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## Resource logics and minimalist grammars (2002)

Venue: | Proceedings ESSLLI’99 workshop (Special issue Language and Computation |

Citations: | 5 - 0 self |

### Citations

2827 |
The Minimalist Program.
- Chomsky
- 1995
(Show Context)
Citation Context ...tion of the generative mechanisms is taken to an extreme in theories of “government and binding,” and even more so in certain recent “minimalist” proposals of the transformational tradition in syntax =-=[14]-=-. In these recent minimalist proposals, two other assumptions of the categorial tradition are adopted: first, the generative mechanisms are assumed to be simple and universal (i.e. all language variat... |

1583 | Head-driven phrase structure grammar - Pollard, Sag - 1994 |

1120 |
Language Identification in the Limit.
- Gold
- 1967
(Show Context)
Citation Context ... extreme nativism is often assumed. It could be that, not only do human languages have special properties, but the range of real grammatical variation is finitely bounded. The classic results of Gold =-=[36]-=- guarantee learnability in the limit from examples (“positive texts”) in this idealized situation, but getting to a more realistic learner is surprisingly interesting even here. The finiteness assumpt... |

774 | Synchronous tree-adjoining grammars. - Shieber, Schabes - 1990 |

744 |
Minimalist Inquiries: The Framework,
- Chomsky
- 2000
(Show Context)
Citation Context ...itions.” Lexical features may be strong or weak, and they may be interpretable or non-interpretable, with different consequences for the configurations in which they are “checked.” In the recent work =-=[15]-=-, Chomsky attempts to locate the strong/weak distinction in PF/LF interface requirements, and he assumes that “covert” and “overt” movement operations apply in the same cycle. In a series of papers St... |

573 | The mathematics of sentence structure’.
- Lambek
- 1958
(Show Context)
Citation Context ...mar of Ajdukiewicz and Bar-Hillel, we obtain a kind of propositional calculus with a directionally sensitive implication, where the structural rules (permutation, contraction, thinning) are suspended =-=[50]-=-. Γ[B,A] ⊢ ∆ permute Γ[A, B] ⊢ ∆ Γ ⊢ ∆ thin Γ,A⊢ ∆ Γ[A, A] ⊢ ∆ contract Γ[A] ⊢ ∆ And in linear logic [30, 31], substructural logics lacking the structural rules have received systematic study. In thes... |

529 | Learnability in optimality theory.
- Tesar, Smolensky
- 2000
(Show Context)
Citation Context ...uages, affixes are pronounced at the ends of words, but some languages have principles that block this placement with the result that the affix appears near the edge of the word. Prince and Smolensky =-=[74]-=- use the example of the Tagalog prefix um- which appears as a prefix except where its consonant would be syllabified as a coda: um+iyák ⇒ u.mi.yák ‘cry’ um+káin ⇒ ku.má.in ‘eat’ um+gradwet ⇒ gru.mad.w... |

507 |
Three models for the description of language
- Chomsky
- 1956
(Show Context)
Citation Context ...gorial grammar is, in that the resources of rewrite grammars (i.e. the categories) are simple atoms. Context free grammars and simpler systems are inappropriate for the description of human languages =-=[13]-=-, and rather than simply ascending the Chomsky hierarchy to more expressive rewrite grammars, linguists proposed special formalisms: transformational grammars, tree adjoining grammars, and later, unif... |

317 |
Prosodic morphology
- McCarthy, Prince
- 1999
(Show Context)
Citation Context ...often be impossible to satisfy all constraints, but the structures that do the best, the “optimal” structures, are the grammatical ones. This kind of account has been extended to templatic morphology =-=[59, 16, 7]-=-, and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) [28, 27,... |

297 | Categorical type Logics’, In
- Moortgat
- 1997
(Show Context)
Citation Context ...ducing hypothetical reasoning allows grammars that are not only mathematically more natural – “complete” in a certain sense – but also formally simpler and semantically natural, has been advocated by =-=[63, 62, 65]-=- and others, and continues to receive serious attention. 2 In a logic with an implication →, a deduction theorem has the form: Γ[A] ⊢ B iff Γ ⊢ A → B. 3s3 Background: some brief remarks 3.1 Resource l... |

194 | Linear logic: Its syntax and semantics’,
- Girard
- 1995
(Show Context)
Citation Context ...ive implication, where the structural rules (permutation, contraction, thinning) are suspended [50]. Γ[B,A] ⊢ ∆ permute Γ[A, B] ⊢ ∆ Γ ⊢ ∆ thin Γ,A⊢ ∆ Γ[A, A] ⊢ ∆ contract Γ[A] ⊢ ∆ And in linear logic =-=[30, 31]-=-, substructural logics lacking the structural rules have received systematic study. In these logics, the constituents of an expression act like resources: they may be consumed and produced in the cour... |

