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Generation and Synchronous TreeAdjoining Grammars
, 1990
"... Treeadjoining grammars (TAG) have been proposed as a formalism for generation based on the intuition that the extended domain of syntactic locality that TAGs provide should aid in localizing semantic dependencies as well, in turn serving as an aid to generation from semantic representations. We dem ..."
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Cited by 635 (39 self)
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Treeadjoining grammars (TAG) have been proposed as a formalism for generation based on the intuition that the extended domain of syntactic locality that TAGs provide should aid in localizing semantic dependencies as well, in turn serving as an aid to generation from semantic representations. We demonstrate that this intuition can be made concrete by using the formalism of synchronous treeadjoining grammars. The use of synchronous TAGs for generation provides solutions to several problems with previous approaches to TAG generation. Furthermore, the semantic monotonicity requirement previously advocated for generation gram mars as a computational aid is seen to be an inherent property of synchronous TAGs.
Logic Programming in a Fragment of Intuitionistic Linear Logic
"... When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses. Attempting to prove a goal of the form D ⊃ G from the context (set of formulas) Γ leads to an attempt to prove the goal G in the extended context Γ ..."
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Cited by 306 (40 self)
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When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses. Attempting to prove a goal of the form D ⊃ G from the context (set of formulas) Γ leads to an attempt to prove the goal G in the extended context Γ ∪ {D}. Thus during the bottomup search for a cutfree proof contexts, represented as the lefthand side of intuitionistic sequents, grow as stacks. While such an intuitionistic notion of context provides for elegant specifications of many computations, contexts can be made more expressive and flexible if they are based on linear logic. After presenting two equivalent formulations of a fragment of linear logic, we show that the fragment has a goaldirected interpretation, thereby partially justifying calling it a logic programming language. Logic programs based on the intuitionistic theory of hereditary Harrop formulas can be modularly embedded into this linear logic setting. Programming examples taken from theorem proving, natural language parsing, and data base programming are presented: each example requires a linear, rather than intuitionistic, notion of context to be modeled adequately. An interpreter for this logic programming language must address the problem of splitting contexts; that is, when attempting to prove a multiplicative conjunction (tensor), say G1 ⊗ G2, from the context ∆, the latter must be split into disjoint contexts ∆1 and ∆2 for which G1 follows from ∆1 and G2 follows from ∆2. Since there is an exponential number of such splits, it is important to delay the choice of a split as much as possible. A mechanism for the lazy splitting of contexts is presented based on viewing proof search as a process that takes a context, consumes part of it, and returns the rest (to be consumed elsewhere). In addition, we use collections of Kripke interpretations indexed by a commutative monoid to provide models for this logic programming language and show that logic programs admit a canonical model.
Categorial Type Logics
 Handbook of Logic and Language
, 1997
"... Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource mana ..."
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Cited by 239 (5 self)
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Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntaxsemantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation
Principles and implementation of deductive parsing
 JOURNAL OF LOGIC PROGRAMMING
, 1995
"... We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generaliz ..."
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Cited by 165 (5 self)
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We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definiteclause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of treeadjoining grammars, categorial grammars, and lexicalized contextfree grammars.
Parsing Strategies with 'Lexicalized' Grammars: Application to Tree Adjoining Grammars
 IN PROCEEDINGS OF THE 12 TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL LINGUISTICS (COLING'88
, 1988
"... In this paper we present a general parsing strategy that arose from the development of an Earicytype parsing algorithm for TAGs (Schabes and Joshi 1988) and from recent linguistic work in TAGs (Abeille 1988). In our approach ..."
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Cited by 115 (16 self)
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In this paper we present a general parsing strategy that arose from the development of an Earicytype parsing algorithm for TAGs (Schabes and Joshi 1988) and from recent linguistic work in TAGs (Abeille 1988). In our approach
Information Structure and the SyntaxPhonology Interface
, 1998
"... The paper proposes a theory relating syntax, semantics, and intonational prosody, and covering a wide range of English intonational tunes and their semantic interpretation in terms of focus and information structure. The theory is based on a version of combinatory categorial grammar which directly p ..."
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Cited by 111 (5 self)
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The paper proposes a theory relating syntax, semantics, and intonational prosody, and covering a wide range of English intonational tunes and their semantic interpretation in terms of focus and information structure. The theory is based on a version of combinatory categorial grammar which directly pairs phonological and logical forms without intermediary representational levels.
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
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Cited by 90 (17 self)
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
A system of interaction and structure
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2004
"... This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, call ..."
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Cited by 87 (15 self)
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This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new topdown symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.
Combinators and Grammars
 Categorial Grammars and Natural Language Structures
, 1988
"... The term Categorial Grammar (CG) names a group of theories of natural language syntax and semantics in which the main responsibility for defining syntactic form is borne by the lexicon. CG is therefore one of the oldest and purest examples of a class of “lexicalized ” theories of grammar which also ..."
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Cited by 85 (3 self)
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The term Categorial Grammar (CG) names a group of theories of natural language syntax and semantics in which the main responsibility for defining syntactic form is borne by the lexicon. CG is therefore one of the oldest and purest examples of a class of “lexicalized ” theories of grammar which also includes HPSG, LFG, TAG, Montague Grammar, Relational Grammar and certain recent versions of the Chomskean theory. The various modern versions of CG are characterized by a much freer notion of derivational syntactic structure than is assumed under most other formal or generative theories of grammar. All forms of CG also follow Montague 1974 in sharing a strong commitment to the Principle of Compositionality—that is to the assumption that syntax and interpretation are homomorphically related, and may be derived in tandem. Significant contributions have been made by Categorial Grammarians to the study of semantics, syntax, morphology, intonational phonology, computational linguistics and human sentence processing. Since the problem of formalizing the grammar of natural languages was first defined in its modern form in the 1950’s, there have been two styles. Chomsky 1957 and much subsequent work in generative grammar begins by capturing the basic facts of English constituent order exemplified in (1) in a Contextfree Phrase Structure Grammar (CFPSG) or system of rewrite rules or “productions ” like (2), which have their origin in early work in recursion theory by Post, among others.
Grammatical Framework: A TypeTheoretical Grammar Formalism
, 2003
"... Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for lineariz ..."
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Cited by 72 (19 self)
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Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate runtime errors in language processing. In the same way as an LF, GF uses...