Abductive Reasoning in a Paraconsistent Framework

• URL: http://arxiv.org/abs/2408.07287v2
• Date: Fri, 23 Aug 2024 14:05:17 GMT
• Title: Abductive Reasoning in a Paraconsistent Framework
• Abstract summary: We consider two expansions of the well-known Belnap-Dunn paraconsistent four-valued logic $mathsfBD$. We show how to reduce abduction in $mathsfBD_circ$ and $mathsfBD_triangle$ to abduction in classical propositional logic.
• Score: 7.4842212802498755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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