{"path":"research/qbaf-gradual-semantics-research.md","content":"# QBAF Gradual Semantics Research: QEM as Optimal Choice\n\n**Date**: March 31, 2026 (Session 7)\n**Status**: Research complete. QEM selected for implementation.\n**Type**: Deep technical research with web search + existing doc synthesis\n\n---\n\n## The Question\n\nWhat is the optimal gradual semantics function for computing argument strength in Deliberus's QBAF, where:\n- Arguments have numeric strength (0.0-1.0)\n- Arguments can both support AND attack each other (bipolar)\n- Critical questions (CQs) have positive and negative polarity claims\n- Most CQs start unanswered at 0.5 (agnostic prior)\n- The system needs to evolve as community contributes evidence\n\n---\n\n## Six Contenders Evaluated\n\n### 1. DF-QuAD (Discontinuity-Free Quantitative Argumentation Debate)\n**Authors**: Rago, Toni, Aurisicchio, Baroni (Imperial/Brescia, KR 2016)\n\nProduct-based aggregation: `SF(a) = 0.5 + 0.5 * (∏(1-att_k) - ∏(1-sup_m))`. Satisfies anonymity, independence, directionality, continuity. **Saturation problem**: once ANY attacker has strength 1, all other attackers become irrelevant. One killer argument erases everything else — problematic for deliberation.\n\n### 2. Euler-based\n**Authors**: Amgoud & Ben-Naim (CNRS-IRIT, ECSQARU 2017)\n\nExponential impact: `s(a) = 1 - (1-w)²/(1+w*exp(E))` where E = sum(supporters) - sum(attackers). Satisfies resilience. **Critical flaw**: arguments at weight 0 or 1 are **immutable** — they can never change regardless of evidence. Also asymmetric treatment of attacks vs supports.\n\n### 3. QEM (Quadratic Energy Model) — SELECTED\n**Authors**: Nico Potyka (Cardiff, KR 2018, updated KR 2024)\n\nEnergy-based with quadratic impact:\n```python\nE = sum(supporter_strengths) - sum(attacker_strengths)\nh(x) = max(x, 0)² / (1 + max(x, 0)²)\n\nif E > 0: strength = w + (1-w) * h(E)     # evidence FOR shifts up\nif E < 0: strength = w - w * h(-E)         # evidence AGAINST shifts down\nif E = 0: strength = w                      # no evidence = stay at prior\n```\n\nSatisfies ALL desirable properties: anonymity, independence, directionality, monotonicity, equivalence, resilience, open-mindedness, symmetry, bounded [0,1], gravity toward initial weight. No saturation. Arguments at 0/1 CAN change. Convergence empirically validated on 3,000+ random graphs.\n\n### 4. h-categorizer\n**Authors**: Besnard & Hunter (2001)\n\n`Cat(a) = 1/(1 + Σ Cat(attackers))`. Elegant but no base scores — purely topology-driven. **Dealbreaker for Deliberus**: CQs have initial states that must be representable.\n\n### 5. Modular Semantics (Mossakowski & Neuhaus, 2018)\nMeta-framework decomposing computation into aggregation + influence + combination functions. Both DF-QuAD and Euler-based expressible within it. Useful as architectural pattern, not a specific semantics.\n\n### 6. Aggregative Semantics (Munro, Bloch, Lesot — March 2026)\nBrand-new (arXiv:2603.06067). Three-stage: aggregate attackers separately, aggregate supporters separately, combine with intrinsic weight. Tested 500 different parameter combinations. Promising but no implementations or adoption yet.\n\n---\n\n## Why QEM Wins for Deliberus\n\n| Property | Why it matters for deliberation |\n|---|---|\n| **Gravity toward initial weight** | Unanswered CQs (0.5) stay at 0.5 until evidence arrives. Epistemic conservatism: \"mapped perspectives, not truth\" |\n| **No saturation** | Every CQ contributes proportionally. Many weak supports can collectively strengthen; one strong attacker doesn't erase everything |\n| **Open-mindedness** | Even extreme claims (0.1 or 0.9) can be moved by sufficient evidence. No position is frozen |\n| **Symmetric** | Attacks and supports have equal impact. No asymmetric advantage to either side |\n| **Explainable** | Energy = supporters - attackers. Users see: \"this claim has +3.2 energy from 5 supporters, -1.1 from 2 attackers\" |\n| **Gravity = Bayesian prior behavior** | The initial weight acts like a Bayesian prior. Evidence updates it proportionally. This IS the rational probabilistic behavior |\n\n---\n\n## The QEM Formula for Deliberus's CQ Model\n\n```python\ndef qem_edge_strength(base_weight: float, pos_strengths: list[float], neg_strengths: list[float]) -> float:\n    \"\"\"Compute QBAF edge strength using QEM gradual semantics.