{"paper":{"title":"Proof-graphs for Minimal Implicational Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Edward Hermann Haeusler (PUC-Rio), Ghent University, Lew Gordeev (Tubingen University, Marcela Quispe-Cruz (PUC-Rio), PUC-Rio)","submitted_at":"2014-04-01T00:38:41Z","abstract_excerpt":"It is well-known that the size of propositional classical proofs can  be huge.  Proof theoretical studies discovered exponential gaps between  normal or cut free  proofs and their respective non-normal proofs. The  aim of this work is to study  how to reduce the weight of propositional deductions. We present the formalism of  proof-graphs for purely implicational logic, which are graphs of a specific shape that are  intended to capture the logical structure of a deduction.  The advantage of this formalism is that formulas can be shared in the reduced proof.\n  In the present paper we give a pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0082","kind":"arxiv","version":1},"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"}