Evidential-Based Higher-Order Set Argumentation Framework
Artificial Intelligence
Summary
The authors propose a new framework called EHSAF that improves how arguments supported by evidence are structured and evaluated, especially when dealing with complex situations like cycles of support or attacks. They introduce two ways to decide which arguments hold: one that allows for uncertainty and another that only accepts arguments firmly backed by evidence. They prove these methods behave differently in tricky cases but are equivalent when there are no cycles. To help computers reason with their framework, they translate it into logical formulas, including versions that handle gradual truth values instead of just true or false. This work connects detailed argument structures with both clear and fuzzy ways to handle evidence, helping bridge qualitative and quantitative reasoning.
Authors
Shuai Tang
Abstract
Evidential argumentation extends Dung's abstract argumentation by requiring arguments and interactions to be backed by chains of evidence rooted in prima-facie elements. However, existing formalisms lack a unified treatment of evidential support, higher-order relations (attacks and supports targeting arbitrary elements), and collective interactions (sources as sets). In this paper, we introduce the Evidential-Based Higher-Order Set Argumentation Framework (EHSAF), which conservatively generalises several existing frameworks within a single expressive setting. We develop two complete semantics for EHSAFs: an \emph{adjacent complete labelling semantics} that admits multiple truth values (true, false, undecided) for arguments in support cycles, reflecting an open epistemic attitude toward future evidence; and an \emph{extension-based complete semantics} that follows a strict evidentialist stance, accepting only arguments with well-founded support chains. We show that these two semantics diverge in the presence of support cycles, and prove their equivalence under support-acyclicity. To enable computational reasoning, we provide a normal propositional encoding of EHSAFs and prove that, in three-valued Łukasiewicz logic, its models correspond precisely to the adjacent complete labellings. We further extend this encoding to continuous fuzzy logics (G{ö}del, Product, and Łukasiewicz), defining a continuous fuzzy normal encoded semantics. We establish that this fuzzy semantics satisfies key properties---continuity, monotonicity, boundary conditions, and solution existence---and that its ternarisation recovers the adjacent complete labellings under natural t-norm conditions. Our framework thus unifies expressive argumentation with principled three-valued and fuzzy semantics, bridging the gap between qualitative and quantitative reasoning about evidence.