Abductive Reasoning in a Paraconsistent Framework
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| author | Bienvenu, Meghyn Inoue, Katsumi Kozhemiachenko, Daniil |
| author_facet | Bienvenu, Meghyn Inoue, Katsumi Kozhemiachenko, Daniil |
| contents | We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic $\mathsf{BD}$: $\mathsf{BD}_\circ$ introduces formulas of the form $\circϕ$ (the information on $ϕ$ is reliable), while $\mathsf{BD}_\triangle$ augments the language with $\triangleϕ$'s (there is information that $ϕ$ is true). We define and motivate the notions of abduction problems and explanations in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ and show that they are not reducible to one another. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance / necessity of hypotheses) in both logics. Finally, we show how to reduce abduction in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ to abduction in classical propositional logic, thereby enabling the reuse of existing abductive reasoning procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abductive Reasoning in a Paraconsistent Framework Bienvenu, Meghyn Inoue, Katsumi Kozhemiachenko, Daniil Logic in Computer Science Artificial Intelligence Logic We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic $\mathsf{BD}$: $\mathsf{BD}_\circ$ introduces formulas of the form $\circϕ$ (the information on $ϕ$ is reliable), while $\mathsf{BD}_\triangle$ augments the language with $\triangleϕ$'s (there is information that $ϕ$ is true). We define and motivate the notions of abduction problems and explanations in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ and show that they are not reducible to one another. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance / necessity of hypotheses) in both logics. Finally, we show how to reduce abduction in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ to abduction in classical propositional logic, thereby enabling the reuse of existing abductive reasoning procedures. |
| title | Abductive Reasoning in a Paraconsistent Framework |
| topic | Logic in Computer Science Artificial Intelligence Logic |
| url | https://arxiv.org/abs/2408.07287 |