184 |
Overregularization in Language Acquisition.
- Marcus, Pinker, et al.
- 1992
(Show Context)
Citation Context ..., but this work moves in the right direction in abandoning the assumption of a finite range of linguistic variation and in using semantic cues — a restricted implementation of principles advocated in =-=[71, 35]-=-. All of these learning models rely on the categorial unification strategy of [11]; unification appears to be quite a general tool for grammatical inference [68]. 5 The claim that human languages are ... |

158 |
Characterizing Mildly Context-Sensitive Grammar Formalisms.
- Weir
- 1988
(Show Context)
Citation Context ...the more useful. For example, Michaelis [60] has shown that the languages definable in Stabler’s minimalist grammars MGs are included in the class of languages defined by context free rewrite systems =-=[99]-=- and by multiple context free grammars MCFGs [84].5 These languages are known to be efficiently recognizable. Seki et al. provide a simple chart-based parsing algorithm, and a method with improved wor... |

140 |
On the Calculus of Syntactic Types",
- Lambek
- 1961
(Show Context)
Citation Context ...n theorem has the form: Γ[A] ⊢ B iff Γ ⊢ A → B. 3s3 Background: some brief remarks 3.1 Resource logics The non-associative and associative Lambek calculi respectively introduced in 1958 [50] and 1961 =-=[51]-=- by Joachim Lambek can be given in the following forms: A ⊢ A axiom Γ[A] ⊢ C ∆ ⊢ B /L Γ[(A/B, ∆)] ⊢ C ∆ ⊢ B Γ[A] ⊢ C \L Γ[(∆,B\A)] ⊢ C Γ[A, B] ⊢ C Γ[(A • B)] ⊢ C Non-associative Lambek calculus, NL •L... |

136 | Speech recognition by composition of weighted finite automata.
- Pereira, Riley
- 1997
(Show Context)
Citation Context ...rphology that is interesting since it extends minimality-theory-like mechanisms to a domain where it is far from clear that the basic elements of resource logical approaches are up to the task. 7 Cf. =-=[52, 70]-=-. Adapting results from [98, 99], [84] shows that multiple context free grammars are closed under intersection with finite automata, and the construction is really quite simple. 15s7 Conclusion Severa... |

135 | Derivational minimalism.
- Stabler
- 1997
(Show Context)
Citation Context ...calculus (for instance the Lambek calculus) is for us totally similar. For instance, although they use a natural deduction presentation for simplicity 3 , the account of Stabler’s minimalist grammars =-=[86]-=- (introduced in the next section) in the plain Lambek calculus given by Lecomte and Retoré in [58] is clearly a by product of the study of proof-nets and their paths. Similarly the work of Joshi, Kuli... |

125 |
On multiple context-free grammars.
- Seki, Matsumara, et al.
- 1991
(Show Context)
Citation Context ...shown that the languages definable in Stabler’s minimalist grammars MGs are included in the class of languages defined by context free rewrite systems [99] and by multiple context free grammars MCFGs =-=[84]-=-. 5 These languages are known to be efficiently recognizable. Seki et al. provide a simple chartbased parsing algorithm, and a method with improved worst-case performance is provided by [67]. We do no... |

122 |
Towards a geometry of interaction,
- Girard
- 1989
(Show Context)
Citation Context ...ecific properties. Linear logic was a priori not designed for linguistic purposes, but for proof theoretical and computational reasons as explained in Girard’s original paper [30] and subsequent ones =-=[32, 31]-=-. In a sense, it is a way to combine the “constructive” behavior of intuitionistic logic and the symmetry of classical logic. The constructive aspect of intuitionistic logic can be seen for instance i... |

120 |
Knowledge of Meaning.
- Larson, Segal
- 1995
(Show Context)
Citation Context ...l human languages are definable by minimalist grammars. 5 Semantics in resource logics and minimalism Semantics is sometimes left out of consideration in transformational syntax (but see, e.g. Larson =-=[53]-=-, Heim and Kratzer [37], Szabolcsi [89]). Semantic proposals in the categorial tradition are explicit and natural, since they can be based on a Curry-Howard correspondence between derivations and sema... |

106 |
Quantales and (non-commutative) Linear Logic’,
- Yetter
- 1990
(Show Context)
Citation Context ...hich can be used for e.g. computing semantic recipes. The absence of structural rules enables the consideration of non-commutative restrictions of linear logic, first introduced by Abrusci and Yetter =-=[2, 100]-=-. For instance one can rediscover the Lambek calculus as being exactly intuitionistic multiplicative linear logic [2, 82, 49, 76]. Non-commutative linear logic proofs, i.e. parse structures, can be vi... |

102 |
Essays in logical semantics.
- Benthem
- 1986
(Show Context)
Citation Context ... in computational logic. The revival of interest in these calculi is mainly due to advances in logic. First van Benthem and Moortgat enriched them with modalities and used techniques from modal logic =-=[94, 96, 63]-=- and also [65] with a slightly different approach. Nevertheless the relation to other logics, in particular with intuitionistic logic and classical logic has only been clarified with the invention of ... |

