Encoding higher-order argumentation frameworks with supports to propositional logic systems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915698365693952 |
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| author | Tang, Shuai |
| author_facet | Tang, Shuai |
| contents | Argumentation frameworks ($AF$s) have been extensively developed, but existing higher-order bipolar $AF$s suffer from critical limitations: attackers and supporters are restricted to arguments, multi-valued and fuzzy semantics lack unified generalization, and encodings often rely on complex logics with poor interoperability. To address these gaps, this paper proposes a higher-order argumentation framework with supports ($HAFS$), which explicitly allows attacks and supports to act as both targets and sources of interactions. We define a suite of semantics for $HAFS$s, including extension-based semantics, adjacent complete labelling semantics (a 3-valued semantics), and numerical equational semantics ([0,1]-valued semantics). Furthermore, we develop a normal encoding methodology to translate $HAFS$s into propositional logic systems ($\mathcal{PLS}$s): $HAFS$s under complete labelling semantics are encoded into Łukasiewicz's three-valued propositional logic ($\mathcal{PL}_3^L$), and those under equational semantics are encoded into fuzzy $\mathcal{PLS}$s ($\mathcal{PL}_{[0,1]}$) such as Gödel and Product fuzzy logics. We prove model equivalence between $HAFS$s and their encoded logical formulas, establishing the logical foundation of $HAFS$ semantics. Additionally, we investigate the relationships between 3-valued complete semantics and fuzzy equational semantics, showing that models of fuzzy encoded semantics can be transformed into complete semantics models via ternarization, and vice versa for specific t-norms. This work advances the formalization and logical encoding of higher-order bipolar argumentation, enabling seamless integration with lightweight computational solvers and uniform handling of uncertainty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Encoding higher-order argumentation frameworks with supports to propositional logic systems Tang, Shuai Logic 68T27, 03B70, 03B50 F.4.1; I.2.4; I.2.3 Argumentation frameworks ($AF$s) have been extensively developed, but existing higher-order bipolar $AF$s suffer from critical limitations: attackers and supporters are restricted to arguments, multi-valued and fuzzy semantics lack unified generalization, and encodings often rely on complex logics with poor interoperability. To address these gaps, this paper proposes a higher-order argumentation framework with supports ($HAFS$), which explicitly allows attacks and supports to act as both targets and sources of interactions. We define a suite of semantics for $HAFS$s, including extension-based semantics, adjacent complete labelling semantics (a 3-valued semantics), and numerical equational semantics ([0,1]-valued semantics). Furthermore, we develop a normal encoding methodology to translate $HAFS$s into propositional logic systems ($\mathcal{PLS}$s): $HAFS$s under complete labelling semantics are encoded into Łukasiewicz's three-valued propositional logic ($\mathcal{PL}_3^L$), and those under equational semantics are encoded into fuzzy $\mathcal{PLS}$s ($\mathcal{PL}_{[0,1]}$) such as Gödel and Product fuzzy logics. We prove model equivalence between $HAFS$s and their encoded logical formulas, establishing the logical foundation of $HAFS$ semantics. Additionally, we investigate the relationships between 3-valued complete semantics and fuzzy equational semantics, showing that models of fuzzy encoded semantics can be transformed into complete semantics models via ternarization, and vice versa for specific t-norms. This work advances the formalization and logical encoding of higher-order bipolar argumentation, enabling seamless integration with lightweight computational solvers and uniform handling of uncertainty. |
| title | Encoding higher-order argumentation frameworks with supports to propositional logic systems |
| topic | Logic 68T27, 03B70, 03B50 F.4.1; I.2.4; I.2.3 |
| url | https://arxiv.org/abs/2512.23507 |