\n\n    base_weight: Initial edge weight (0.5 for unanswered, adjustable)\n    pos_strengths: Strengths of positive CQ polarity claims (supporters)\n    neg_strengths: Strengths of negative CQ polarity claims (attackers)\n    \"\"\"\n    energy = sum(pos_strengths) - sum(neg_strengths)\n    h = lambda x: max(x, 0)**2 / (1 + max(x, 0)**2)\n\n    if energy > 0:\n        return base_weight + (1 - base_weight) * h(energy)\n    elif energy < 0:\n        return base_weight - base_weight * h(-energy)\n    else:\n        return base_weight\n```\n\n**Behavior examples:**\n- All CQs unanswered (0.5 each): energy ≈ 0 → strength = 0.5 (agnostic)\n- 3 positive CQs at 0.8, 1 negative at 0.3: energy = 2.4 - 0.3 = 2.1 → h(2.1) = 0.815 → strength = 0.5 + 0.5 × 0.815 = 0.91 (strong support)\n- 1 positive at 0.6, 2 negative at 0.9: energy = 0.6 - 1.8 = -1.2 → h(1.2) = 0.59 → strength = 0.5 - 0.5 × 0.59 = 0.20 (challenged)\n\n---\n\n## Recent Academic Landscape (Oct 2025 — Mar 2026)\n\n35 papers surveyed. Key findings organized by relevance:\n\n### Directly Aligned with Deliberus\n\n1. **\"Argumentative Human-AI Decision-Making\"** (Vasileiou, Rago, Toni, Yeoh — AAMAS 2026 Blue Sky): Vision paper arguing AI should reason WITH humans, not FOR them. Decisions must be contestable and revisable. **This IS Deliberus's thesis in academic form.**\n\n2. **\"Explaining Online Debate Evolution under Bipolar Gradual Semantics\"** (Sorbonne, ICAART 2026): Tracks argument strength changes as debates evolve over time. Almost exactly Deliberus's problem domain.\n\n3. **\"ArgLLM-App\"** (Dejl, Gorur, Toni — Imperial, Feb 2026): Working web system combining LLMs + computational argumentation. Closest existing system. Key difference: binary decisions vs Deliberus's multi-perspective deliberation.\n\n### Validates Our Architecture\n\n4. **\"ArgRAG\"** (Zhu, Potyka et al., PMLR Oct 2025): Uses QBAFs to make RAG explainable. First production application of QBAF gradual semantics with LLMs. Retrieved docs become arguments with bipolar strength.\n\n5. **\"Can LLMs Judge Debates?\"** (Sanayei et al., EMNLP 2025): LLMs fail at non-linear argument dependencies and miss attack/support cascades. **Validates our design**: formal graph structure is needed because LLMs can't \"just figure out\" argument strength.\n\n6. **\"ClaimFlow\"** (Pramanick et al., TU Darmstadt, Mar 2026): 304 papers → 1,084 claims → 832 cross-paper relations (supports/extends/qualifies/refutes). 63.5% of claims never reused; only 11.1% ever challenged. Validates our relation types.\n\n7. **\"Fact in Fragments\"** (Zheng et al., Nov 2025): Decomposing complex claims into atomic facts improves verification. Validates DnDScore (Pass 2a/2b).\n\n### QBAF Theory Advances\n\n8. **\"Change in QBAF: Explanations\"** (Kampik et al., Sep 2025): Formalizes sufficient, necessary, and counterfactual explanations for QBAF strength changes. Directly applicable to \"why did this claim's standing change?\"\n\n9. **\"Set Contribution Functions for QBAFs\"** (IJCAI 2025): Measures how SETS of arguments contribute collectively. Relevant to argument bundles.\n\n10. **\"Aggregative Semantics\"** (Munro et al., Mar 2026): Newest research. Three-stage decomposition matches Deliberus's CQ model (positive CQs ≠ negative CQs aggregated separately).