β-Reduction and Antecedent–Anaphora Relations in the Language of Acyclic Recursion

Abstract

In this paper, I introduce briefly the formal language of Acyclic Recursion ${L^{\lambda}_{ar}}$ (see Moschovakis ). Then I present the β-reduction rule of the calculus of the referential synonymy in ${L^{\lambda}_{ar}}$ and some arguments for its restricted manifestation with respect to preserving the algorithmic sense of the ${L^{\lambda}_{ar}}$-terms. This paper demonstrates further evidence for the need of restricted β-reduction. It also contributes to exploration of the inherent potentials of ${L^{\lambda}_{ar}}$ for underspecified semantic representations. I show that the restricted β-reduction, in combination with “underspecified” terms, gives rise to various distinctions between antecedent-anaphora and co-denotation relations in NL.

My work on this paper was conducted during my visit at TiLPS, Tilburg University, in the Autumn, 2008. I would like to thank my colleagues there for the fruitful time.