  Systems obtained by quotienting a subshift of finite type (SFT) by another
SFT are called finitely presented in the literature. Analogously, if a sofic
shift is quotiented by a sofic equivalence relation, we call the resulting
system sofically presented. Generalizing an observation of Fried, for all
discrete countable monoids M, we show that M-subshift/SFT systems are precisely
the expansive dynamical M-systems, where S_1/S_2 denotes the class of systems
obtained by quotienting subshifts in S_1 by (relative) subshifts in S_2. We
show that for all finitely generated infinite monoids M, M-SFT \subsetneq
M-sofic \subsetneq M-SFT/SFT = M-sofic/SFT \subsetneq M-SFT/sofic =
M-sofic/sofic, and that Ma\~n\'e's theorem about the dimension of expansive
systems characterizes the virtually cyclic groups.
  In the case of one-dimensional actions, Ma\~ne's theorem generalizes to
sofically presented systems, which also have finite topological dimension. The
basis of this is the construction of an explicit metric for a sofically
presented system. We show that any finite connected simplicial complex is a
connected component of a finitely presented system, and prove that conjugacy of
one-dimensional sofically presented dynamical systems is undecidable. A key
idea is the introduction of so-called automatic spaces. We also study the
automorphism groups and periodic points of sofically presented systems.
  We also perform two case studies. First, in the context of $\beta$-shifts, we
define the $\beta$-kernel -- the least subshift relation that identifies $1$
with its orbit. We give a classification of the $\beta$-shift/$\beta$-kernel
pair as a function of $\beta$. Second, we revisit the classical study of toral
automorphisms in our framework, and in particular for the classical "golden
mean" toral automorphism we explicitly compute the kernel of the standard
presentation.
