We present a model for semantic proto-role labeling (SPRL) using an adapted bidirectional LSTM encoding strategy that we call "Neural-Davidsonian": predicate-argument structure is represented as pairs of hidden states corresponding to predicate and argument head tokens of the input sequence. We demonstrate: (1) state-of-the-art results in SPRL, and (2) that our network naturally shares parameters between attributes, allowing for learning new attribute types with limited added supervision.