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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 98 (23 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...
Multimodal Linguistic Inference
, 1995
"... In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives =; ffl; n, together with a package of structural postulates characterizing the resourc ..."
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Cited by 50 (8 self)
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In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives =; ffl; n, together with a package of structural postulates characterizing the resource management properties of the ffl connective. Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get a Kripke style interpretation in terms of a single ternary accessibility relation modeling the notion of linguistic composition for each individual system. The simple systems each have their virtues in linguistic analysis. But none of them in isolation provides a basis for a full theory of grammar. In the second part of the paper, we consider two types of mixed Lambek systems. The first type is obtained by combining a number of unimodal systems into one multimodal logic. The...
Structural Control
 SPECIFYING SYNTACTIC STRUCTURES, PATRICK BLACKBURN, MAARTEN DE RIJKE (EDS.)
, 1988
"... In this paper we study Lambek systems as grammar logics: logics for reasoning about structured linguistic resources. The structural parameters of precedence, dominance and dependency generate a cube of resourcesensitive categorial type logics. From the pure logic of residuation NL, one obtains L, N ..."
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Cited by 45 (9 self)
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In this paper we study Lambek systems as grammar logics: logics for reasoning about structured linguistic resources. The structural parameters of precedence, dominance and dependency generate a cube of resourcesensitive categorial type logics. From the pure logic of residuation NL, one obtains L, NLP and LP in terms of Associativity, Commutativity, and their combination. Each of these systems has a dependency variant, where the product is split up into a leftheaded and a rightheaded version. We develop a theory of systematic communication between these systems. The communication is twoway: we show how one can fully recover the structural discrimination of a weaker logic from within a system with a more liberal resource management regime, and how one can reintroduce the structural flexibility of a stronger logic within a system with a more articulate notion of structuresensitivity. In executing this programme we follow the standard logical agenda: the categorial formula language is enriched with extra control operators, socalled structural modalities, and on the basis of these control operators, we prove embedding theorems for the two directions of substructural communication. But our results differ from the Linear Logic style of embedding with S4like modalities in that we realize the communication in both directions in terms of a
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 41 (10 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
Continuation semantics for the Lambek–Grishin calculus
 INFORMATION AND COMPUTATION
, 2010
"... ..."
On the semantic readings of proofnets
 Proceedings of formal Grammar
, 1996
"... A la mémoire de ..."
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Generalized Quantifiers in Declarative and Interrogative Sentences
 Journal of Language and Computation
, 2000
"... In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discou ..."
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Cited by 15 (2 self)
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In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discourse level comes into play for our treatment of questions. Our formalization uses a type logic sensitive to both the syntactic and semantic properties of natural language. We will show how an account of the linguistic data follows naturally from the logical relations inherent in the type logic.
The Dual Analysis of Adjuncts/Complements in Categorial Grammar
"... The distinction between COMPLEMENTS and ADJUNCTS has a long tradition in grammatical theory, and it is also included in some way or other in most current formal linguistic theories. But it is a highly vexed distinction for several reasons, one of which is that no diagnostic criteria have emerge ..."
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Cited by 12 (0 self)
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The distinction between COMPLEMENTS and ADJUNCTS has a long tradition in grammatical theory, and it is also included in some way or other in most current formal linguistic theories. But it is a highly vexed distinction for several reasons, one of which is that no diagnostic criteria have emerged that will reliably distinguish adjuncts from complements in all cases  too many examples seem to fall into the crack between ...
Model Theoretic Syntax
 The Glot International State of the Article Book 1, Studies in Generative Grammar 48, Mouton de Gruyter
, 1998
"... this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) gramm ..."
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Cited by 11 (1 self)
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this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) grammars, in the sense that distinctions between the different tree logics reduce to apparently superficial distinctions in how much memory allocation is hidden in the logic. The problem which researchers set themselves was not just breaking the context free barrier but remaining decidable in the process. This is a very difficult problem, and it must be admitted right off that it is somewhat artificial in that there is no a priori reason to suppose that natural languages can be described in a decidable logic. The arguments on either side are something like the following. First, the rather slight increases in computational complexity required to get the "mildly context sensitive" languages do suggest that this might be possible. The hunch here would be that the qualities that characterize the mildly context sensitive languages (polynomial parsability, constant growth property) as being like the contextfree languages are going to turn out to be reflections of decidability. The problems must not be underestimated, however! It is well known that the monadic second order logic of trees is one of the most powerful decidable logics known. It seems unlikely that any primitive relations can be added to the repertoire of tree description primitives that we have already seen, without making the logic undecidable. Many attempts have been made within logic and all have failed. So it is equally tempting to conjecture that the contextfree boundary coincides in some deep sense with the bounda...