Abductive Reasoning in a Paraconsistent Framework
<|reference_start|>Abductive Reasoning in a Paraconsistent Framework: 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 $\circ\phi$ (the information on $\phi$ is reliable), while $\mathsf{BD}_\triangle$ augments the language with $\triangle\phi$'s (there is information that $\phi$ 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.<|reference_end|>
@article{bienvenu2024abductive,
    title={Abductive Reasoning in a Paraconsistent Framework},
    author={Meghyn Bienvenu and Katsumi Inoue and Daniil Kozhemiachenko},
    journal={arXiv preprint arXiv:2408.07287},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07287},
    primaryClass={cs.LO cs.AI math.LO}
}