{"path":"research/folded-routes-and-shared-premises/folding-paths-report-2026-10-23.md","content":"# Folding and unfolding a long inferential chain: a research helper's report, as returned (2026-10-23)\n\n*A research helper (Claude Sonnet 5.5) was asked, read-only, for prior art on folding a path of\nlinks into one drawn connection and unfolding it, how such tools label a folded path, how strength\nalong a chain is computed, and user studies on folded against flat chains; a follow-up asked for\nthe sources on whether probabilistic support carries along a chain. Kept verbatim; nothing below\nwas rewritten. Two items it cites are arXiv papers dated August 2026 that it could not cross-check.\nRead by the note that uses it: [../folded-routes-and-shared-premises.md](../folded-routes-and-shared-premises.md).*\n\n---\n\nRESEARCH REPORT: folding and unfolding a long inferential chain in an argument map\n\nStatus tags: [full text] = read in full; [part] = read in part, including long excerpts returned by search; [abstract only]; [secondary] = reported by another paper. Nothing is invented. Where I found no source I say so. Two arXiv items below are dated August 2026 (2608.*) and I could not cross-check them elsewhere.\n\n0. HEADLINE ANSWERS\n- No source I found tests \"folded chain vs the same chain drawn flat\" for readers' understanding of inferential chains in argument maps. The nearest evidence is indirect (section 4).\n- Whether a folded path can carry one derived strength depends on the kind of step. If each step is a deductive entailment, composition is safe. If steps are probabilistic or defeasible, the literature says \"supports\" is generally not transitive and a single derived arrow is not automatically meaningful (section 5).\n\n1. PRIOR ART FOR FOLDING A PATH INTO ONE DRAWN EDGE AND UNFOLDING IT\n\n1a. Degree of interest (DOI). van Ham & Perer 2009, \"Search, Show Context, Expand on Demand\". https://perer.org/papers/adamPerer-DOIGraphs-InfoVis2009.pdf [part]\n- It extends Furnas's DOI from trees to graphs. The user picks a focus, the system extracts a bounded high-interest subgraph, and the user expands it in a chosen direction.\n- Interest is \"diffused\" over the graph, because plain thresholding gives disconnected pieces. A node's interest is the maximum of its own and a fraction of its best neighbour's.\n- The method is node-centred and has no notion of folding a path into one edge. It supplies the selection logic for what to unfold first. DOI also hides the low-interest part of a very high-degree node and marks where more can be found.\n- The paper is tested on a legal citation graph (300,000+ nodes, 3.3 million edges). The abstract states the method was demonstrated by exploration of that graph. I saw no user study in the excerpts.\n\n1b. Meta-edges in compound graphs.\n- Raitner, \"Visual Navigation of Compound Graphs\" (GD 2004). https://raitner.de/wp-content/uploads/2010/07/gd04.pdf [abstract + introduction]. A view contracts subgraphs into meta nodes. The stated design goal is a mental-map-preserving update: untouched nodes keep their levels and order, and \"expanded edges take the same course as the corresponding contracted edge\". Useful as a rule for unfolding, since the unfolded chain should leave the folded edge's route.\n- Doğrusöz et al. 2018, PLOS ONE, Cytoscape.js expand-collapse. https://doi.org/10.1371/journal.pone.0197238 [abstract + part]. Meta edges stand in for edges whose end is hidden. They keep only one meta edge per hidden original edge, the result is independent of the order of expand/collapse, and each meta edge stores a pointer to its original edge. They also report that plain unhide operations without a specialised layout re-calculation tangle the map and ruin the user's mental map.\n- Limit: both fold regions (nodes), not a path between two chosen nodes.\n\n1c. Path-preserving views, with a correctness criterion. This is the closest formal match I found. ZOOM*UserViews / WOLVES (provenance workflows).\n- Sources: https://ceur-ws.org/Vol-526/InvitedPaper_3.pdf [part]; https://www.cis.upenn.edu/~sanjeev/papers/icdt09_user_views.pdf [part]; https://web.njit.edu/~ychen/publications/sigmod09.pdf [abstract/snippet].\n- A user view partitions modules into composite modules. Internal steps and the data passed between them are hidden.