Branching Quantification v. Two-way Quantification

We discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

[1]  Jaakko Hintikka,et al.  Partially Ordered Quantifiers vs. Partially Ordered Ideas , 1976 .

[2]  Marcello Frixione,et al.  Tractable Competence , 2001, Minds and Machines.

[3]  Paul Dekker,et al.  On the semantics of branching quantifier sentences , 2003 .

[4]  G. H. Slusser,et al.  Statistical analysis in psychology and education , 1960 .

[5]  Annabel Cormack,et al.  On ‘Formal Games and Forms for Games’ , 1980 .

[6]  Jaakko Hintikka,et al.  Quantifiers vs. Quantification Theory , 1973 .

[7]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[8]  DOV M. GABBAY,et al.  BRANCHING QUANTIFIERS, ENGLISH, AND MONTAGUE-GRAMMAR , 1974 .

[9]  M. Dalrymple,et al.  Reciprocal Expressions and the Concept of Reciprocity , 1998 .

[10]  G. Sher.  Ways of branching quantifers , 1990 .

[11]  F. Guenthner,et al.  A Note on the Representation of Branching Quantifiers , 1976 .

[12]  Annabel Cormack,et al.  Ambiguity and quantification , 1981 .

[13]  Kent Bach.  Semantic nonspecificity and mixed quantifiers , 1982 .

[14]  Howard Lasnik,et al.  Reciprocity and plurality , 1991 .

[15]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[16]  J. Barwise,et al.  Generalized quantifiers and natural language , 1981 .

[17]  Nina Gierasimczuk,et al.  Hintikka's Thesis revisited , 2007 .

[18]  Marcin Mostowski,et al.  Computational complexity of the semantics of some natural language constructions , 2004, Ann. Pure Appl. Log..

[19]  Janina Radó,et al.  How to provide exactly one interpretation for every sentence, or what eye movements reveal about quantifier scope , 2008 .

[20]  Annabel Cormack,et al.  Quantification and pragmatics , 1982 .

[21]  Irena Bellert.  Feature system for quantification structures in natural language , 1989 .

[22]  G. A. Ferguson,et al.  Statistical analysis in psychology and education , 1960 .

[23]  R. May.  Logical Form: Its Structure and Derivation , 1985 .

[24]  Jakub Szymanik,et al.  Quantifiers in TIME and SPACE : computational complexity of generalized quantifiers in natural language , 2009 .

[25]  Neil Immerman,et al.  Descriptive Complexity , 1999, Graduate Texts in Computer Science.

[26]  Robert May,et al.  Interpreting logical form , 1989 .

[27]  Jan Tore Lønning,et al.  Plurals and Collectivity , 1997, Handbook of Logic and Language.

[28]  Anna Szabolcsi,et al.  Variation, Distributivity, and the Illusion of Branching , 1997 .

[29]  Ray Jackendoff,et al.  Semantic Interpretation in Generative Grammar , 1972 .

[30]  K. Jon Barwise,et al.  On branching quantifiers in English , 1979, J. Philos. Log..

[31]  Kasia M. Jaszczolt.  Semantics and Pragmatics: Meaning in Language and Discourse , 2002 .

[32]  Erik Stenius,et al.  Comments on Jaakko Hintikka's paper “Quantifiers vs. Quantification theory”* , 1976 .

[33]  Philippe Schlenker.  Scopal Independence: A Note on Branching and Wide Scope Readings of Indefinites and Disjunctions , 2006, J. Semant..

[34]  Livio Robaldo,et al.  Independent Set Readings and Generalized Quantifiers , 2010, J. Philos. Log..

[35]  Merlijn Sevenster,et al.  Branches of imperfect information : logic, games, and computation , 2002 .

[36]  E. Spelke,et al.  Ontological categories guide young children's inductions of word meaning: Object terms and substance terms , 1991, Cognition.

[37]  Bart Geurts,et al.  Monotonicity and Processing Load , 2005, J. Semant..

[38]  Gerard Casey.  Minds and machines , 1992 .

[39]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[40]  M. Krynicki,et al.  Quantifiers : logics, models, and computation , 1995 .