A. Angluin, Inductive inference of formal languages from positive data, Information and Control, vol.45, issue.2, pp.117-135, 1980.
DOI : 10.1016/S0019-9958(80)90285-5

L. Blum and M. Blum, Toward a mathematical theory of inductive inference, Information and Control, vol.28, issue.2, pp.125-155, 1975.
DOI : 10.1016/S0019-9958(75)90261-2

W. Buszkowski and G. Penn, Categorial grammars determined from linguistic data by unification, Studia Logica, vol.65, issue.4, pp.431-454, 1990.
DOI : 10.1007/BF00370157

[. Buszkowski, Generative capacity of non-associative lambek calculus, Bulletin of the Polish Academy of Science and Mathematics, 1986.

N. Chomsky, Three models for the description of language, IEEE Transactions on Information Theory, vol.2, issue.3, pp.113-124, 1956.
DOI : 10.1109/TIT.1956.1056813

]. N. De-bruijn, Lambda calculus notation with nameless dummies, Indagationes Mathematicae, pp.381-392, 1972.

]. M. Ful88 and . Fulk, Saving the phenomenon: Requirements that inductive machines not contradict known data, Information and Computation, vol.79, issue.3, pp.193-209, 1988.

G. Gazdar, Applicability of Indexed Grammars to Natural Languages, Natural Language Parsing and Linguistic Theories, pp.69-94, 1988.
DOI : 10.1007/978-94-009-1337-0_3

]. E. Gol67 and . Gold, Language identification in the limit, Information and Control, vol.10, pp.447-474, 1967.

I. Guesserian, Pushdown tree automata, Mathematical Systems Theory, vol.2, issue.1, pp.237-263, 1983.
DOI : 10.1007/BF01744582

M. Kanazawa, Learnable Classes of Categorial Grammars. Center for the Study of Language and Information (CSLI), 1998.

J. Lambek, The Mathematics of Sentence Structure, The American Mathematical Monthly, vol.65, issue.3, pp.154-170, 1958.
DOI : 10.2307/2310058

R. Montague, The proper treatment of quantification in ordinary english, Approaches to Natural Language, pp.221-242, 1997.

M. Moortgat, Categorial type logics, Handbook of Logic and Language, 1997.

J. Nicolas, Grammatical inference as unification, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00073042

N. Daniel, L. R. Osherson, M. Gleitmann, and . Liberman, An Invitation to Cognitive Science, Massachusetts Institute of Technology, vol.1, 1995.

N. Daniel, S. Osherson, D. Weinstein, E. De-jongh, and . Martin, Formal learning theory, Handbook of Logic and Language, 1997.

M. Pentus, Abstract, The Journal of Symbolic Logic, vol.2, issue.02, pp.648-660, 1997.
DOI : 10.1016/S0019-9958(67)91172-2

[. Pinker, The Language Instict, 1994.

[. Retoré, The logic of categorial grammar: lecture notes, 2005.

D. Roorda, Resource Logics: Proof-Theoretical Investigations, 1991.

]. T. Shi90 and . Shinohara, Inductive inference from positive data is powerful, The 1990 Workshop on Computational Learning Theory, pp.97-110, 1990.

[. Steedman, Categorial grammar, Lingua, vol.90, issue.3, pp.221-258, 1993.
DOI : 10.1016/0024-3841(93)90024-Q

I. Tellier, Rôle de la compositionnalité dan l'acquisition d'une langue, Actes de CAP99, pp.107-114, 1999.

J. W. Thatcher, Characterizing derivation trees of context-free grammars through a generalization of finite automata theory, Journal of Computer and System Sciences, vol.1, issue.4, pp.317-322, 1967.
DOI : 10.1016/S0022-0000(67)80022-9

[. Tiede, Deductive Systems and Grammars: Proofs as Grammatical Structures, 1999.

. Van-benthem, LOGICAL SYNTAX, Theoretical Linguistics, vol.14, issue.2-3, pp.119-142, 1987.
DOI : 10.1515/thli.1987.14.2-3.119

[. Wansing, The Logic of Information Structures, 1993.
DOI : 10.1007/3-540-56734-8

]. K. Wri89 and . Wright, Identifications of unions of languages drawn from an identifiable class, The 1989 Workshop on Computational Learning Theory, pp.328-333, 1989.

[. Zielonka, A simple and general method of solving the finite axiomatizability problems for Lambek's syntactic calculi, Studia Logica, vol.27, issue.1, pp.35-39, 1989.
DOI : 10.1007/BF00370632

L. Constraints-on and .. Functions, 13 3.4.1 Non-restrictive Constraints, p.15

T. Languages and A. , 34 6.2.1 Local Tree Languages, Context-free Tree Languages . . . . . . . . . . . . . . . . . . . . . . . . . . 36

I. Unité-de-recherche, . Lorraine, . Loria, and . Technopôle-de-nancy, Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-l` es-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex

I. Editeur and . De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399