  Geometry of Interaction (GoI) is a kind of semantics of linear logic proofs
that aims at accounting for the dynamical aspects of cut-elimination. We
present here a parametrized construction of a Geometry of Interaction for
Multiplicative Additive Linear Logic (MALL) in which proofs are represented by
families of directed weighted graphs. Contrarily to former constructions
dealing with additive connectives, we are able to solve the known issue of
obtaining a denotational semantics for MALL by introducing a notion of
observational equivalence. Moreover, our setting has the advantage of being the
first construction dealing with additives where proofs of MALL are interpreted
by finite objects. The fact that we obtain a denotational model of MALL relies
on a single geometric property, which we call the trefoil property, from which
we obtain, for each value of the parameter, adjunctions. We then proceed to
show how this setting is related to Girard's various constructions: particular
choices of the parameter respectively give a combinatorial version of his
latest GoI, a refined version of older Geometries of Interaction based on
nilpotency. This shows the importance of the trefoil property underlying our
constructions since all known GoI construction to this day rely on particular
cases of it.
