  In this paper we provide an alternative semantics for Equilibrium Logic and
its monotonic basis, the logic of Here-and-There (also known as G\"odel's G3
logic) that relies on the idea of "denotation" of a formula, that is, a
function that collects the set of models of that formula. Using the
three-valued logic G3 as a starting point and an ordering relation (for which
equilibrium/stable models are minimal elements) we provide several elementary
operations for sets of interpretations. By analysing structural properties of
the denotation of formulas, we show some expressiveness results for G3 such as,
for instance, that conjunction is not expressible in terms of the other
connectives. Moreover, the denotational semantics allows us to capture the set
of equilibrium models of a formula with a simple and compact set expression. We
also use this semantics to provide several formal definitions for entailment
relations that are usual in the literature, and further introduce a new one
called "strong entailment". We say that $\alpha$ strongly entails $\beta$ when
the equilibrium models of $\alpha \wedge \gamma$ are also equilibrium models of
$\beta \wedge \gamma$ for any context $\gamma$. We also provide a
characterisation of strong entailment in terms of the denotational semantics,
and give an example of a sufficient condition that can be applied in some
cases.
