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40
Lambek Grammars Based on Pregroups
 Logical Aspects of Computational Linguistics, LNAI 2099
, 2001
"... Lambek [13] introduces pregroups as a new framework for syntactic structure. In this paper we prove some new theorems on pregroups and study grammars based on the calculus of free pregroups. We prove that these grammars are equivalent to contextfree grammars. We also discuss the relation of pregrou ..."
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Cited by 34 (6 self)
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Lambek [13] introduces pregroups as a new framework for syntactic structure. In this paper we prove some new theorems on pregroups and study grammars based on the calculus of free pregroups. We prove that these grammars are equivalent to contextfree grammars. We also discuss the relation of pregroups to the Lambek calculus. 1 Introduction and
TemperleyLieb Algebra: From Knot Theory to . . .
"... Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics. ..."
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Cited by 20 (4 self)
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Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics.
Symmetric categorial grammar
 Journal of Philosophical Logic
, 2009
"... is lost or not), is a phenomenon which a linguistic semantics ought to explain, rather than ignore. (van Benthem 1986, p 213) The LambekGrishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of typeforming operations (product and residual left a ..."
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Cited by 14 (2 self)
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is lost or not), is a phenomenon which a linguistic semantics ought to explain, rather than ignore. (van Benthem 1986, p 213) The LambekGrishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of typeforming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the CurryHoward derivational semantics, and structurepreservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language form and meaning. 1 1
Logic and artificial intelligence
 The Stanford Encyclopedia of Philosophy. Fall 2003. http://plato.stanford.edu/archives/fall2003/entries/logicai
"... www.rthomaso.eecs.umich.edu ..."
Learning rigid lambek grammars and minimalist grammars from structured sentences
 Third workshop on Learning Language in Logic, Strasbourg
, 2001
"... Abstract. We present an extension of Buszkowski’s learning algorithm for categorial grammars to rigid Lambek grammars and then for minimalist categorial grammars. The Kanazawa proof of the convergence in the Gold sense is simplified and extended to these new algorithms. We thus show that this techni ..."
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Cited by 10 (1 self)
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Abstract. We present an extension of Buszkowski’s learning algorithm for categorial grammars to rigid Lambek grammars and then for minimalist categorial grammars. The Kanazawa proof of the convergence in the Gold sense is simplified and extended to these new algorithms. We thus show that this technique based on principal type algorithm and type unification is quite general and applies to learning issues for different type logical grammars, which are larger, linguistically more accurate and closer to semantics. 1
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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Cited by 5 (0 self)
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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
Representation of Residuated Semigroups in Some Algebras of Relations (The Method of Canonical Models)
 Fundamenta Informaticae
, 1997
"... We prove some theorems on representation of residuated semigroups and monoids in algebras of binary relations. One of them has been proved in Andr'eka and Mikul'as [3], and the other are new, though also closely related to some results in [3]. The main novelty of this paper is a simple met ..."
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Cited by 5 (5 self)
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We prove some theorems on representation of residuated semigroups and monoids in algebras of binary relations. One of them has been proved in Andr'eka and Mikul'as [3], and the other are new, though also closely related to some results in [3]. The main novelty of this paper is a simple method of proof, based upon a construction of canonical models for Lambek calculi by means of labeled formulas, whereas [3] uses graphtheoretic constructions. We handle labeled formulas in a way similar to Kurtonina [15] and the second author [14], but we make no use of Labeled Deductive Systems, which is an essential simplification.