Binding On the Fly: Cross-Sentential Anaphora in Variable— Free Semantics

In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora. Kluwer Academic Publishers. pp. 215--227 (2003)

Anna Szabolcsi
New York University
Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is that reflexive and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained.
Keywords combinator  variable-free  pronominal anaphora  dynamic semantics  cross-sentential
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
Towards a Variable-Free Semantics.Pauline Jacobson - 1999 - Linguistics and Philosophy 22 (2):117-185.

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Citations of this work BETA

Decomposing Modal Quantification.A. Brasoveanu - 2010 - Journal of Semantics 27 (4):437-527.
Pronouns.Daniel Büring - 2011 - In Claudia Maienborn & Paul Portner (eds.), Semantics: An International Handbook of Natural Language Meaning. Berlin: Mouton De Gruyter. pp. 971-996.

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