Interpretation and inference with maximal referential terms

Several authors proposed to import in Natural Language (NL) semantics the ideas lying behind the well-known Skolem theorem, defined in First Order Logic. In these proposals, logical forms include referential (functional) terms, inserted as argument of Generalized Quantifiers. The referential terms have to be maximized with respect to the model where formulae are evaluated, in order to provide the proper truth conditions. This article presents two recent proposals belonging to this approach, i.e. Steedman (2007) [60], and Robaldo (2009) [50], and compares their way to incorporate the maximality requirement. The comparison highlights that the latter provides a more adequate and flexible management of the model theoretic interpretation of the formulae and the inferences that may be carried out starting from them.