{"path":"research/how-independent-reasons-add/argumentation-builders-on-probability.md","content":"# What the builders of gradual semantics say about probability and about adding independent reasons\n\n*Research helper report, kept verbatim. Written 2026-10-23 (night of 22 to 23 October) for his question:\n\"oh I meant to ask, does this new insight contradict modern argumentation theory and what the ppl who built\nQEM/QBAF or other modern argumentation theory software etc think?\" The helper (Explore, Sonnet) was briefed\nto skip what `../strength-calculus-literature/` already covers. Its own constraint note explains why it gives\nalmost no verbatim quotes. Two points it raises are answered in `../how-independent-reasons-add.md` § 9: its\nside note on 0.57 (the shipped code feeds QEM offsets from 0.5, not raw strengths; both figures hold) and the\nedge cases at strength 0 and 1.*\n\n---\n\nREPORT: Does log-odds addition with an explicit independence check contradict gradual argumentation theory?\n\nConstraint note. My output rules allow only one short verbatim quote (under 15 words) from observed sources, so you will not get the quotes you asked for. I give one quote (section 6), paraphrase everything else, and name the section, page or URL so you can pull the exact sentences. Formulas are quoted as math. \"(mine)\" marks my own derivations, which you can check. I did not find any quote or number that I had to invent. Items I could not find are marked NOT FOUND.\n\nStatus tags: FULL TEXT (all or nearly all read), PART (relevant sections read), ABSTRACT ONLY, SECONDARY (search-result summaries only).\n\n1. Why Potyka chose the quadratic impact\n\n- Potyka, \"Continuous Dynamical Systems for Weighted Bipolar Argumentation\", KR 2018, pp.148-157, cdn.aaai.org/ocs/17985/17985-78635-1-PB.pdf · FULL TEXT\n  - Section 2 gives two defects of earlier semantics.\n    - QuAD and DF-QuAD aggregate by multiplication. One strength-1 attacker or supporter saturates the aggregate, so one or one hundred such arguments look the same. This violates some Amgoud and Ben-Naim 2017 axioms.\n    - The Euler-based semantics fixes saturation with a linear sum, but treats attack and support asymmetrically. His example: base 0.5 plus one supporter gives about 0.589 (up 0.089). One attacker gives about 0.425 (down 0.075). Initial weights of 0 or 1 also break its axioms.\n  - Section 3 lists three design properties. Energy 0 gives back the base weight. Every attacker or supporter with positive strength pushes the strength toward 0 or 1. Positive and negative energy have symmetrical impact.\n  - Remark 1 says h is 0 for x <= 0, strictly increasing, and bounded by 1.\n  - Section 4 shows all Amgoud and Ben-Naim axioms hold, plus Duality.\n  - The conclusion takes a \"portfolio\" stance: the model may have flaws, and different behaviour suits different contexts.\n  - The introduction calls probabilistic degrees of belief \"one natural choice\" next to game-theoretic and ranking tools.\n  - Why exactly x squared, and small contributions near the base: NOT FOUND. (Mine: for small E, h(E) is about E squared, so E = 0.1 gives about 0.0099.)\n- Potyka, tutorial, arXiv:1811.12787 · PART\n  - It repeats the same two complaints. Strength in equilibrium is base + (1 - base) h(E) for E > 0.\n  - Its Directionality remark contrasts weighted semantics with probabilistic approaches (quoted in section 6).\n- Potyka, \"Extending Modular Semantics for Bipolar Weighted Argumentation\", AAMAS 2019, tech report arXiv:1809.07133v2 · PART\n  - QE is the p = 2 member of the p-Max influence family.\n  - Raising p increases the influence of aggregates above 1 and decreases it for aggregates below 1. This is his only comment on small aggregates.\n- Potyka, AAAI 2021, arXiv:2012.05738 · PART\n  - The MLP-based semantics is s = logistic(ln(base/(1-base)) + sum of w times s_b).\n  - He says QE was introduced to fix Euler's problems. He finds it \"more surprising\" that the MLP semantics satisfies the properties almost perfectly without being designed for them. It fails open-mindedness only at base scores 0 and 1.