Quantification, Witness Sets and Conservativity
Udo Klein · PUB – Publications at Bielefeld University (Bielefeld University) · 2012
I would like to thank the audience at the WCCFL29 conference as well as Marcus Kracht for valuable comments.1 See Egg (2011) for a survey of theories of underspecification. 2 For example, in Hole Semantics introduced in Bos (1996) an object-level formula SR (e.g. a formula of Predicate Logic) is a possible specification of an underspecified meta-level representation UR (consisting of a set of metavariables called holes, a set of labeled formulas possibly containing holes, and a set of constraints on the relation between holes and labeled formulas) iff the bijective mapping between holes and labels that characterizes the object-level formula SR satisfies the constraints of the underspecified representation UR.3 For example, Ambiguous Predicate Logic (APL) introduced in Jaspars & van Eijck (1996) allows for formulas of Predicate Logic to be prefixed with a structured list of scope-bearing operators, which essentially represent a partial ordering on the scope-bearing operators.Further, APL defines a rewrite relation on formulas, such that SR is a possible specification of an underspecified representation UR iff it is possible to rewrite UR into SR by means of the specified rewrite relation.