98 |
Phase Semantics and Sequent Calculus for Pure Noncommutative Classical Linear Logic
- Abrusci
- 1991
(Show Context)
Citation Context ...hich can be used for e.g. computing semantic recipes. The absence of structural rules enables the consideration of non-commutative restrictions of linear logic, first introduced by Abrusci and Yetter =-=[2, 100]-=-. For instance one can rediscover the Lambek calculus as being exactly intuitionistic multiplicative linear logic [2, 82, 49, 76]. Non-commutative linear logic proofs, i.e. parse structures, can be vi... |

92 | Efficient generation in primitive optimality theory.
- Eisner
- 1997
(Show Context)
Citation Context ..., 16, 7], and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) =-=[28, 27, 8]-=-. For grammatical formalisms that allow intersection with finite automata, this kind of reasoning could be integrated with syntax by intersecting a finite transducer with the syntax 7 In this workshop... |

90 | Lexico-Logical Form: A radically minimalist theory. - BRODY - 1995 |

84 | Phonological derivation in Optimality Theory.
- Ellison
- 1994
(Show Context)
Citation Context ..., 16, 7], and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) =-=[28, 27, 8]-=-. For grammatical formalisms that allow intersection with finite automata, this kind of reasoning could be integrated with syntax by intersecting a finite transducer with the syntax 7 In this workshop... |

71 |
Resource Logics. Proof-Theoretical Investigations
- Roorda
- 1991
(Show Context)
Citation Context ...mutative restrictions of linear logic, first introduced by Abrusci and Yetter [2, 100]. For instance one can rediscover the Lambek calculus as being exactly intuitionistic multiplicative linear logic =-=[2, 82, 49, 76]-=-. Non-commutative linear logic proofs, i.e. parse structures, can be viewed as linear logic proofs, even when the proof is lifted to the corresponding semantical types. And using the embedding of intu... |

70 |
Categorial grammars determined from linguistic data by unification
- Buszkowski, Penn
- 1990
(Show Context)
Citation Context ...range of linguistic variation and in using semantic cues — a restricted implementation of principles advocated in [71, 35]. All of these learning models rely on the categorial unification strategy of =-=[11]-=-; unification appears to be quite a general tool for grammatical inference [68]. 5 The claim that human languages are definable by these grammars is challenged by Michaelis and Kracht 1996, on the bas... |

57 | Derivational minimalism is mildly context-sensitive.
- Michaelis
- 2001
(Show Context)
Citation Context ...al account of whatever computations enter into human language processing. In this respect, though, the traditional tools of formal language theory are still the more useful. 11sFor example, Michaelis =-=[60]-=- has shown that the languages definable in Stabler’s minimalist grammars MGs are included in the class of languages defined by context free rewrite systems [99] and by multiple context free grammars M... |

48 |
Language in action: categories, lambdas and dynamic logic
- Benthem
- 1991
(Show Context)
Citation Context ... in computational logic. The revival of interest in these calculi is mainly due to advances in logic. First van Benthem and Moortgat enriched them with modalities and used techniques from modal logic =-=[94, 96, 63]-=- and also [65] with a slightly different approach. Nevertheless the relation to other logics, in particular with intuitionistic logic and classical logic has only been clarified with the invention of ... |

45 | Structural control
- Kurtonina, Moortgat
- 1997
(Show Context)
Citation Context ... binary connectives and to other modalities. Such postulates enable a controlled used of structural properties (like associativity), and there exist faithful embeddings between this family of systems =-=[48]-=-. A pleasant linguistic property of MMCG is that the base logic can be viewed as the universal way for assembling constituents while the use of modalities in lexical entries and above all the postulat... |

44 | Recognition can be Harder than Parsing.
- Lang
- 1994
(Show Context)
Citation Context ...rphology that is interesting since it extends minimality-theory-like mechanisms to a domain where it is far from clear that the basic elements of resource logical approaches are up to the task. 7 Cf. =-=[52, 70]-=-. Adapting results from [98, 99], [84] shows that multiple context free grammars are closed under intersection with finite automata, and the construction is really quite simple. 15s7 Conclusion Severa... |

41 | Pomset logic: A non-commutative extension of classical linear logic
- Retoré
- 1997
(Show Context)
Citation Context ...or linguistic description. For instance one can have at the same time commutative and non-commutative connectives. The first way was to introduce a single non-commutative connective which is selfdual =-=[75, 77]-=-. The second way introduced by de Groote and subsequently enriched by Ruet, Abrusci, Demaille resembles the multimodal approach: one has at the same time the Lambek connectives and the commutative lin... |

