  In this paper we consider the task of conversational semantic parsing over
general purpose knowledge graphs (KGs) with millions of entities, and thousands
of relation-types. We focus on models which are capable of interactively
mapping user utterances into executable logical forms (e.g., Sparql) in the
context of the conversational history. Our key idea is to represent information
about an utterance and its context via a subgraph which is created dynamically,
i.e., the number of nodes varies per utterance. Rather than treating the
subgraph as a sequence, we exploit its underlying structure and encode it with
a graph neural network which further allows us to represent a large number of
(unseen) nodes. Experimental results show that dynamic context modeling is
superior to static approaches, delivering performance improvements across the
board (i.e., for simple and complex questions). Our results further confirm
that modeling the structure of context is better at processing discourse
information, (i.e., at handling ellipsis and resolving coreference) and longer
interactions.
