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15
Lambek calculus is NPcomplete
 THEORETICAL COMPUTER SCIENCE
, 2003
"... We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete. ..."
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We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete.
Memoisation of Categorial Proof Nets: Parallelism in Categorial Processing
, 1996
"... We introduce a method of memoisation of categorial proof nets. Exploiting the planarity of noncommutative proof nets, and unifiability as a correctness criterion, parallelism is simulated through construction of a proof net matrix of most general unifiers for modules, in a manner analogous to the C ..."
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Cited by 19 (2 self)
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We introduce a method of memoisation of categorial proof nets. Exploiting the planarity of noncommutative proof nets, and unifiability as a correctness criterion, parallelism is simulated through construction of a proof net matrix of most general unifiers for modules, in a manner analogous to the CockeYoungerKasami algorithm for context free grammar. 1 Memoisation of categorial proof nets: parallelism in categorial processing 1 Introduction If the evolutionary tendency of grammatical formalisms could be summed up in one word, that word could well be lexicalism. The lexicon was once considered the locus of all and only idiosyncratic information; it may be hard now to find any proponents at all of such a view. Rather, one hears of the balance or tradeoff between lexicon and syntax: the tenet that the lexicon should comprise only what is idiosyncratic is, simply, no longer held. The notion that there is a compromise to be struck between lexicon and syntax is in turn rejected in the...
CLASSICAL NONASSOCIATIVE LAMBEK CALCULUS
"... We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polyno ..."
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Cited by 13 (1 self)
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We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.
Resource logics and minimalist grammars
 Proceedings ESSLLI’99 workshop (Special issue Language and Computation
, 2002
"... This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are lar ..."
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This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are largely informal apart from a few research papers. The study of resource logics, on the other hand, is formal and stems naturally from a long logical tradition. So although there appear to be promising connections between these traditions, there is at this point a rather thin intersection between them. The papers in this workshop are consequently rather diverse, some addressing general similarities between the two traditions, and others concentrating on a thorough study of a particular point. Nevertheless they succeed in convincing us of the continuing interest of studying and developing the relationship between the minimalist program and resource logics. This introduction reviews some of the basic issues and prior literature. 1 The interest of a convergence What would be the interest of a convergence between resource logical investigations of
ProductFree Lambek Calculus Is NPComplete
 In Logical Foundations of Computer Science. Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
, 2009
"... In this paper we prove that the derivability problems for productfree Lambek calculus and productfree Lambek calculus allowing empty premises are NPcomplete. Also we introduce a new derivability characterization for these calculi. ..."
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In this paper we prove that the derivability problems for productfree Lambek calculus and productfree Lambek calculus allowing empty premises are NPcomplete. Also we introduce a new derivability characterization for these calculi.
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 4 (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
Proof theory and formal grammars: applications of normalization
 In Benedikt Löwe, Wolfgang Malzkom, and Thoralf Räsch, editors, Foundations of the formal sciences II
, 2003
"... One of the main areas of interaction between logic and linguistics in the last 20 years has been the proof theoretical approach to formal grammars. This approach dates back to Lambek’s work in the 1950s. Lambek proposed to ..."
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One of the main areas of interaction between logic and linguistics in the last 20 years has been the proof theoretical approach to formal grammars. This approach dates back to Lambek’s work in the 1950s. Lambek proposed to
The derivability problem for lambek calculus with one division
 Artificial Intelligence Preprint Series
, 2006
"... In this paper we prove that the derivability problem for Lambek calculus with one division is decidable in polynomial time and present an algorithm for it. ..."
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In this paper we prove that the derivability problem for Lambek calculus with one division is decidable in polynomial time and present an algorithm for it.
kvalued NonAssociative Lambek Categorial Grammars are not Learnable from Strings
 in: ACL (Ed.), Proccedings of the 41st Annual Meeting of the Association for Computational Linguistics (ACL
"... This paper is concerned with learning categorial grammars in Gold's model. In contrast to kvalued classical categorial grammars, kvalued Lambek grammars are not learnable from strings. This result was shown for several variants but the question was left open for the weakest one, the no ..."
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This paper is concerned with learning categorial grammars in Gold's model. In contrast to kvalued classical categorial grammars, kvalued Lambek grammars are not learnable from strings. This result was shown for several variants but the question was left open for the weakest one, the nonassociative variant NL.