grammars

Abstract: In this paper, we introduce grammar formalisms called multi-bracketed contextual and multi-bracketed contextual rewriting grammars. These formalisms possess an induced Dyck-structure to control the derivation process and to provide phrase-structure trees. The generative capacity of these classes is compared to Chomsky grammars and to tree adjoining grammars with and without local constraints. It will be shown that multi-bracketed contextual rewriting grammars cover the basic natural language constructions duplication, multiple agreement and cross-serial dependencies.

Proof-Nets, Hybrid Logics and Minimalist Representations

Abstract: In this paper, we aim at giving a logical account of the representationalist view of minimalist grammars by referring to the notion of Proof-Net in Linear Logic. We propose, at the same time, a hybrid logic which mixes one logic (Lambek calculus) for building up elementary proofs and another one for combining the proofs so obtained. Because the first logic is non-commutative and the second one is commutative, this brings us a way to combine commutativity and non-commutativity in the same framework. The dynamic of cut-elimination in proof-nets is used to formalise the move-operation. Otherwise, we advocate a proof-net formalism which allows us to consider formulae as nodes to which it is possible to assign weights which determine the final phonological interpretation.

Eventualities in Time

Abstract: This paper addresses the general question of how eventualities should be localized in time. The answer given here is mainly inspired by the model theory of Discourse Representation Theory (DRT) as presented in Kamp and Reyle (1993). We show that there is a mathematical problem concerning the localization function used in that book. And we propose a remedy for this problem. The general picture that emerges should be interesting not only for DRT but for other theories using an eventuality-based semantics as well.

The Algebraic Structure of Transitive Closure and its Application to Attributed Type Signatures

Abstract: This paper identifies a misconception about the algebraic structure underlying the view of transitive closure as a matrix multiplication problem. This is the mathematical basis of the technique that has been used for the efficient compilation of partially ordered sets of objects or types in programming languages for the past ten years. It also shows that the correct structure, a closed semi-ring, can also be extended to objects or type signatures that are augmented with attributes, constraints on the multiple inheritance of those attributes, and/or constraints on what types of values the attributes can take. As a specific example in the realm of linguistic knowledge representation, it is shown that every operation necessary for computing the closure of attributed type signature specifications in the logic of typed feature structures (Carpenter, 1992), the logical underpinning of the linguistic theory, Head-driven Phrase Structure Grammar (Pollard and Sag, 1987, 1994), can be reduced to matrix arithmetic using this construction. Other practical consequences of using the correct structure, such as the algorithmic complexity of multiplication and closure operations, are also discussed.

Uniquely Parsable Unification Grammars and Their Parser Implemented in Prolog

Abstract: A uniquely parsable grammar (UPG) introduced by Morita and coworkers is a formal grammar with a restricted type of rewriting rules, where parsing can be performed without backtracking. By extending a UPG, we introduce a uniquely parsable unification grammar (UPUG), and we investigate its applicability to parsing. A unification grammar (UG) is a system such that a sequence of terms is rewritten by a set of rules, and the rewriting process accompanies unification of terms as in Prolog. We first define a general framework of a UG and then give a UPUG-condition so that it has the property of unique parsability. Since the class of UPGs is a subclass of UPUGs and is known to be universal in language generating ability, the class of UPUGs is also universal. We then show a simple parsing method for UPUGs. Based on it, we give a Prolog implementation of a parser which will be useful for natural language analysis and other applications.

Parallel Communicating Grammar Systems As Language Analyzers

Abstract: Parallel communicating grammar systems consist of several grammars, and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such grammar systems with context-free productions. In accepting parallel communicating grammar systems, rules of the form α→A with a word α and a nonterminal A are applied as in the generating case, and the language consists of all terminal words which can derive the axiom. We consider the usual variant and a restricted variant of accepting parallel communicating grammar systems and prove that all types of these accepting grammar systems characterize the family of recursively enumerable languages if the usual variant is considered, and that of context-free languages if the restricted one is used. The first result also holds if λ-rules are forbidden. Moreover, we study analyzing parallel communicating grammar systems the derivations of which perform the generating counterparts backwards. This requires a modification of the concept of generating derivation yielding to strong-returning parallel communicating grammar systems which also generate the family of recursively enumerable languages.

Context-Sensitive Node Admissibility

Abstract: McCawley introduced the notion of `node admissibility conditions' as a way of studying the duality between generation and analysis, especially for context-free grammars. Subsequently, Peters and Ritchie formalized a `reasonable' generalization of context-free node admissibility for context-sensitive analysis and then proved that any language analyzable by a set of such context-sensitive node admissibility conditions is a context-free language. In this paper, I propose a stronger notion of context-sensitive node admissibility, in which local contextual dependencies are overtly represented and subject to a global consistency condition – a condition motivated by the relations among the elements in the frontier of a tree rewriting system for context-sensitive grammars. I show that this notion is adequate for context-sensitive grammars in the sense that a language is analyzable relative to this stronger notion if and only if it is generated by a context-sensitive grammar.

'Leenwoordfonologie' in het Esperanto

Abstract: It is well-known that loanwords show a specialised phonological behaviour in many (and probably all) languages of the world. A good theory of phonology should be able to deal with such phenomena. Within generative grammar, several theories have been developed to account for them. This paper gives evidence from Esperanto for an approach based on Ito and Mester's (1995) constraint-based theory of strata, Esperanto is a special type of language, among other things because almost all words in it are loanwords in some sense (i.e. borrowed from other languages). Still, it can be shown that some words behave differently from others even in this very unusual type of system: these are infrequent, learned words. Because in an Optimality-Theoretic grammar, the technical methodology to deal with 'loanwords' and very formal speech is practically the same, this theory can straightforwardly account for the special phonology of loanwords in Esperanto