40 |
Mathematical linguistics and proof theory
- Buszkowski
(Show Context)
Citation Context ...al semantics (bi-modules) for L. Furthermore the relation to rewrite grammar is by now rather clear [69, 92, 91]. (For more details on mathematical aspects the reader is referred to Buszkowski survey =-=[10]-=-.) Nevertheless these calculi remained far from other logics until the 1980’s, mainly because they are resource sensitive (lacking contraction and weakening) and also non-commutative. They are also in... |

33 | P.: Partially commutative linear logic: sequent calculus and phase semantics
- Groote
(Show Context)
Citation Context ...d the commutative linear connectives, with structural rules linking the two — nevertheless it is less powerful, because it is still decidable, and does not involve structural modalities or postulates =-=[24, 83, 6, 23]-=-. There also exists a classical calculus with a left and a right negation [2], with ways to introduce modalities enabling displacement [3], or more sophisticated behaviors. Although these systems have... |

33 | Remnant movement and complexity - Stabler - 1999 |

30 | Semilinearity as a syntactic invariant - Michaelis, Kracht - 1997 |

29 | Incremental processing and acceptability - Morrill - 2000 |

28 | Evaluation, implementation, and extension of Primitive Optimality Theory
- Albro
- 1998
(Show Context)
Citation Context ...often be impossible to satisfy all constraints, but the structures that do the best, the “optimal” structures, are the grammatical ones. This kind of account has been extended to templatic morphology =-=[59, 16, 7]-=-, and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) [28, 27,... |

26 |
Abrusci and Paul Ruet. Non-commutative logic I: The multiplicative fragment
- Michele
(Show Context)
Citation Context ...d the commutative linear connectives, with structural rules linking the two — nevertheless it is less powerful, because it is still decidable, and does not involve structural modalities or postulates =-=[24, 83, 6, 23]-=-. There also exists a classical calculus with a left and a right negation [2], with ways to introduce modalities enabling displacement [3], or more sophisticated behaviors. Although these systems have... |

26 |
Réseaux et Séquents Ordonnés. Thèse de Doctorat, spécialité mathématiques
- Retoré
- 1993
(Show Context)
Citation Context ...or linguistic description. For instance one can have at the same time commutative and non-commutative connectives. The first way was to introduce a single non-commutative connective which is selfdual =-=[75, 77]-=-. The second way introduced by de Groote and subsequently enriched by Ruet, Abrusci, Demaille resembles the multimodal approach: one has at the same time the Lambek connectives and the commutative lin... |

23 |
The invention of language by children: Environmental and biological influences on the acquisition of language.
- Gleitman, Newport
- 1995
(Show Context)
Citation Context ..., but this work moves in the right direction in abandoning the assumption of a finite range of linguistic variation and in using semantic cues — a restricted implementation of principles advocated in =-=[71, 35]-=-. All of these learning models rely on the categorial unification strategy of [11]; unification appears to be quite a general tool for grammatical inference [68]. 5 The claim that human languages are ... |

23 | Product-free Lambek calculus and context-free grammars
- Pentus
- 1997
(Show Context)
Citation Context ...d sub-formula property (which make parsing decidable) complete truth value semantics, and denotational semantics (bi-modules) for L. Furthermore the relation to rewrite grammar is by now rather clear =-=[69, 92, 91]-=-. (For more details on mathematical aspects the reader is referred to Buszkowski survey [10].) Nevertheless these calculi remained far from other logics until the 1980’s, mainly because they are resou... |

23 |
Logique non-commutative et programmation concurrente. Thése de doctorat, spécialité logique et fondements de l’informatique, Université Paris 7
- Ruet
- 1997
(Show Context)
Citation Context ...d the commutative linear connectives, with structural rules linking the two — nevertheless it is less powerful, because it is still decidable, and does not involve structural modalities or postulates =-=[24, 83, 6, 23]-=-. There also exists a classical calculus with a left and a right negation [2], with ways to introduce modalities enabling displacement [3], or more sophisticated behaviors. Although these systems have... |

20 |
The Principle of Minimal Compliance
- Richards
- 1998
(Show Context)
Citation Context ...censing of wh-elements in multiple-wh constructions has certain special properties: one dependency is involved in licensing another. In rather different sorts of proposals, Brody [9, §2] and Richards =-=[81]-=- agree with Kayne’s basic idea. Consider the following examples: 1. * whatj do you wonder who bought tj? 2. whoi ti wonders who bought whatj? 3. (a) whoi ti wonders who bought whatj? (b) (whatj)whoiti... |

19 | Proof nets and the complexity of processing center embedded constructions
- Johnson
- 1998
(Show Context)
Citation Context ...litics,...) andtoencode Tree-Adjoining Grammars[72]. The 6sproof nets may also reveal linguistically and psychologically significant properties of constructions. For example, using proof nets Johnson =-=[40]-=- obtained measures of the instantaneous complexity of center-embedded constructions, and this work has been pursued by Morrill [66] to catch other phenomena. It is a pity that linear logic enjoys the ... |

