On Limit Points for Some Variants of Rigid Lambek Grammars

In this paper we give some learnability results in the field of categorial grammars. We show that in contrast to k-valued classical categorial grammars, different classes of Lambek grammars are not learnable from strings following Gold's model. The results are obtained by the construction of limit points in each considered class: non associative Lambek grammars with empty sequences and Lambek grammars without empty sequences and without product. Such results express the difficulty of learning categorial grammars from unstructured strings and the need for structured examples.

[1]  Makoto Kanazawa.  Learnable Classes of Categorial Grammars , 1998 .

[2]  Christophe Costa Florêncio.  Consistent Identification in the Limit of Any of the Classes k -Valued Is NP-hard , 2001, LACL.

[3]  Claudia Casadio,et al.  Semantic Categories and the Development of Categorial Grammars , 1988 .

[4]  Emmon W. Bach,et al.  Categorial Grammars and Natural Language Structures , 1988 .

[5]  J. Lambek.  The Mathematics of Sentence Structure , 1958 .

[6]  Wojciech Buszkowski,et al.  Mathematical Linguistics and Proof Theory , 1997, Handbook of Logic and Language.

[7]  Jacques Nicolas.  Grammatical Inference as Unification , 1999 .

[8]  Mati Pentus,et al.  Lambek grammars are context free , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[9]  Takeshi Shinohara.  Inductive inference from positive data is powerful , 1990, COLT '90.

[10]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[11]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[12]  Dana Angluin,et al.  Inductive Inference of Formal Languages from Positive Data , 1980, Inf. Control..

[13]  Michael Moortgat,et al.  Categorial Type Logics , 1997, Handbook of Logic and Language.

[14]  Annie Foret,et al.  Rigid Lambek Grammars Are Not Learnable from Strings , 2002, COLING.

[15]  Y. Bar-Hillel.  A Quasi-Arithmetical Notation for Syntactic Description , 1953 .

[16]  Isabelle Tellier,et al.  A Tool for Language Learning Based on Categorial Grammars and Semantic Information , 2002, ICGI.