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Higher-Order Quadripolar Argumentation Framework and Encoded Semantics — arXiv:2609.15008

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.15008
License (as archived): CC0-1.0
Archived: 2026-10-16T01:38:27.054Z
SHA-256 of the archived text: bcd1fd5c0bcc06a7c05981a86e316a8b200e54ee3fc1c697a31af5ceba66bd8c
Stable URL of this page: https://metraipolis.com/documento/dc_e4e768a642bd

How to cite

Higher-Order Quadripolar Argumentation Framework and Encoded Semantics — arXiv:2609.15008 — arXiv (en), https://arxiv.org/abs/2609.15008 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e4e768a642bd (Metraipolis archive dc_e4e768a642bd, sha256 bcd1fd5c0bcc06a7c05981a86e316a8b200e54ee3fc1c697a31af5ceba66bd8c)

BibTeX

@misc{dce4e768a642bd,
  title = {Higher-Order Quadripolar Argumentation Framework and Encoded Semantics — arXiv:2609.15008},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.15008},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e4e768a642bd; sha256 bcd1fd5c0bcc06a7c05981a86e316a8b200e54ee3fc1c697a31af5ceba66bd8c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.15008. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.LO).
Categorie arXiv: Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2609.15008 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T01:22:41.485Z dalla pagina https://arxiv.org/catchup/math.LO/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).