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22
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...
Proof nets for the Lambekcalculus — an overview
 Proceedings of the Third Roma Workshop ”Proofs and Linguistic Categories
, 1996
"... 1 Introduction: the interest of proof nets for categorial grammar There are both linguistic and mathematical reasons for studying proof nets the perspective of categorial grammar. It is now well known that the Lambek calculus corresponds to intuitionnistic noncommutative multiplicative linear logic ..."
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Cited by 16 (2 self)
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1 Introduction: the interest of proof nets for categorial grammar There are both linguistic and mathematical reasons for studying proof nets the perspective of categorial grammar. It is now well known that the Lambek calculus corresponds to intuitionnistic noncommutative multiplicative linear logic — with no empty antecedent, to be absolutely precise. As natural deduction underlines the constructive contents of intuitionistic
Meaning Helps Learning Syntax
 in [ICGI 98
, 1998
"... . In this paper, we propose a new framework for the computational learning of formal grammars with positive data. In this model, both syntactic and semantic information are taken into account, which seems cognitively relevant for the modeling of natural language learning. The syntactic formalism use ..."
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Cited by 10 (2 self)
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. In this paper, we propose a new framework for the computational learning of formal grammars with positive data. In this model, both syntactic and semantic information are taken into account, which seems cognitively relevant for the modeling of natural language learning. The syntactic formalism used is the one of Lambek categorial grammars and meaning is represented with logical formulas. The principle of compositionality is admitted and defined as an isomorphism applying to trees and allowing to automatically translate sentences into their semantic representation(s). Simple simulations of a learning algorithm are extensively developed and discussed. 1 Introduction Natural language learning seems, from a formal point of view, an enigma. As a matter of fact, every human being, given nearly exclusively positive examples ([25]), is able at the age of about five to master his/her mother tongue. Though every natural language has at least the power of contextfree grammars ([22]), this cla...
Lambek Calculus with Nonlogical Axioms
 Language and Grammar, Studies in Mathematical Linguistics and Natural Language
, 2002
"... We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions of Associa ..."
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Cited by 5 (3 self)
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We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions of Associative Lambek Calculus generate all recursively enumerable languages; here we give a new proof of this fact. We also obtain similar results for systems with permutation and n ary operations.
Lambek calculus proofs and tree automata
 Logical Aspects of Computational Linguistics Third International Conference, LACL '98, Selected Papers, volume 2014 of Lecture Notes in Artificial Intelligence
, 2001
"... Abstract. We investigate natural deduction proofs of the Lambek calculus from the point of view of tree automata. The main result is that the set of proofs of the Lambek calculus cannot be accepted by a finite tree automaton. The proof is extended to cover the proofs used by grammars based on the La ..."
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Cited by 5 (1 self)
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Abstract. We investigate natural deduction proofs of the Lambek calculus from the point of view of tree automata. The main result is that the set of proofs of the Lambek calculus cannot be accepted by a finite tree automaton. The proof is extended to cover the proofs used by grammars based on the Lambek calculus, which typically use only a subset of the set of all proofs. While Lambek grammars can assign regular tree languages as structural descriptions, there exist Lambek grammars that assign nonregular structural descriptions, both when considering normal and nonnormal proof trees. Combining the results of Pentus (1993) and Thatcher (1967), we can conclude that Lambek grammars, although generating only contextfree languages, can extend the strong generative capacity of contextfree grammars. Furthermore, we show that structural descriptions that disregard the use of introduction rules cannot be used for a compositional semantics following the CurryHoward isomorphism. 1
Relationship Between Strong And Weak Generative Power Of Formal Systems
 In Proceedings of the Fifth International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+5
, 2000
"... The relationship between strong and weak generative powers of formal systems is explored, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We examine a whole range of old and new results from this perspective. H ..."
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Cited by 4 (0 self)
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The relationship between strong and weak generative powers of formal systems is explored, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We examine a whole range of old and new results from this perspective. However, the main goal of this paper is to investigate the strong generative power of Lambek categorial grammars in the context of crossing dependencies, in view of the recent work of Tiede (1998).
A description of the nonsequential execution of Petrinets in partially commutative linear logic
, 2000
"... We encode the execution of Petri nets in Partially Commutative Linear Logic, an intuitionistic logic introduced by Ph. de Groote which contains both commutative and non commutative connectives. We are thus able to faithfully represent the concurrent firing of Petri nets as long as it can be depicted ..."
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Cited by 4 (3 self)
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We encode the execution of Petri nets in Partially Commutative Linear Logic, an intuitionistic logic introduced by Ph. de Groote which contains both commutative and non commutative connectives. We are thus able to faithfully represent the concurrent firing of Petri nets as long as it can be depicted by a seriesparallel order. This coding is inspired from the description of contextfree languages by Lambek grammars.
Pregroup Grammars and Contextfree Grammars
"... Pregroup grammars were introduced by Lambek [20] as a new formalism of typelogical grammars. They are weakly equivalent to contextfree grammars ..."
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Cited by 3 (1 self)
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Pregroup grammars were introduced by Lambek [20] as a new formalism of typelogical grammars. They are weakly equivalent to contextfree grammars
kValued NonAssociative Lambek Grammars Are Learnable From FunctionArgument Structures
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2003
"... This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and kvalued nonassociative Lambek grammars are learnable from functionargument structured sentences. In fact, functionargument structures are natural syntactical decompositions of sentences in sub ..."
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Cited by 3 (1 self)
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This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and kvalued nonassociative Lambek grammars are learnable from functionargument structured sentences. In fact, functionargument structures are natural syntactical decompositions of sentences in subcomponents with the indication of the head of each subcomponent. This result is