  Interpreting a seemingly-simple function word like "or", "behind", or "more"
can require logical, numerical, and relational reasoning. How are such words
learned by children? Prior acquisition theories have often relied on positing a
foundation of innate knowledge. Yet recent neural-network based visual question
answering models apparently can learn to use function words as part of
answering questions about complex visual scenes. In this paper, we study what
these models learn about function words, in the hope of better understanding
how the meanings of these words can be learnt by both models and children. We
show that recurrent models trained on visually grounded language learn gradient
semantics for function words requiring spatial and numerical reasoning.
Furthermore, we find that these models can learn the meanings of logical
connectives and and or without any prior knowledge of logical reasoning, as
well as early evidence that they are sensitive to alternative expressions when
interpreting language. Finally, we show that word learning difficulty is
dependent on frequency in models' input. Our findings offer proof-of-concept
evidence that it is possible to learn the nuanced interpretations of function
words in visually grounded context by using non-symbolic general statistical
learning algorithms, without any prior knowledge of linguistic meaning.
