Hypothesis-Driven Disjunctive Reasoning in Logical Argumentation

Abstract

Disjunctive reasoning, or reasoning by cases, plays a central role in defeasible frameworks and normative systems. This paper adopts a cautious approach, suggesting that rebutting disjunctive paths may render the inference defeasible, particularly in the context of default-based reasoning. To formalize this, we introduce explicit hypotheses to track reasoning paths. Building on prior work, we refine a class of Argument Calculi into a robust method for disjunctive reasoning in nonmonotonic logics, for both normative and doxastic interpretations of our system. We propose meta-theoretical properties tailored to disjunctive reasoning: disjunctive consistency and hypothetical consistency, which constrain argument behavior involving disjunction. By systematically comparing Argument Calculi against several properties, we analyze their implications for consistency and nonmonotonic inference in default-based frameworks.