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...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...

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... 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...

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...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...

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...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...

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...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...

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...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...

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...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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...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...

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...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...

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..., 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 ...

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...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...

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...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...

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...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...

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...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...

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...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...

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...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...

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...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...

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...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...

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... 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 ...

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...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...

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..., 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...

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..., 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...

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...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...

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...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...

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...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...

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... 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 ...

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... 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...

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...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...

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...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...

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...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...

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...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...

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...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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...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...

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...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...

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..., 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 ...

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...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...

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...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...

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...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...

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...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 ...

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...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...

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...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...

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...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...

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...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...

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..., 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...

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...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...

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...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...

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... 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...

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...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...

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...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...

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... 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...

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...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...

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...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...

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...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...

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..., 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...

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...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...

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...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...

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... 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...

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...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...

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...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...

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...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...

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...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...

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...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...

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...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...

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... 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...

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...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...

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...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...

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...

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...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...

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...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...

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...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 ...

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...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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...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...

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...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...

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...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...

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...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...

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... 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 : ...

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...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...