Encoding argumentation frameworks with set attackers to propositional logic systems
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914174218534912 |
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| author | Tang, Shuai Wu, Jiachao Zhou, Ning |
| author_facet | Tang, Shuai Wu, Jiachao Zhou, Ning |
| contents | Argumentation frameworks ($AF$s) have been a useful tool for approximate reasoning. The encoding method is an important approach to formally model $AF$s under related semantics. The aim of this paper is to develop the encoding method from classical Dung's $AF$s ($DAF$s) to $AF$s with set attackers ($AFSA$s) including higher-level argumentation frames ($HLAF$s), Barringer's higher-order $AF$s ($BHAF$s), frameworks with sets of attacking arguments ($SETAF$s) and higher-order set $AF$s ($HSAF$s). Regarding syntactic structures, we propose the $HSAF$s where the target of an attack is either an argument or an attack and the sources are sets of arguments and attacks. Regarding semantics, we translate $HLAF$s and $SETAF$s under respective complete semantics to Łukasiewicz's 3-valued propositional logic system ($PL_3^L$). Furthermore, we propose complete semantics of $BHAF$s and $HSAF$s by respectively generalizing from $HLAF$s and $SETAF$s, and then translate to the $PL_3^L$. Moreover, for numerical semantics of $AFSA$s, we propose the equational semantics and translate to fuzzy propositional logic systems ($PL_{[0,1]}$s). This paper establishes relationships of model equivalence between an $AFSA$ under a given semantics and the encoded formula in a related propositional logic system ($PLS$). By connections of $AFSA$s and $PLS$s, this paper provides the logical foundations for $AFSA$s associated with complete semantics and equational semantics. The results advance the argumentation theory by unifying $HOAF$s and $SETAF$s under logical formalisms, paving the way for automated reasoning tools in AI, decision support, and multi-agent systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Encoding argumentation frameworks with set attackers to propositional logic systems Tang, Shuai Wu, Jiachao Zhou, Ning Logic 68T27, 03B70, 03B50 F.4.1; I.2.4; I.2.3 Argumentation frameworks ($AF$s) have been a useful tool for approximate reasoning. The encoding method is an important approach to formally model $AF$s under related semantics. The aim of this paper is to develop the encoding method from classical Dung's $AF$s ($DAF$s) to $AF$s with set attackers ($AFSA$s) including higher-level argumentation frames ($HLAF$s), Barringer's higher-order $AF$s ($BHAF$s), frameworks with sets of attacking arguments ($SETAF$s) and higher-order set $AF$s ($HSAF$s). Regarding syntactic structures, we propose the $HSAF$s where the target of an attack is either an argument or an attack and the sources are sets of arguments and attacks. Regarding semantics, we translate $HLAF$s and $SETAF$s under respective complete semantics to Łukasiewicz's 3-valued propositional logic system ($PL_3^L$). Furthermore, we propose complete semantics of $BHAF$s and $HSAF$s by respectively generalizing from $HLAF$s and $SETAF$s, and then translate to the $PL_3^L$. Moreover, for numerical semantics of $AFSA$s, we propose the equational semantics and translate to fuzzy propositional logic systems ($PL_{[0,1]}$s). This paper establishes relationships of model equivalence between an $AFSA$ under a given semantics and the encoded formula in a related propositional logic system ($PLS$). By connections of $AFSA$s and $PLS$s, this paper provides the logical foundations for $AFSA$s associated with complete semantics and equational semantics. The results advance the argumentation theory by unifying $HOAF$s and $SETAF$s under logical formalisms, paving the way for automated reasoning tools in AI, decision support, and multi-agent systems. |
| title | Encoding argumentation frameworks with set attackers to propositional logic systems |
| topic | Logic 68T27, 03B70, 03B50 F.4.1; I.2.4; I.2.3 |
| url | https://arxiv.org/abs/2504.08370 |