Abductive Reasoning in a Paraconsistent Framework
This work addresses the challenge of handling inconsistency in logical reasoning for AI and knowledge representation, though it appears incremental as it builds on established paraconsistent frameworks.
The paper tackles the problem of abductive reasoning from inconsistent theories by using paraconsistent logics, specifically extensions of Belnap-Dunn logic, and shows that abduction tasks in these logics can be reduced to classical propositional logic for reuse of existing procedures.
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.