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Higher-Order Quadripolar Argumentation Framework and Encoded Semantics

  • Shuai Tang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{tang2026higherorder,
  title = {{Higher-Order Quadripolar Argumentation Framework and Encoded Semantics}},
  author = {Shuai Tang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15008},
  eprint = {2609.15008},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15008},
}
RIS
TY  - UNPB
TI  - Higher-Order Quadripolar Argumentation Framework and Encoded Semantics
AU  - Shuai Tang
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15008
UR  - https://arxiv.org/abs/2609.15008
AB  - 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.
ER  -