# Evidential-Based Higher-Order Set Argumentation Framework

arXiv: https://arxiv.org/abs/2608.27824 · HTML: https://mlsanity.com/paper/2608.27824/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 32 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [Encoding Argumentation Frameworks to Propositional Logic Systems](https://mlsanity.com/paper/2503.07351/) (2025)

## Abstract (arXiv)

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 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 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 Lukasiewicz logic, its models correspond precisely to the adjacent complete labellings. We further extend this encoding to continuous fuzzy logics (G"odel, Product, and Lukasiewicz), 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.