\n- A good view is \"sound\" (no dependency path is introduced that does not exist in the original) and \"complete\" (no path is removed) between the modules the user cares about. Unsound views are said to be \"misleading and lead to incorrect provenance analysis\".\n- Their repair prefers splitting an unsound composite over merging, since merging loses information. Their example: the folded view showed a dependency path from an input I6 to an output O2 that does not exist in the original workflow.\n- Transfer to Deliberus: when a long chain is folded, the folded edge should neither imply a dependency that the real chain lacks (a fold that swallows a side premise or a side attacker) nor drop one.\n\n1d. Folding a path into one labelled \"super edge\". Coscia et al., \"Semantic Bundling\" (arXiv 2608.04002). https://arxiv.org/html/2608.04002 [full text up to the usage scenarios].\n- For two distant entities the system enumerates simple paths up to a maximum length, optionally groups them (shortest, most distinct, through user-named intermediaries, by topic, or by clusters), and has an LLM write one summary triple as the edge label plus a natural-language summary.\n- Each summary sentence is linked to the triples beneath it, so a reader can click through. The paper names the risk: \"fluency can be misleading\" and LLMs can assert connections the data do not support.\n- Evidence level: usage scenarios on two datasets only. I saw no user study.\n- This is the nearest published analogue to Fredrik's \"10 hops shown as one edge\", including the LLM-written label. The design lessons are grounding (every label sentence traceable) and letting the user choose which paths and which intermediaries to keep.\n\n1e. Proof and argument-map viewers that unfold \"inferential leaps\".\n- Proofscape / PISE (Kieffer). https://skieffer.info/publications/kieffer2014proofscape-pre.pdf [abstract + part]; https://skieffer.info/publications/kieffer2024studying.pdf [full text, last section truncated]. This is the single closest match for \"a link is a chain folded up\".\n - An argument map where \"extra steps can be spliced in … to clarify difficult inferential leaps\"; the user is told an expansion exists and can open it.\n - Two drawing modes: \"unified\" (expansion at the same scale, inserted between the two nodes; all nodes stay legible and edges can connect across the boundary, but it needs space and the layout shifts) and \"embedded\" (the expansion is scaled down to roughly one node's size; you zoom in to read it; much less layout disruption, but no edges across levels and nodes at different levels are not legible together).\n - The author says explicitly that mental-map stability is a central issue and poses, as open questions, whether embedded mode is less disruptive and whether to use a pop-up instead. No answers are tested in that paper.\n - Also: cited lemmas open and close in place, giving \"theory-wide exploration\".\n- Concludia \"vouching\". https://concludia.org/docs/vouching [part]. A reader who has reviewed the support beneath a statement can mark it, and the view setting hides vouched areas. The statement stays visible and its support collapses, so attention goes to the unresolved part. Folding is per reader and tied to reviewed status, not only to depth. No user study cited.\n- Argdown. https://argdown.org/guide/creating-oldschool-argument-maps-and-inference-trees.html [part]. By default it hides premises and inferential steps inside argument nodes. A setting (\"explodeArguments\") puts every inferential step in its own node. You asked to skip Argdown basics; I mention it only because it is a built-in two-level fold of the same kind.\n- Graphionale (arXiv 2608.27932, UIST 2026). https://arxiv.org/html/2608.27932 [part; I read its formative study and system sections directly and its results section via a summarising fetch]. LLM rationales as argument maps with collapse/expand of support and objection branches.\n- Hippo (arXiv 2506.23678). https://arxiv.org/pdf/2506.23678v1.pdf [search excerpt only]. It lets users collapse a subtree of a reasoning tree, and a summary of the subtree is appended below the node.\n\n1f. Collapsing mediators in probabilistic and causal diagrams.