\n  - He chose the logistic function because values in 0 to 1 give a \"nice and simple interpretation\". Probability, log-odds and naive Bayes: NOT FOUND (grep).\n- Potyka and Booth, KR 2024, proceedings.kr.org/2024/56/kr2024-0056-potyka-et-al.pdf · FULL TEXT, including Fig. 4 read as an image\n  - It defines the MLP influence as iota_m(b,a) = logistic(ln(b/(1-b)) + a).\n  - Future work says it would be \"interesting to explore how QBAFs compare to probabilistic\" approaches. He treats that comparison as open.\n- Attractor and Uncertainpy README, github.com/nicopotyka/Uncertainpy · PART\n  - It shows only QuadraticEnergyModel in its example. It has no preference statement and no probability or log-odds statement. NOT FOUND. Talks: NOT FOUND.\n- Potyka, Yin and Toni, AAAI 2023, arXiv:2211.11699 · PART\n  - This is Dung-style bipolar argumentation with Markov networks, not QBAF strengths. No log-odds or QBAF link found.\n\n2. Do leading authors say strengths are, or are not, probabilities?\n\n- Amgoud, Doder and Vesic, \"Evaluation of Argument Strength in Attack Graphs\", Artificial Intelligence (2022; ScienceDirect pii S0004370221001582; I read the IRIT preprint www.irit.fr/~Leila.Amgoud/AIJ-V0.pdf) · PART\n  - This is the clearest \"are not\". In related work they say the weight w expresses intrinsic strength, not the probability of existence of the argument. Their principles are therefore unsuitable for the probabilistic setting.\n  - On Hunter and Thimm, they say such probability information belongs in the base weight, not the strength. Probabilities are given as extra input, so cannot be a semantics' output.\n  - They also state \"we assume that arguments are pairwise independent\".\n  - In the introduction, a base weight \"may represent\" probability of belief, certainty, votes or source trust.\n- Potyka tutorial, arXiv:1811.12787 · PART. It separates weighted approaches from probabilistic ones on Directionality (section 6).\n- Amgoud and Ben-Naim, IJAR 99 (2018) 39-55 · PART. Base strength may stand for premise certainty, link strength, values or trust. The output is just \"overall strength\". No probability commitment.\n- Baroni, Rago and Toni, AAAI 2018 · PART. The initial evaluation is on \"a chosen scale\". The principles are justified \"from a dialectical viewpoint\", with no probability reading.\n- Irwin, Rago and Toni, \"Forecasting Argumentation Frameworks\", KR 2022, arXiv:2205.11590 · PART\n  - Strength comes from DF-QuAD. They leave stricter rationality notions that \"may derive from probabilistic conceptions of argument strength\" to future work. So DF-QuAD strength is not treated as one.\n- Thieyre, Beynier, Destercke, Maudet and Vesic, KR 2026, proceedings.kr.org/2026/59 · PART. An initial weight may capture prior confidence, an initial bias, or aggregated user votes.\n- The other side:\n  - Morveli-Espinoza, Nieves and Tacla, NMR 2023, ceur-ws.org/Vol-3464/paper9.pdf · ABSTRACT ONLY. They say studied gradual semantics \"determine precise probability values\".\n  - Alviano, Giordano and Theseider Dupre, arXiv:2212.07523 · PART. They show a degree sigma(A) can be read as a subjective probability, the conditional probability of A given a labelling. This uses fuzzy-event probability, not Bayesian updating.\n  - Zhou et al., arXiv:2510.02339 · PART. They use the final score as a predicted probability in a Brier score.\n- NOT FOUND: explicit sentences from Cyras, Kampik, Bonzon, Delobelle, Doder (other than the AIJ paper), Vesic, Toni or Baroni. Delobelle and Villata 2019 concerns explaining impact, not probability.\n\n3. Work that compares or reconciles gradual semantics with probability or Bayes\n\n- DF-QuAD's aggregator is v1 + v2 - v1*v2, the probabilistic sum or noisy-OR. Irwin et al. (above) print the formula.\n  - Rago, Vasileiou, Toni, Son and Yeoh, arXiv:2410.22209v7 · PART. They suggest a probabilistic sum for disjunctive premises. It would match the intuition that independent supporting lines of reasoning strengthen a statement. They do not claim a theorem.