---
abstract: 'We present a new asynchronous model of computation named *Stellar Resolution* based on first-order unification [@herbrand1930recherches; @robinson1965machine]. This model of computation is obtained as a formalisation of Girard’s transcendental syntax programme, sketched in a series of three articles [@girard2017transcendental; @girard2016transcendental; @girard2016transcendental3]. 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 [@girard2016transcendental3]. 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 [@girard1987linear], their cut-elimination and the correctness criterion of Danos-Regnier [@danos1989structure]. Further use of realisability techniques lead to dynamic semantics for Multiplicative Linear Logic, following previous Geometry of Interaction models.'
author:
- |
    Boris Eng\
    Université Sorbonne Paris Nord\
    LIPN – UMR 7030\
    `engboris@hotmail.fr`
- |
    Thomas Seiller\
    CNRS\
    LIPN – UMR 7030\
    `seiller@lipn.fr`
bibliography:
- 'references.bib'
title: 'Stellar Resolution: Multiplicatives'
---

Introduction {#sec:intro}
============

We present a new asynchronous model of computation named *Stellar Resolution* based on first-order unification [@herbrand1930recherches; @robinson1965machine]. This model arises from work in proof theory, and more precisely proof-theoretic semantics 