{"paper":{"title":"Geometry of Interaction for MALL via Hughes-vanGlabbeek Proof-Nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Masahiro Hamano","submitted_at":"2015-03-31T06:13:06Z","abstract_excerpt":"This paper presents, for the first time, a Geometry of Interaction (GoI) interpretation inspired from Hughes-vanGlabbeek (HvG) proof-nets for multiplicative additive linear logic (MALL). Our GoI dynamically captures HvG's geometric correctness criterion-the toggling cycle condition-in terms of algebraic operators. Our new ingredient is a scalar extension of the *-algebra in Girard's *-ring of partial isometries over a boolean polynomial ring with literals of eigenweights as indeterminates. In order to capture feedback arising from cuts, we construct a finer grained execution formula. The expan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08925","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}