17 | Proof nets for the Lambek-calculus — an overview
- Lamarche, Retoré
- 1996
(Show Context)
Citation Context ...mutative restrictions of linear logic, first introduced by Abrusci and Yetter [2, 100]. For instance one can rediscover the Lambek calculus as being exactly intuitionistic multiplicative linear logic =-=[2, 82, 49, 76]-=-. Non-commutative linear logic proofs, i.e. parse structures, can be viewed as linear logic proofs, even when the proof is lifted to the corresponding semantical types. And using the embedding of intu... |

17 | Pomset logic as an alternative categorial grammar
- Lecomte, Retore
- 1995
(Show Context)
Citation Context ...ctives to be revealed, and this is already happening. One of the first uses was the use of the calculus of Pomset logic (linear logic plus a non-commutative self-dual connectives): Lecomte and Retoré =-=[56, 57]-=- defined a grammar which associates a partial proof-net (and not just a formula) with each lexical item. This way they are able to describe some phenomena which hitherto fell out of the scope of categ... |

17 |
Handsome proof-nets: perfect matchings and cographs
- Retoré
(Show Context)
Citation Context ...guistic applications, they may well be, since one often requires additional mechanisms. A great outcome of the linear logic already used in linguistics is its natural syntax, the so-called proof nets =-=[30, 31, 93, 5, 49, 76, 80]-=-. A proof-net represents a proof as a graph, which consists of two parts: the subformula tree of the formula it proves, plus some edges linking dual atoms called axioms. These axioms are the represent... |

15 |
Non-associative Lambek categorial grammar in polynomial time, Mathematical logic Quarterly 41
- Aarts, Trautwein
- 1995
(Show Context)
Citation Context ...ypotheses are even more structured than a total order: they are provided with a binary tree. This calculus enjoys the same properties as the Lambek calculus and is even decidable in polynomial time — =-=[1]-=- showed it for product free NL, and recently de Groote [25] extended the result to full NL. As the associative calculus is already too restrictive for linguistic purposes, this “base logic” is extende... |

15 |
Derivational and Representational Views of Minimalist Transformational Grammars
- Cornell
- 1999
(Show Context)
Citation Context ..., since they can be based on a Curry-Howard correspondence between derivations and semantic values. The implications of this idea for treatments of movement are rather carefully considered by Cornell =-=[21]-=- and Vermaat [97]. Vermaat argues that while movement can be handled syntactically in MMCG with structural postulates, we can get a natural semantic treatment by treating movement as involving the abs... |

14 | Controlling movement: Minimalism in a deductive perspective
- Vermaat
- 1999
(Show Context)
Citation Context ...source-logical settings as well as any other. The axioms proposed by Cornell [20] to realize movement implement the asymmetries of the transformational account, as do the axioms considered by Vermaat =-=[97]-=-, and we see similar asymmetries even in the less traditional proposals of Lecomte [55] and [57]. In these works, categorial grammar is a framework in which universals can be expressed, and it is natu... |

13 | The Turing-completeness of Multimodal Categorial Grammars - CARPENTER - 1995 |

13 |
The Antisymmetry of Syntax. Number 25 in Linguistic Inquiry Monographs
- Kayne
- 1994
(Show Context)
Citation Context ...ut differently, they handle tree structures, which are the standard way to depict parse structure. But it may as well be a property of linguistic interaction to never be symmetric. For instance Kayne =-=[47]-=- suggests such properties. Nevertheless, as is usually the case, richer structures enable the proof of results that would be ignored otherwise, as for example, in proving properties of natural numbers... |

13 |
Towards a Minimal Logic for Minimalist Grammars
- Lecomte, Retoré
- 1999
(Show Context)
Citation Context ... use a natural deduction presentation for simplicity 3 , the account of Stabler’s minimalist grammars [86] (introduced in the next section) in the plain Lambek calculus given by Lecomte and Retoré in =-=[58]-=- is clearly a by product of the study of proof-nets and their paths. Similarly the work of Joshi, Kulick, and Kurtonina [41, 42] on Partial Proof-Trees as building blocks of a categorial grammar, usin... |

11 |
Type-Logical Grammar: Categorial Logical of Signs
- Morrill
- 1994
(Show Context)
Citation Context ...ducing hypothetical reasoning allows grammars that are not only mathematically more natural – “complete” in a certain sense – but also formally simpler and semantically natural, has been advocated by =-=[63, 62, 65]-=- and others, and continues to receive serious attention. 2 In a logic with an implication →, a deduction theorem has the form: Γ[A] ⊢ B iff Γ ⊢ A → B. 3s3 Background: some brief remarks 3.1 Resource l... |

