Developing a semantic representation for predictive TAG parsing This talk is intended to present our on-going efforts in constructing a semantic formalism that preserves the incremental properties of PLTAG while remaining both flexible and formally robust. PLTAG is a Tree-Adjoining Grammar variant which supports strict parser incrementality and near-future syntactic prediction by using modified and augmented LTAG operations and a lexical induction process that generates underspecified "prediction trees" alongside LTAG-style elementary trees. Of particular note is its unification-based prediction/verification mechanism that allows for the explicit incorporation of expectation into the syntactic structure. Existing approaches to robust semantic parsing often adopt neo-Davidsonian/minimally recursive approaches due to their flexibility in representing variable argument structures, adjuncts, and so on. We adopt a neo-Davidsonian approach as well, but we have the added burden of connecting a highly restricted, psycholinguistically-motivated syntactic parsing algorithm to the process that constructs semantic representations. We describe our approach to augmenting the PLTAG lexicon with semantic information, including how we represent prediction. We then give a high-level overview of how a PLTAG parse can result in a neo-Davidsonian representation. Finally, we bring up three issues for discussion: (1) the binding of unbound variables during adjunction, (2) linguistically-plausible limits on quantifier scope and underspecification, and (3) potential conflicts between minimally-recursive approaches and leading-edge work in distributional semantics.