A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars (original) (raw)
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Recently, learning algorithms in Gold's model have been proposed for some particular classes of classical categorial grammars . We are interested here in learning Lambek categorial grammars.
k-Valued non-associative Lambek grammars are learnable from generalized functor-argument structures
Theoretical Computer Science, 2006
This paper is concerned with learning categorial grammars from positive examples in the model of Gold. Functor-argument structures (written FA) are usual syntactical decompositions of sentences in sub-components distinguishing the functional parts from the argument parts defined in the case of classical categorial grammars also known as AB-grammars. In the case of nonassociative type-logical grammars, we propose a similar notion that we call generalized functor-argument structures and we show that these structures capture the essence of non-associative Lambek (NL) calculus without product. We show that (i) rigid and k-valued non-associative Lambek (NL without product) grammars are learnable from generalized functor-argument structured sentences. We also define subclasses of k-valued grammars in terms of arity. We first show that (ii) for each k and each bound on arity the class of FA-arity bounded k-valued NL languages of FA structures is finite and (iii) that FA-arity bounded k-valued NL grammars are learnable both from strings and from FA structures as a corollary. Result (i) is obtained from (ii); this learnability result (i) is interesting and surprising when compared to other results: in fact we also show that (iv) this class has infinite elasticity. Moreover, these classes are very close to classes like rigid associative Lambek grammars learned from natural deduction structured sentences (that are different and much richer than FA or generalized FA) or to k-valued non-associative Lambek grammars unlearnable from strings or even from bracketed strings. Thus, the class of k-valued non-associative Lambek grammars learned from generalized functor-argument sentences is at the frontier between learnable and unlearnable classes of languages.
< i> k-Valued Non-Associative Lambek Grammars are Learnable from Function-Argument 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 k-valued non-associative Lambek grammars are learnable from function-argument structured sentences. In fact, function-argument structures are natural syntactical decompositions of sentences in sub-components with the indication of the head of each sub-component.
k-valued non-associative Lambek categorial grammars are not learnable from strings
Proceedings of the 41st Annual Meeting on …, 2003
This paper is concerned with learning categorial grammars in Gold's model. In contrast to k-valued classical categorial grammars, k-valued 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 non-associative variant NL.
2011
Stabler proposes an implementation of the Chomskyan Minimalist Program, Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars - MCG, based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface, Amblard 07. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated languages.
Analyzing the Core of Categorial Grammar
Even though residuation is at the core of Categorial Grammar , it is not always immediate to realize how standard logical systems like Multi-modal Categorial Type Logics (MCTL) (Moortgat, 1997) actually embody this property. In this paper, we focus on the basic system NL (Lambek, 1961) and its extension with unary modalities NL(3) , and we spell things out by means of Display Calculi (DC) . The use of structural operators in DC permits a sharp distinction between the core properties we want to impose on the logical system and the way these properties are projected into the logical operators. We will show how we can obtain Lambek residuated triple \, / and • of binary operators, and how the operators 3 and 2 ↓ introduced by Moortgat (1996) are indeed their unary counterpart.
k-Valued Non-Associative Lambek Grammars are Learnable from Function-Argument 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 k-valued non-associative Lambek grammars are learnable from function-argument structured sentences. In fact, function-argument structures are natural syntactical decompositions of sentences in sub-components with the indication of the head of each sub-component. This result is interesting and surprising because for every k, the class of k-valued NL grammars has infinite elasticity and one could think that it is not learnable, which is not true. Moreover, these classes are very close to unlearnable classes like k-valued associative Lambek grammars learned from function-argument sentences or k-valued non-associative Lambek calculus grammars learned from well-bracketed list of words or from strings. Thus, the k-valued non-associative Lambek grammars learned from function-argument sentences is at the frontier between learnable and unlearnable classes of languages.
Minimalist Grammars and Minimalist Categorial Grammars: Toward Inclusion of Generated Languages
Stabler proposes an implementation of the Chomskyan Minimalist Program [1] with Minimalist Grammars (MG) [2]. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars (MCG), based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface [3]. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated languages.