{
  "abstract": "This paper introduces the Higher-Order Quadripolar Argumentation Framework (HQAF), which extends bipolar frameworks by allowing attacks and three types of supports---necessary, deductive, and evidential---to interact at higher order. In HQAF, each interaction may have as its source and target an argument, an attack, or a support. We provide a 3-valued semantics via adjacent complete labellings and equational systems, and define encoded semantics directly in propositional logics, mainly Łukasiewicz three-valued logic for the 3-valued case and fuzzy logics based on continuous t-norms (Gödel, Product, Łukasiewicz) for the fuzzy case. Model equivalence between HQAF and its normal encoding is established. The fuzzy equational semantics is shown to be a specific formalism of the fuzzy encoded semantics, and ternarization connects fuzzy models to 3-valued complete labellings. The study is confined to non-set HQAF; collective interactions are reserved for future work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15008",
  "author_total": 1,
  "authors": [
    {
      "name": "Shuai Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2gbfxqhaenwt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15008",
  "fulltext_url": null,
  "id": "f2gbfxqhaenwt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15008",
  "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",
      "math.LO"
    ],
    [
      "openalex",
      "1702|Multi-Agent Systems and Negotiation"
    ]
  ],
  "openalex": "W7213240730",
  "pdf_url": "https://arxiv.org/pdf/2609.15008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2gbfxqhaenwt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15008"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Higher-Order Quadripolar Argumentation Framework and Encoded Semantics",
  "title_text": "Higher-Order Quadripolar Argumentation Framework and Encoded Semantics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/f2gbfxqhaenwt",
  "venue": "arXiv",
  "versions": []
}