{
  "abstract": "In this paper, we establish exponential separations between Extended Frege systems for a range of intuitionistic substructural and linear logics. More precisely, for any logic $L$ below the intuitionistic logic obtained by extending $\\mathbf{ILL}$ with structural rules, and any logic $M$ not contained in $L$, we construct a family of $\\mathsf{FL_e}$-provable formulas that have short proofs in $M$-Frege but require proofs of exponential size in $L$-Extended Frege. The same result holds in the $!$-free settings, using $\\mathbf{IMALL}$ and $\\mathbf{FL_e}$ in place of $\\mathbf{ILL}$. The key ingredient in proving these separations is a variant of the feasible disjunction property for $L$-Frege, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00422",
  "author_total": 1,
  "authors": [
    {
      "name": "Amirhossein Akbar Tabatabai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7argendcrcp61.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00422",
  "fulltext_url": null,
  "id": "7argendcrcp61",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00422",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7206159799",
  "pdf_url": "https://arxiv.org/pdf/2609.00422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7argendcrcp61.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Exponential Gaps Between Intuitionistic Linear Extended Frege Systems",
  "title_text": "Exponential Gaps Between Intuitionistic Linear Extended Frege Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/7argendcrcp61",
  "venue": "arXiv",
  "versions": []
}