  In this paper we propose an axiomatization for the notion of strong emergence
phenomenon between field theories depending on additional parameters, which we
call parameterized field theories. We present sufficient conditions ensuring
the existence of such phenomena between two given Lagrangian theories. More
precisely, we prove that a Lagrangian field theory depending linearly on an
additional parameter emerges from every multivariate polynomial theory
evaluated at differential operators which have well-defined Green functions
(or, more generally, that has a right-inverse in some extended sense). As a
motivating example, we show that the phenomenon of gravity emerging from
noncommutativy, in the context of a real or complex scalar field theory, can be
recovered from our emergence theorem. We also show that, in the same context,
we could also expect the reciprocal, i.e., that noncommutativity could emerge
from gravity. Some other particular cases are analyzed.
