Unrestrained b-reduction  

Oleh:

Klein, Udo ; Sternefeld, Wolfgang

Jenis: Article from Proceeding
Dalam koleksi: Proceedings of the 23rd Semantics and Linguistic Theory Conference, held at the University of California, Santa Cruz, May 3 - 5, 2013, page 257–275.
Topik: beta-reduction; lambda-conversion; semantic reconstruction; syntactic reconstruction; l-calculus
Fulltext: 3676-7350-1-PB.pdf (161.18KB)

Isi artikel

A major argument for syntactic reconstruction is based on the wellknown fact that semantic reconstruction by b-reduction is possible only if the term to be substituted for a variable does not contain any variable that would become bound as a result of substitution: e.g., the expression (lx 2 8x 1 P(x ) cannot be b-reduced to 8x 1 P(x 1 ; x 1 ), since the underlined occurrence of x 1 ; x would become bound. This way, we derive a theoretical argument for syntactic reconstruction. However, syntactic reconstruction is not without its problems, simply because the surface form and the reconstructed form may still differ with respect to other syntactic, semantic, and information theoretic properties. This is particularly troublesome for minimalist theories which do not allow for multiple levels of representation. 1 In this paper we propose a technique that might help to overcome these dif?culties (i.e., the limitation imposed by b-reduction on semantic reconstruction) by de?ning a translation function T for expressions of a predicate logic L with l-abstraction into expressions of a higher-order language L , with the desirable property T((lx 2 8x 1 P(x 1 ; x 2 ))(x 1 )) = T(8x 1 P(x 1 ; x 1 1 )). In linguistic applications this will facilitate the binding of a pronoun without presupposing c-command. We will sketch a formal proof showing that unrestricted b-reduction is a property of the target expressions in L 1 , the translations of L 0 under T.

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