  We present a new asynchronous model of computation named Stellar Resolution
based on first-order unification. This model of computation is obtained as a
formalisation of Girard's transcendental syntax programme, sketched in a series
of three articles. As such, it is the first step towards a proper formal
treatment of Girard's proposal to tackle first-order logic in a
proofs-as-program approach. After establishing formal definitions and basic
properties of stellar resolution, we explain how it generalises traditional
models of computation, such as logic programming and combinatorial models such
as Wang tilings. We then explain how it can represent multiplicative
proof-structures, their cut-elimination and the correctness criterion of Danos
and Regnier. Further use of realisability techniques lead to dynamic semantics
for Multiplicative Linear Logic, following previous Geometry of Interaction
models.