\n- Mossakowski and Neuhaus, \"Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs\", arXiv:1807.06685 · PART\n  - Their \"sigmoid\" aggregation sums values passed through the inverse of tanh. This is a log-odds sum on the scale 0 to 1 (mine: atanh(d) = half of logit((1+d)/2)).\n  - Their stated motive is only to keep degrees bounded.\n- Munro, Bloch and Lesot, \"Aggregative Semantics for QBAFs\", arXiv:2603.06067 · PART\n  - In postulates P5 to P8 they use x1*x2/(1 - x1 - x2 + 2*x1*x2). That is the same as multiplying odds with neutral value 0.5 (mine; two 0.9 values give 0.988).\n  - They call it a \"hybrid\" or \"compromise\" operator. They do not name Bayes.\n  - It weakens when both inputs are below 0.5 and reinforces when both are above 0.5.\n- Thieyre et al., KR 2026 · PART. Belief functions over initial weights. They assume independent masses, and say this suits unknown or heterogeneous sources on online platforms but ignores correlations. They test on Kialo graphs.\n- Spaans and Doder, ECAI 2023 · SECONDARY. Gradual semantics when probabilities cover which arguments or attacks exist.\n- Hunter, Polberg and Thimm, \"Epistemic graphs\", Artificial Intelligence 2020 · SECONDARY. A probabilistic belief framework with positive and negative influences.\n- Tests against outcomes or people:\n  - Irwin et al. · PART. They claim improved forecasting accuracy with the full pipeline. This does not test strength as probability.\n  - Zhou et al. · PART. Brier scores for argumentative LLMs. Direct prompting for base scores did best. I did not see the numbers.\n  - Freedman et al., AAAI 2025, arXiv:2405.02079 · SECONDARY. Accuracy comparable to chain-of-thought.\n  - Teovanovic, Vesic and Yun, Artificial Intelligence 2025 (AAMAS 2022 version) · SECONDARY. Human compliance with principles.\n  - Pireaud et al., KR 2026 #102 · ABSTRACT ONLY. Learnable gradual semantics predict persuasion.\n  - Oren and Yun, IJCAI 2026 · PART. People confuse initial weights with final acceptability degrees. This matters for what your users type as reason strengths.\n- NOT FOUND: any paper comparing gradual strengths with Bayesian posteriors, or deriving a QBAF from a Bayesian network, or the reverse.\n\n4. Conservativeness, padding and independence discounts\n\n- Potyka and Booth 2024 · FULL TEXT. In Fig. 4, MLP-based semantics fails open-mindedness (only at base 0 or 1), absolute conservativeness and relative conservativeness (RC). It passes Duality.\n  - DF-QuAD passes RC but fails open-mindedness. QE is open-minded but fails RC. Only their new CRC semantics gets both.\n  - The text says only sum aggregation gives open-mindedness. Because the sum is unbounded, arguments of strength about 0.01 can matter a lot in large numbers.\n  - Mine: 20 reasons at 0.55 from start 0.5 give 0.982 under log-odds addition. Your channel shares this property, and your independence check is the remedy.\n- Amgoud, Bonzon, Delobelle, Doder, Konieczny and Maudet, KR 2018, cdn.aaai.org/ocs/18077/18077-78629-1-PB.pdf · PART\n  - Fully similar arguments count once. For partial similarity the redundant part is \"not counted twice\". They call their perspective normative.\n  - This supports your approach.\n- Munro et al. 2026 (P5): idempotent aggregation suits non-independent sources. Independent redundant information may reinforce.\n- Tang, \"Higher-Order Quadripolar Argumentation\", arXiv:2609.15008 · PART. The product t-norm models independent attacks and supports, and is non-idempotent. The Goedel (max) version takes the strongest only.\n- NOT FOUND: any paper pairing the logistic/MLP semantics with an independence or similarity discount.\n\n5. Software\n\n- Carneades (Gordon and Walton, CMNA 2006, cgi.csc.liv.ac.uk/~floriana/CMNA6/CMNA06Gordon.pdf; Gordon, Prakken and Walton 2007) · PART. Ordinal 0-10 weights. An argument's weight is its weakest premise. The preponderance standard compares the best pro with the best con. They rejected a 0-1 probability scale, doubting users can estimate weights that finely. This is max-style, not odds-multiplying.