10 |
Calcul de Lambek et logique linéaire. Traitement Automatique des Langues 37(2
- Retoré
- 1996
(Show Context)
Citation Context ...mutative restrictions of linear logic, first introduced by Abrusci and Yetter [2, 100]. For instance one can rediscover the Lambek calculus as being exactly intuitionistic multiplicative linear logic =-=[2, 82, 49, 76]-=-. Non-commutative linear logic proofs, i.e. parse structures, can be viewed as linear logic proofs, even when the proof is lifted to the corresponding semantical types. And using the embedding of intu... |

10 | Meaning helps learning syntax
- Tellier
- 1998
(Show Context)
Citation Context ... understanding about what is possible in human languages, but the study the acquisition problem for finite sets of languages has led to some insights. The acquisition models of Kanazawa [45], Tellier =-=[90]-=-, Fulop [29] and others in the categorial tradition yield learnability results without the finiteness assumption, but they are idealized in other respects. Kanazawa establishes learnability of k-rigid... |

9 | On the logic and learning of language
- Fulop
- 2004
(Show Context)
Citation Context ...ng about what is possible in human languages, but the study the acquisition problem for finite sets of languages has led to some insights. The acquisition models of Kanazawa [45], Tellier [90], Fulop =-=[29]-=- and others in the categorial tradition yield learnability results without the finiteness assumption, but they are idealized in other respects. Kanazawa establishes learnability of k-rigid grammars fr... |

9 |
Deductive Systems and Grammars: Proofs as Grammatical Structures
- Tiede
- 1999
(Show Context)
Citation Context ...d sub-formula property (which make parsing decidable) complete truth value semantics, and denotational semantics (bi-modules) for L. Furthermore the relation to rewrite grammar is by now rather clear =-=[69, 92, 91]-=-. (For more details on mathematical aspects the reader is referred to Buszkowski survey [10].) Nevertheless these calculi remained far from other logics until the 1980’s, mainly because they are resou... |

8 | The architecture of the language faculty. Number 28 - Jackendoff - 1997 |

8 |
Grammatical inference as unification. Rapport de Recherche RR-3632, INRIA
- Nicolas
- 1999
(Show Context)
Citation Context ...ntation of principles advocated in [71, 35]. All of these learning models rely on the categorial unification strategy of [11]; unification appears to be quite a general tool for grammatical inference =-=[68]-=-. 5 The claim that human languages are definable by these grammars is challenged by Michaelis and Kracht 1996, on the basis of an argument that Old Georgian is not semilinear. 6 See [44] and [39]. 12s... |

7 | Three formal extensions to Primitive Optimality Theory
- Albro
- 1998
(Show Context)
Citation Context ..., 16, 7], and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) =-=[28, 27, 8]-=-. For grammatical formalisms that allow intersection with finite automata, this kind of reasoning could be integrated with syntax by intersecting a finite transducer with the syntax 7 In this workshop... |

7 |
Partial proof trees, resource sensitive logics and syntactic constraints
- Joshi, Kulick
- 1996
(Show Context)
Citation Context ...e next section) in the plain Lambek calculus given by Lecomte and Retoré in [58] is clearly a by product of the study of proof-nets and their paths. Similarly the work of Joshi, Kulick, and Kurtonina =-=[41, 42]-=- on Partial Proof-Trees as building blocks of a categorial grammar, using TAG-like operations, resemble construction in proof nets of [72, 57], although they also use natural deduction. 3.2 Minimalist... |

6 |
Categorial Investigations. Foris
- Moortgat
- 1988
(Show Context)
Citation Context ...ducing hypothetical reasoning allows grammars that are not only mathematically more natural – “complete” in a certain sense – but also formally simpler and semantically natural, has been advocated by =-=[63, 62, 65]-=- and others, and continues to receive serious attention. 2 In a logic with an implication →, a deduction theorem has the form: Γ[A] ⊢ B iff Γ ⊢ A → B. 3s3 Background: some brief remarks 3.1 Resource l... |

5 | A minimalist grammar for the copy language - Cornell - 1996 |

5 | Island effects in type logical approaches to the minimalist program
- Cornell
- 1998
(Show Context)
Citation Context ... 6.2 Asymmetries, chains and islands In most minimalist proposals, feature checking is asymmetric in the sense that the checking feature and the checked feature are not both deleted [14, 17]. Cornell =-=[22]-=- takes some first steps toward implementing analyses like these in a resource logical framework, but the need for these asymmetries and for the visibility of deleted elements might also signal that we... |

5 |
Learnable Classes of Categorial Grammmars
- Kanazawa
- 1998
(Show Context)
Citation Context ...rrent state of understanding about what is possible in human languages, but the study the acquisition problem for finite sets of languages has led to some insights. The acquisition models of Kanazawa =-=[45]-=-, Tellier [90], Fulop [29] and others in the categorial tradition yield learnability results without the finiteness assumption, but they are idealized in other respects. Kanazawa establishes learnabil... |

