{
  "abstract": "We investigate the relationship between base-extension semantics, Beth semantics, and Prawitz's ecumenical logic. We first present a base-extension semantics for the propositional fragment of Prawitz's system and prove that it is sound and complete. The semantics interprets intuitionistic and classical operators directly within a common proof-theoretic framework, without reducing the classical operators to their intuitionistic counterparts by means of a translation. We then analyse the effect of incorporating Beth-style clauses into base-extension semantics. When arbitrary bases are admitted and $\\bot$ is governed by atomic explosion, these clauses trivialise. By contrast, when $\\bot$ is treated as a basic sentence and attention is restricted to consistent bases, the Beth-style clauses for atoms and disjunction characterise, respectively, classical atoms and classical disjunction in Prawitz's system. We also obtain equivalent, path-independent formulations of the classical clauses for atoms, disjunction, and implication. These results reveal that the consistency constraint is not merely a technical restriction: within base-extension semantics, it transforms clauses originally associated with intuitionistic semantics into semantic characterisations of classical operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38871",
  "author_total": 3,
  "authors": [
    {
      "name": "Victor Barroso-Nascimento"
    },
    {
      "name": "Joaquim T. Waddington"
    },
    {
      "name": "Elaine Pimentel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0db0vrgr572vn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38871",
  "fulltext_url": null,
  "id": "0db0vrgr572vn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38871",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38871",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0db0vrgr572vn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38871",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38871"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Connecting Base-Extension Semantics, Beth Semantics, and Ecumenical Logic",
  "title_text": "Connecting Base-Extension Semantics, Beth Semantics, and Ecumenical Logic",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0db0vrgr572vn",
  "venue": "arXiv",
  "versions": []
}