\n- Arg&Dec and designVUE (Aurisicchio, Baroni, Pellegrini and Toni, TAFA 2015) · SECONDARY. QuAD gradual semantics.\n- ArgLLM (Freedman et al.) uses DF-QuAD. ArgRAG (arXiv:2508.20131) uses QE. MArgE (arXiv:2508.02584) uses gradual semantics · SECONDARY.\n- Kialo · SECONDARY. User impact votes. Thieyre et al. apply gradual semantics to Kialo graphs offline. I found no statement that Kialo propagates strength itself.\n- Agena, BARD and Fenton and Neil idioms · SECONDARY.\n  - BARD is arXiv:2003.01207 (Nicholson, Korb et al.), with Lagnado and Hahn on the team. Fenton, Neil and Lagnado is Cognitive Science 37(1):61-102 (2013).\n  - Both use Bayesian networks, which update on all evidence jointly and handle dependence through structure.\n  - I could not confirm an explicit likelihood-ratio statement.\n- Rationale, OVA, ArgDF, ArguMed (DefLog), Tecuci's Disciple-EBR: no numeric combination rule found. NOT FOUND.\n- No tool outside Bayesian-network tools was found that adds log-odds across reasons.\n\n6. Strongest objections\n\n- Potyka tutorial, arXiv:1811.12787, section 2 · PART. Gradual semantics keep Directionality. Probabilistic approaches do not, which is the key point of difference: \"influence in both directions due to the nature of probability theory\".\n  - If strength means P(claim | record), a posterior should also flow back to the reasons. Your channel only flows forward.\n- Potyka and Booth 2024 (swamping) · FULL TEXT. An unbounded sum lets many near-worthless reasons overwhelm a base belief. This is the objection a QBAF author would lead with, and it is the one your independence check must answer.\n- Amgoud, Doder and Vesic (Principles 19 to 21) · PART. A semantics must pick one of three incompatible strategies: cardinality precedence, quality precedence or compensation.\n  - Their quality example is a Fields medalist outweighing three students. Log-odds addition is compensation.\n- Gordon and Walton, and Oren and Yun · PART. Users cannot give calibrated numbers and confuse base weights with outcomes.\n- Pollock, via Verheij, \"Arguments and Their Strength\", COMMA 2014, ai.rug.nl/~verheij/publications/pdf/comma2014.pdf · PART (Pollock SECONDARY). \"Generic Bayesianism\" fails on multi-premise inference, and Pollock preferred a weakest-link rule. Verheij answers that these concerns can be handled probabilistically.\n\nOverall answer\n\nLog-odds addition with an explicit independence check does not contradict mainstream gradual argumentation. It sits inside the modular framework: Potyka's MLP-based semantics already uses logit(base) plus a sum, and Mossakowski and Neuhaus have a tanh log-odds sum. DF-QuAD's aggregator is the probabilistic sum. The independence check matches the similarity-aware literature (Amgoud et al. KR 2018, Munro et al. 2026). It does depart on specific points.\n\n- Conservativeness. This channel fails absolute and relative conservativeness, as the MLP semantics does (Fig. 4). Unbounded sums let padding win. Your independence discount is the right remedy, but no paper pairs it with a logit-additive semantics.\n- Strict monotony and counting. Collapsing dependent reasons to the best one gives up counting for those reasons. Amgoud et al. endorse this for similar arguments.\n- Neutrality. Potyka's QE gives a zero-strength supporter no effect (KR 2018, Neutrality). Under your formula a fully relevant strength-0 reason gives alone value 0 and logit minus infinity (mine). At strength 1 you get the saturation Potyka criticised in QuAD. Clamp or define these cases.\n- Interpretation. The mainstream treats strength as a dialectical quantity, and Amgoud, Doder and Vesic say it is not a probability. Calling it P(claim | record) is your interpretive choice, and Potyka and Booth call that comparison open. Directionality is the main structural reason the two diverge.\n\nOne side note. Plain QE (base 0.5, supporters at 0.9) gives 0.724 for one and 0.882 for two (mine). I could not reproduce your quoted 0.57 and 0.70, so the shipped code may use other settings.\n"}