Unrestrained beta reduction

Udo Klein, Wolfgang Sternefeld

Abstract


A major argument for syntactic reconstruction is based on the well-known fact that semantic reconstruction by beta-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. 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.

In this paper we propose a technique that might help to overcome these difficulties (ie. the limitation imposed by beta-reduction on semantic reconstruction) by defining a translation function T for expressions of a predicate logic L0 with lambda-abstraction into expressions of a higher-order language L1, with the desirable property that the translation of a formula in L0 is equivalent with the translation of its unrestricted reduction. In linguistic applications this will facilitate the binding of a pronoun without presupposing c-command. We will sketch a formal proof showing
that unrestricted beta-reduction is a property of the target expressions in L1, the translations of L0 under T.

Keywords


beta-reduction; lambda-conversion; semantic reconstruction; syntactic reconstruction; lambda-calculus

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DOI: https://doi.org/10.3765/salt.v23i0.2684

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