2024/08/01 by Meghyn Bienvenu, Katsumi Inoue, Bienvenu, Meghyn +3
Computer Science · #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation
paper · pdf · doi:10.48550/arxiv.2408.07287
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 BD: BD_∘ introduces formulas of the form ∘ϕ (the information on ϕ is reliable), while 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 BD_∘ and 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 BD_∘ and BD_\triangle to abduction in classical propositional logic, thereby enabling the reuse of existing abductive reasoning procedures.