\n\n### Key Research Group\n\n**Francesca Toni's group at Imperial College London** is the closest academic alignment to Deliberus. They published ArgLLM-App, the AAMAS vision paper, and collaborate with Potyka (QEM inventor). Potential future collaboration partner.\n\n---\n\n## Implementation Notes\n\n**Energy scale**: With many CQs (e.g., 6 per scheme), energy can grow to ±6. h(6) = 36/37 = 0.97 — nearly maxed. Consider normalizing by CQ count if you want more gradual response, or keep cumulative if you want more CQs = more certainty.\n\n**Cyclic graphs**: Current extraction produces acyclic graphs. QEM handles cycles via Runge-Kutta integration (empirically convergent). Cross-extraction auto-connect edges could create cycles — QEM handles this gracefully.\n\n**Open-mindedness vs conservativeness**: Potyka's KR 2024 paper addresses this tension. Very weak arguments in QEM can accumulate to override strong priors. If this is undesirable, bounded-conservative variants exist.\n\n---\n\n## QEM Properties Observed in Production Use (Jul 2026)\n\nTwo properties surfaced by the hinge-score work (QBAF sensitivity analysis over the decomposition channel — the `/claims/{id}/hinge` endpoint; see [dogfood-run-1-friction-log.md §I2/§I4](dogfood-run-1-friction-log.md)):\n\n- **Additivity protects pebbles from burial.** Subclaim energy is a sum of per-child deviations from the prior, so a sibling sitting at 0.5 contributes exactly zero: a claim's hinge among nine agnostic siblings equals its solo hinge. Templated CQ scaffolding can crowd the *reading* experience but cannot drown a crux in the *strength math*; only high-saturation sibling sets (many strongly-supported children pushing the energy onto the impact curve's flat tail) shrink the marginal hinge. Discovered by a test whose first version wrongly assumed DF-QuAD-style dilution — pinned as `test_neutral_siblings_do_not_dilute_saturated_ones_do`.\n- **Calibration: one leaf flip ≈ 2 percentage points at shipped weights.** With `weight_per_subclaim = 0.3`, clamping a single child granted↔denied swings ±0.15 energy through the shallow region of h(x), moving the parent ~0.022 in strength. The hinge is therefore a *ranking* instrument at current graph maturity, not a drama meter; the subclaim weight is the tuning knob if single cruxes should ever visibly swing conclusions — to be tuned from observed engagement, not up front.\n\n---\n\n## Cross-References\n\n- [conceptual-threads.md §Thread 5](../conceptual-threads.md) — Probabilistic Argument Graph (QBAF as formal backbone)\n- [inductive-reasoning-research.md](../inductive-reasoning-research.md) — BIRD framework, Bayesian integration\n- [scheme-bounded-decomposition-and-evidence-as-subgraph.md](scheme-bounded-decomposition-and-evidence-as-subgraph.md) — CQ architecture that feeds into QBAF\n- [walton-argument-schemes.md](walton-argument-schemes.md) — 96 schemes providing CQ templates\n- [prediction-markets-argumentation.md](prediction-markets-argumentation.md) — LMSR for factual claims; QBAF for argument structure\n- [.claude/specs/scheme-bounded-decomposition/](../../.claude/specs/scheme-bounded-decomposition/) — spec referencing QBAF badge computation\n\n### Key Academic References\n\n- Potyka, N. \"Continuous Dynamical Systems for Weighted Bipolar Argumentation.\" KR 2018.\n- Potyka, N. & Booth, R. \"Balancing Open-Mindedness and Conservativeness.\" KR 2024.\n- Rago, A. et al. \"Discontinuity-Free Decision Support with Quantitative Argumentation Debates.\" KR 2016.\n- Amgoud, L. & Ben-Naim, J. \"Weighted Bipolar Argumentation Graphs: Axioms and Semantics.\" IJCAI 2018.\n- Munro, Y. et al. \"Aggregative Semantics for QBAFs.\" arXiv:2603.06067, Mar 2026.\n- Vasileiou, S.L. et al. \"Argumentative Human-AI Decision-Making.\" AAMAS 2026.\n- Kampik, T. et al. \"Change in QBAF: Explanations.\" arXiv:2509.18215, Sep 2025.\n"}