The Problem of Learning the Semantics of Quantifiers

This paper is concerned with a possible mechanism for learning the meanings of quantifiers in natural language. The meaning of a natural language construction is identified with a procedure for recognizing its extension. Therefore, acquisition of natural language quantifiers is supposed to consist in collecting procedures for computing their denotations. A method for encoding classes of finite models corresponding to given quantifiers is shown. The class of finite models is represented by appropriate languages. Some facts describing dependencies between classes of quantifiers and classes of devices are presented. In the second part of the paper examples of syntax-learning models are shown. According to these models new results in quantifier learning are presented. Finally, the question of the adequacy of syntax-learning tools for describing the process of semantic learning is stated.

[1]  Yasubumi Sakakibara,et al.  Learning context-free grammars from structural data in polynomial time , 1988, COLT '88.

[2]  Hans Joerg Tiede,et al.  Identifiability in the Limit of Context-Free Generalized Quantifiers , 1999 .

[3]  Ursula Bellugi,et al.  Control of grammar in imitation, comprehension, and production , 1963 .

[4]  Yiannis N. Moschovakis,et al.  What Is an Algorithm? , 2012, SOFSEM.

[5]  Rocco De Nicola,et al.  A Partial Ordering Semantics for CCS , 1990, Theor. Comput. Sci..

[6]  M. van Lambalgen,et al.  Moschovakis' notion of meaning as applied to linguistics , 2004 .

[7]  Brian MacWhinney,et al.  The Handbook of Child Language , 1995 .

[8]  H. Benedict,et al.  Early lexical development: comprehension and production , 1979, Journal of Child Language.

[9]  Marcin Mostowski,et al.  Computational semantics for monadic quantifiers , 1998, J. Appl. Non Class. Logics.

[10]  Robin Clark,et al.  Learning First Order Quantifier Denotations An Essay in Semantic Learnability , 1996 .

[11]  J. Benthem.  Essays in Logical Semantics , 1986 .

[12]  Dag Normann,et al.  Logic Colloquium 2005 , 2007 .

[13]  S. Stick,et al.  Comprehension and production of comparatives and superlatives , 1979, Journal of Child Language.

[14]  Yiannis N. Moschovakis,et al.  Sense and denotation as algorithm and value , 1993 .

[15]  Jakub Szymanik.  Computational semantics for monadic quantifiers in natural language , 2007 .

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

[17]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[18]  Pavel Tichý,et al.  Intension in terms of Turing machines , 1969 .

[19]  Eve V. Clark,et al.  The Lexicon in Acquisition , 1996 .

[20]  C. D. Fernald.  Control of grammar in imitation, comprehension, and production: Problems of replication , 1972 .

[21]  M. Seligman,et al.  Language in the two-year old , 1976, Cognition.

[22]  Harry Bunt,et al.  Underspecification in Semantic Representations : Which Technique for What Purpose? , 2003 .

[23]  G. Frege.  Über Sinn und Bedeutung , 1892 .

[24]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..