{
  "abstract": "The reflection calculus with one modality is denoted by $\\mathsf{RC}_1$ and its quantified generalization is known as $\\mathsf{QRC}_1$. These decidable calculi are of interest since they generate the strictly positive fragments of the (quantified) provability logic for theories like Peano Arithmetic and Heyting Arithmetic. We introduce analytic cut-free calculi ${\\mathrm{GRC1}}$ and ${\\mathrm{GQRC1}}$ for $\\mathsf{RC}_1$ and $\\mathsf{QRC}_1$ respectively. The new calculi derive sequents of the form $A\\Longrightarrow B$ with $A,B$ strictly positive formulas. In particular, the new calculi do not use (multi)sets nor nested sequents. For both ${\\mathrm{GRC1}}$ and ${\\mathrm{GQRC1}}$ it is shown that the cut-rule is admissible. As a consequence, it is proven that the calculi are deductively equivalent to $\\mathsf{RC}_1$ and $\\mathsf{QRC}_1$ respectively. The cutfree systems are used to prove uniform interpolation for the two reflection calculi. In addition, ${\\mathrm{GRC1}}$ is used to give a syntactic proof of Dashkov's Theorem to the extent that $\\mathsf{RC}_1$ is the strictly positive fragment of the provability logic ${\\mathsf{GL}}$. The paper also introduces non-analytic calculi that are conceptually easier but proof-theoretically behave badly. It is shown that even those systems allow direct cut-elimination: the benefits of the strict positivity outweigh the draw-backs of a non-analytic calculus in these cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01248",
  "author_total": 2,
  "authors": [
    {
      "name": "Joost J. Joosten"
    },
    {
      "name": "Cosimo Perini Brogi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxsa2er3cry30.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01248",
  "fulltext_url": null,
  "id": "fxsa2er3cry30",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01248",
  "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",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01248",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxsa2er3cry30.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01248",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01248"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Modular proof analysis and cut elimination for the Reflection Calculi $\\mathsf{RC}_1$ and $\\mathsf{QRC}_1$",
  "title_text": "Modular proof analysis and cut elimination for the Reflection Calculi RC_1 and QRC_1",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:10Z",
  "url": "https://research.draconitic.com/paper/fxsa2er3cry30",
  "venue": "arXiv",
  "versions": []
}