5 | Words as modules: a lexicalised grammar in the framework of linear logic proof nets
- Lecomte, Retore
- 1996
(Show Context)
Citation Context ...ctives to be revealed, and this is already happening. One of the first uses was the use of the calculus of Pomset logic (linear logic plus a non-commutative self-dual connectives): Lecomte and Retoré =-=[56, 57]-=- defined a grammar which associates a partial proof-net (and not just a formula) with each lexical item. This way they are able to describe some phenomena which hitherto fell out of the scope of categ... |

5 | An Efficient Recognition Algorithm for Multiple Context-Free Languages
- Nakanishi, Takada, et al.
- 2000
(Show Context)
Citation Context ...ars MCFGs [84]. 5 These languages are known to be efficiently recognizable. Seki et al. provide a simple chartbased parsing algorithm, and a method with improved worst-case performance is provided by =-=[67]-=-. We do not expect efficient decision methods for the whole class of MMCGs. 6 It could be that the decision problem for the languages define by real MMCG grammars for human languages is efficiently so... |

5 | Lambek calculus proofs and tree automata
- Tiede
(Show Context)
Citation Context ...d sub-formula property (which make parsing decidable) complete truth value semantics, and denotational semantics (bi-modules) for L. Furthermore the relation to rewrite grammar is by now rather clear =-=[69, 92, 91]-=-. (For more details on mathematical aspects the reader is referred to Buszkowski survey [10].) Nevertheless these calculi remained far from other logics until the 1980’s, mainly because they are resou... |

5 |
Logiques linéaires hybrides et leurs modalités. Thése de doctorat, spécialité informatique, Ecole Nationale Supérieure des Télécommunications de Paris, juin
- Demaille
- 1999
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Citation Context ...d the commutative linear connectives, with structural rules linking the two — nevertheless it is less powerful, because it is still decidable, and does not involve structural modalities or postulates =-=[24, 83, 6, 23]-=-. There also exists a classical calculus with a left and a right negaINRIA Resource Logics and Minimalist Grammars 9 tion [2], with ways to introduce modalities enabling displacement [3], or more soph... |

4 |
Exchange connectives for non-commutative intuitionistic propositional calculus
- Abrusci
- 1994
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Citation Context ...s not involve structural modalities or postulates [24, 83, 6, 23]. There also exists a classical calculus with a left and a right negation [2], with ways to introduce modalities enabling displacement =-=[3]-=-, or more sophisticated behaviors. Although these systems have not been used in linguistic applications, they may well be, since one often requires additional mechanisms. A great outcome of the linear... |

4 |
A type logical perspective on minimalist derivations
- Cornell
- 1997
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Citation Context ... we do not need the full power of MMCGs parsing to handle human languages. This Chomskian expectation can be realized in resource-logical settings as well as any other. The axioms proposed by Cornell =-=[20]-=- to realize movement implement the asymmetries of the transformational account, as do the axioms considered by Vermaat [97], and we see similar asymmetries even in the less traditional proposals of Le... |

4 |
Non-associative Lambek calculus in polynomial time
- Groote
- 1999
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Citation Context ...y are provided with a binary tree. This calculus enjoys the same properties as the Lambek calculus and is even decidable in polynomial time — [1] showed it for product free NL, and recently de Groote =-=[25]-=- extended the result to full NL. As the associative calculus is already too restrictive for linguistic purposes, this “base logic” is extended in two related directions. One extension consists in allo... |

4 | Acquiring and parsing languages with movement - Stabler - 1996 |

3 |
Abrusci and Elena Maringelli. A new correctness criterion for cyclic multiplicative proof-nets
- Michele
- 1998
(Show Context)
Citation Context ...guistic applications, they may well be, since one often requires additional mechanisms. A great outcome of the linear logic already used in linguistics is its natural syntax, the so-called proof nets =-=[30, 31, 93, 5, 49, 76, 80]-=-. A proof-net represents a proof as a graph, which consists of two parts: the subformula tree of the formula it proves, plus some edges linking dual atoms called axioms. These axioms are the represent... |

3 | Representational minimalism. SFB 340 - Cornell - 1997 |

3 | An LTAG perspective on categorial inference
- Joshi, Kulick, et al.
- 1998
(Show Context)
Citation Context ...e next section) in the plain Lambek calculus given by Lecomte and Retoré in [58] is clearly a by product of the study of proof-nets and their paths. Similarly the work of Joshi, Kulick, and Kurtonina =-=[41, 42]-=- on Partial Proof-Trees as building blocks of a categorial grammar, using TAG-like operations, resemble construction in proof nets of [72, 57], although they also use natural deduction. 3.2 Minimalist... |

3 | Benthem and A. ter Meulen, editors. Handbook of Logic and Language - van - 1997 |

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Logiques linaires hybrides et leurs modalits. Thse de doctorat, spcialit informatique, Ecole Nationale Suprieure des Tlcommunications de Paris, juin
- Demaille
- 1999
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Citation Context |