\n- Evans, \"Graphs for margins of Bayesian networks\". https://arxiv.org/html/1408.1809v2 [abstract only]. Marginalising out latent variables does not in general give another DAG; the correct object is a \"latent projection\" onto a richer graph class (mDAGs). Moral: simply deleting a mediator and joining its neighbours is not generally a faithful picture of the margin.\n- Sasyniuk, \"Depicting variable elimination with Bayesian networks\". https://doi.org/10.82465/4619 [abstract + snippet]. Eliminating a variable adds compensating edges so the dependencies are preserved. Same moral.\n- Zeng 2023 MIT thesis, \"Causal Graph Summarization\". https://hdl.handle.net/1721.1/151569 [abstract/snippet only]: summarising a causal graph by removing nodes or edges \"would introduce spurious causal information\".\n\n1g. Not found: no source describing a standard \"compound edge\" or \"meta-edge\" for a path between two selected nodes in an argument-mapping tool, other than Semantic Bundling above (a general KG tool, not an argument tool) and PISE's reverse direction (expansion of a step).\n\n2. WHAT A FOLDED PATH SHOULD SHOW, AND HOW TOOLS LABEL IT\nDirect evidence from user studies on edge labels: none found. What exists is design statements and indirect results.\n- Hop count: not shown as a value in any tool I read. Proofscape signals only that an expansion exists. The only quantitative trace is Graphionale's formative-study participant who suggested \"about three to four layers, with three to five nodes per layer\" (a suggestion from one participant, not a tested condition). [part] https://arxiv.org/html/2608.27932\n- Weakest link, strength, or disputed intermediates on the folded edge: not shown in any visual tool I found.\n - The closest are Bayesian-network explanation tools. Koiter's GeNIe work (https://www.kbs.twi.tudelft.nl/docs/MSc/2006/JRKoiter/thesis.pdf [part]) draws arc thickness for strength of influence and colour for its sign, and draws a path's \"flow of evidence\" with an actual versus potential weight of evidence per link. It reports a \"qualitative empirical evaluation\" that found the technique \"easy to use and understand\"; no numbers.\n - Kyrimi et al. 2016 (https://proceedings.mlr.press/v52/kyrimi16.pdf [part]) is a secondary source on this: in one cited tool (Haddawy's BANTER) the strength of a chain is the minimum impact of any variable in it. Their own progressive-explanation design reveals the explanation in levels.\n- Graphionale's co-design participants (N=10, thematic analysis) asked for graphs where \"support, rejection, grouping, and reasoning strength\" are visible at a glance (their design goal DG3), and for progressive disclosure to bound complexity (DG4). Stated wishes, not measured benefit. [part]\n- ZOOM's soundness/completeness (1c) is a design rule for what a folded edge must not misstate. It is stated formally in the provenance papers; I did not find it tested with users.\n- Semantic Bundling's own lesson (1d): the label is a single triple, and the user must be able to trace it to the underlying steps.\n\n3. HOW STRENGTH ALONG A CHAIN IS COMPUTED, AND PITFALLS OF A COMBINED VALUE\n- Weakest link (minimum). Pollock, \"Degrees of Justification\". https://www.johnpollock.us/ftp/PAPERS/Degrees.pdf [part]. Argument strength is the minimum of the strengths of its premises and the reasons used. He rejects the probability calculus here with this argument: 100 independent premises each at probability .99 give a conjunction of only about .37 (\"the probability of the conjunction will be only .37\"), yet an engineer using 100 measurements to size a girder is not thereby unjustified. He also rejects \"accrual\" (two independent arguments yielding more than the better one), though he adds that weak defeaters may still \"diminish\" a conclusion. Prakken's 2005 accrual paper (https://webspace.science.uu.nl/~prakk101/papers/icail05hp.pdf [part]) argues that accrual can be weaker than its parts when reasons are not independent, and that the strength of an accrual in general \"cannot be calculated from the strengths of its elements\".\n- Weakest link vs last link (ASPIC+). Modgil & Prakken tutorial, https://webspace.science.uu.nl/~prakk101/pubs/ASPICtutorial.pdf [part]. Two standard ways to compare arguments: weakest link (compare all uncertain elements) and last link (compare only the last defeasible rules). They give worked examples showing each is more suitable in different cases. Pitfall for a display: the two rules can rank the same chains differently, so a folded edge's \"strength\" depends on a policy choice that should be stated.