Research on Language and Computation 2: 307–308, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 307 Preface Choice Functions in Semantics KLAUS VON HEUSINGER 1 AND RUTH KEMPSON 2 1 Institute for General and German Linguistics, University of Stuttgart, Keplerstr. 17 D-70174, Stuttgart (E-mail: vonheusinger@ilg.uni-stuttgart.de); 2 King’s College London, The Strand, London, WC2R 2LS (E-mail: kempson@dcs.kcl.ac.uk) Interest in the use of choice functions is increasing in formal semantics, demonstrated by recent discussions of the adequacy of analyses with choice functions. Their syntactic counterpart, the epsilon operator, was intro- duced into meta-mathematics in the epsilon calculus of Hilbert and Bern- ays (1939), which provides an explicit study of arbitrary names used as predicate logic proof terms, the epsilon operator being a generalized iota operator underpinning uses of both existential and universal quantification. Semantically, a choice function  is a function that assigns to a non-empty set s one of its elements, as defined in (1) or alternatively in (2). Intuitively, a choice function selects one element out of a set. (1) (s) ∈ s if s = φ (2) f is a choice function (i.e. CH(f ) holds) iff P(f (P), where P is non- empty. This very general characterization makes choice functions an attractive and flexible semantic tool. For instance, choice functions, like Skolem func- tions, allow us to interpret the linguistic expressions associated with them in situ. The specific reading of the indefinite NP in (3) can be interpreted in situ if the indefinite article is associated with a choice function which takes wide scope, as illustrated in (4). (3) Every student read a book. (4) CH(f )& ∀x [student(x ) → read(x ), f (book)] The range of application of choice functions in formal semantics has not yet been fully determined. The following contributions use choice functions as formal tools in as different domains as anaphoric definite descriptions, focus semantics, indefinite NPs, and conditionals, and there is also discus- sion of pragmatically related issues.