2 |
de Groote and Christian Retoré. Semantic readings of proof nets
- Philippe
- 1996
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Citation Context ...he embedding into intuitionistic logic is especially important since that is the very reason for the simple interface with Montague semantics where semantic recipes are proofs in intuitionistic logic =-=[26]-=-. Furthermore linear logic enables the consideration of various extensions which can be used for syntactic analysis: systems mixing commutative and non-commutative connectives, and the proof net synta... |

2 | editors. An invitation to cognitive sciences, Vol. 1: Language - Gleitman, Liberman - 1995 |

2 | Lambek calculus: recognizing power and complexity
- Kanazawa
- 1998
(Show Context)
Citation Context ...cal inference [68]. 5 The claim that human languages are definable by these grammars is challenged by Michaelis and Kracht 1996, on the basis of an argument that Old Georgian is not semilinear. 6 See =-=[44]-=- and [39]. 12sReflecting again on the previous section, one troubling aspect of the four points of convergence listed on page 3 is that they are purely “metatheoretical” in the sense that, even if we ... |

2 | R eseaux et S equents Ordonn es. These de Doctorat, specialite Mathematiques, Universite Paris 7, fevrier - Retore - 1993 |

1 | Abrusci and Claudia Casadio, editors. Third Roma Workshop - Michele - 1996 |

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syllabification: derivations or constraints
- Berber
- 1997
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Citation Context ...often be impossible to satisfy all constraints, but the structures that do the best, the “optimal” structures, are the grammatical ones. This kind of account has been extended to templatic morphology =-=[59, 16, 7]-=-, and the computation of optimal structures is elegantly formalized as a finite sequence of operations on finite automata (intersections of weighted automata and pruning of sub-optimal paths) [28, 27,... |

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On the generative capacity of multi-modal categorial logics
- Jäger
- 1987
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Citation Context ...ence [68]. 5 The claim that human languages are definable by these grammars is challenged by Michaelis and Kracht 1996, on the basis of an argument that Old Georgian is not semilinear. 6 See [44] and =-=[39]-=-. 12sReflecting again on the previous section, one troubling aspect of the four points of convergence listed on page 3 is that they are purely “metatheoretical” in the sense that, even if we grant tha... |

1 |
hybrid logics and minimalist representations
- Proof-nets
(Show Context)
Citation Context ...alize movement implement the asymmetries of the transformational account, as do the axioms considered by Vermaat [97], and we see similar asymmetries even in the less traditional proposals of Lecomte =-=[55]-=- and [57]. In these works, categorial grammar is a framework in which universals can be expressed, and it is natural to expect that at least some of the special properties that human languages actuall... |

1 |
Incremental processing and acceptability. Research Report LSI98-48-R, Universitat Politècnica di Catalunya
- Morrill
- 1998
(Show Context)
Citation Context ...t properties of constructions. For example, using proof nets Johnson [40] obtained measures of the instantaneous complexity of center-embedded constructions, and this work has been pursued by Morrill =-=[66]-=- to catch other phenomena. It is a pity that linear logic enjoys the perfect symmetries of classical linear logic, an involutive negation and de Morgan laws, while all that has been done for linguisti... |

1 |
Lexicalized proof-nets in Pomset logic and TAG
- Pogodalla
(Show Context)
Citation Context ...exical item. This way they are able to describe some phenomena which hitherto fell out of the scope of categorial grammars (relatively free word order, clitics,...) andtoencode Tree-Adjoining Grammars=-=[72]-=-. The 6sproof nets may also reveal linguistically and psychologically significant properties of constructions. For example, using proof nets Johnson [40] obtained measures of the instantaneous complex... |

1 | guest editor. Recent advances in logical and algebraic approaches to grammar - Retoré - 1998 |

1 | Acquiring grammars with movement - Stabler - 1998 |

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Lectures on Linear Logic, volume 29
- Troelstra
- 1992
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Citation Context ... resources: they may be consumed and produced in the course of a proof. RR n˚3780 4 Christian Retoré and Edward Stabler This is easy to explain by analogy with automata or Petri nets, as explained in =-=[93]-=-. In the presence of contraction or thinning (a.k.a. weakening), an implication cannot be viewed as a transition changing the state, since from and one can deduce but also and : ... |

1 |
A Study of Tree Adjoining Languages
- Vijayashanker
- 1987
(Show Context)
Citation Context ...d are, perhaps, not very appealing from a psycholinguistic viewpoint. And it is clear that a lot can be achieved without it, as in combinatory categorial grammar. 7Cf. [52, 70]. Adapting results from =-=[98, 99]-=-, [84] shows that multiple context free grammars are closed under intersection with finite automata, and the construction is really quite simple. INRIA Resource Logics and Minimalist Grammars 21 Still... |