  This paper uses computational experiments to explore the role of exposure in
the emergence of construction grammars. While usage-based grammars are
hypothesized to depend on a learner's exposure to actual language use, the
mechanisms of such exposure have only been studied in a few constructions in
isolation. This paper experiments with (i) the growth rate of the
constructicon, (ii) the convergence rate of grammars exposed to independent
registers, and (iii) the rate at which constructions are forgotten when they
have not been recently observed. These experiments show that the lexicon grows
more quickly than the grammar and that the growth rate of the grammar is not
dependent on the growth rate of the lexicon. At the same time,
register-specific grammars converge onto more similar constructions as the
amount of exposure increases. This means that the influence of specific
registers becomes less important as exposure increases. Finally, the rate at
which constructions are forgotten when they have not been recently observed
mirrors the growth rate of the constructicon. This paper thus presents a
computational model of usage-based grammar that includes both the emergence and
the unentrenchment of constructions.
