Rough Sets and Learning by Unification

We apply basic notions of the theory of rough sets, due to Pawlak [30, 31], to explicate certain properties of unification-based learning algorithms for categorial grammars, introduced in [6, 11] and further developed in e.g. [18, 19, 24, 25, 26, 9, 28, 14, 15, 3]. The outcomes of these algorithms can be used to compute both the lower and the upper approximation of the searched language with respect to the given, finite sample. We show that these methods are also appropriate for other kinds of formal grammars, e.g. context-free grammars and context-sensitive grammars.

[1]  Michael Moortgat,et al.  Structural Equations in Language Learning , 2001, LACL.

[2]  S. Kapur.  Computational Learning of Languages , 1992 .

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

[4]  Terry A. Osborn,et al.  Learning Languages , 2020, World Language Education as Critical Pedagogy.

[5]  J.F.A.K. van Benthem,et al.  Language in Action: Categories, Lambdas and Dynamic Logic , 1997 .

[6]  Sean A. Fulop.  Semantic Bootstrapping of Type-Logical Grammar , 2005, J. Log. Lang. Inf..

[7]  Jacek Marciniec.  Optimal Unification of Infinite Sets of Types , 2004, Fundam. Informaticae.

[8]  Gerald Penn,et al.  Categorial grammars determined from linguistic data by unification , 1990, Stud Logica.

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

[10]  Barbara Dziemidowicz.  Optimal Unification and Learning Algorithms for Categorial Grammars , 2002, Fundam. Informaticae.

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

[12]  Makoto Kanazawa,et al.  Identification in the limit of categorial grammars , 1993, J. Log. Lang. Inf..

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

[14]  Wojciech Buszkowski.  Algebraic Structures in Categorial Grammar , 1998, Theor. Comput. Sci..

[15]  Stéphane Demri,et al.  Incomplete Information: Structure, Inference, Complexity , 2002, Monographs in Theoretical Computer Science An EATCS Series.

[16]  Claudia Casadio.  Recensione a: J. van Benthem, A. ter Meulen (eds.), Handbook of Logic and Language , 1997 .

[17]  David I. Beaver,et al.  The Handbook of Logic and Language , 1997 .

[18]  J. Lambek.  Bilinear logic in algebra and linguistics , 1995 .

[19]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[20]  Jacek Marciniec.  Infinite Set Unification with Application to Categorial Grammar , 1997, Stud Logica.

[21]  Andrzej Skowron,et al.  Knowledge Representation Techniques (Studies in Fuzziness and Soft Computing) , 2006 .

[22]  Daniel N. Osherson,et al.  Formal Learning Theory , 1997 .

[23]  Jacek Marciniec,et al.  Learning Categorial Grammar by Unification with Negative Constraints , 1994, J. Appl. Non Class. Logics.

[24]  Andrzej Skowron,et al.  Knowledge Representation Techniques - A Rough Set Approach , 2006, Studies in Fuzziness and Soft Computing.

[25]  Keith Wright.  Identification of unions of languages drawn from an identifiable class , 1989, COLT '89.

[26]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[27]  Annie Foret,et al.  k-Valued non-associative Lambek grammars are learnable from generalized functor-argument structures , 2006, Theor. Comput. Sci..

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

[29]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[30]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..