2020/07/09 by Boris Eng, Eng, Boris, Thomas Seiller +1
Chemistry · Computer Science · Engineering · #Chemical synthesis and alkaloids #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.2007.16077
openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.