New Logic System Handles Contradictory Hypotheses in Abductive Reasoning

Abductive reasoning, which involves inferring the best explanation for observed phenomena, often encounters situations where explanatory hypotheses might be contradictory. Traditional logical systems typically falter in such scenarios, leading to a "trivialization" where any conclusion can be derived, rendering the system useless. This research tackles this fundamental challenge by introducing a novel approach to handle inconsistencies. Building upon Maurice Pagnucco's foundational work on abductive expansion, this paper presents a new paraconsistent AGM-like abductive expansion operation. This operation is designed to assimilate contradictory explanatory hypotheses without collapsing into an absurd epistemic state. Its development was made possible by the recent creation of RCbr, a Logics of Formal Inconsistencies (LFI) that is self-extensional, meaning it satisfies the replacement property crucial for belief revision. This new operation is part of a system called AGMpabd and represents a significant step in formalizing abductive reasoning under inconsistency. While this initial paper focuses on the core expansion operation, a subsequent work is planned to further enhance it by assigning a more explicit epistemic role to paraconsistent negation and consistency operators. This work marks the first instance of such an operation in the AGM literature, offering a robust framework for reasoning with conflicting information.