{
  "abstract": "In the implicit version of a propositional proof system Q, we work with Q-proofs that are not written down directly, but are succinctly encoded by circuits. Thus implicit Q-proofs are potentially exponentially shorter than usual Q-proofs. We study narrow implicit proofs, a restricted version of this notion, in which lines in the encoded proof can only have polynomial size. We use a cut-elimination construction to show that G_{i+1} is equivalent to narrow implicit G_i, for i >= 1, where G_i is the extension of Frege allowing reasoning with Sigma^q_i quantified propositional formulas. We show that G_1 is equivalent to implicit resolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10535",
  "author_total": 2,
  "authors": [
    {
      "name": "Pavel Pudlák"
    },
    {
      "name": "Neil Thapen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y32kvfwhttfj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10535",
  "fulltext_url": null,
  "id": "1y32kvfwhttfj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10535",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
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  ],
  "openalex": "W7164182393",
  "pdf_url": "https://arxiv.org/pdf/2606.10535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1y32kvfwhttfj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2606.10535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Quantified propositional calculi and narrow implicit proofs",
  "title_text": "Quantified propositional calculi and narrow implicit proofs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/1y32kvfwhttfj",
  "venue": "arXiv",
  "versions": []
}