\n- Wei & Prakken 2016 (https://doi.org/10.3233/aac-160003 [abstract/snippet]) argue that Pollock's treatment gives counterintuitive outcomes in some cases and modify it.\n- Product (multiplication). Appropriate only under independence. Under screening off, the difference measure P(r|p) − P(r|¬p) equals [P(q|p) − P(q|¬p)] × [P(r|q) − P(r|¬q)] (Atkinson & Peijnenburg, eq. 7, citing Reichenbach). https://link.springer.com/article/10.1007/s11229-021-03165-w [part]. So multiplication is exact for that measure only when the intermediate screens off. Long products also shrink steadily with length (Pollock's .37 example), which is the standard objection to showing one product as a measure of how good a long chain is.\n- Dependencies are the practical trap. Schum & Martin (1982, https://doi.org/10.2307/3053534 [abstract only]): when people mentally combine a large amount of probabilistic evidence they treat contradictory testimony as corroborative and double-count redundant testimony; when asked about fine-grained logical details these inconsistencies \"do not occur\". Strittmatter, Pilditch & Lagnado 2024 (https://escholarship.org/uc/item/7jt638nj [abstract only]): people perceive dependencies when asked but do not discount for them in belief updating. Pilditch et al. (https://discovery.ucl.ac.uk/id/eprint/10108145/1/Dependencies%20in%20evidence%20reports%20-%20Pilditch%2C%20Hahn%2C%20Fenton%2C%20Lagnado.pdf [part]): dependence is not always a disadvantage, and lay reasoners do not appreciate when it helps. Implication: a single combined number invites readers to treat shared premises as independent.\n- Known pitfalls summarised: (1) the number depends on a policy (min, product, last link); (2) it hides which link carries the risk; (3) it ignores shared premises across chains; (4) it can make a long, well-founded chain look weaker than a short, flimsy one; (5) a fluent LLM-written summary can look more grounded than it is (Semantic Bundling, C4).\n\n4. USER-STUDY EVIDENCE ON UNDERSTANDING LONG CHAINS, FOLDED VS FLAT\nNothing tests this directly. Related evidence:\n- Graphionale (N=204, graphical vs textual LLM rationales). https://arxiv.org/html/2608.27932 [results read via summary, not by me directly]. For verbal reasoning, graphs reduced over-trust (Δ −0.144, p = .033) and raised error correction (Δ +0.127, p = .040), more on hard questions; for visual reasoning graphs hurt calibration. Task load was higher with graphs in both domains. Participants preferred the format that calibrated worse in each modality. Progressive disclosure was rated the most helpful of four graph features (mean 5.66/7), but the authors state they did not manipulate node count, depth or expand/collapse, so this is a rating, not an effect.\n- Borgwardt et al. 2020 (https://lat.inf.tu-dresden.de/research/papers/2020/BorgwardtHKW20.pdf [abstract + part]): short proofs, whether condensed formal or condensed textual, were rated easier than detailed ones, and long text proofs were called \"long-winded and repetitive\". They found no effect of prior logic experience.\n- Alrabbaa et al. 2021 (https://lat.inf.tu-dresden.de/research/papers/2021/AlrabbaaBKKRW21.pdf [abstract + conclusion]): interactive vs static, tree vs text. No difference in performance or rated comprehensibility, but tree-shaped proofs ranked higher overall. Their conclusion names the open trade-off \"between giving no details … and giving too many details\", with laypeople possibly wanting the gist and experts the formal detail. Not a folded-vs-flat test as such.\n- Proof-reading studies: mathematics majors tend to focus on calculation instead of structure and do not work out how new statements follow from earlier ones (Samkoff & Weber summary of earlier work, https://sites.math.rutgers.edu/~jpmejia/files/Samkoff_Weber_(2015JMB).pdf [part]); the Mejía-Ramos et al. comprehension model separates local understanding (why one step follows) from holistic understanding (summary, modular structure) (Weber 2015, https://doi.org/10.1007/s40753-015-0011-0 [abstract + part]). This is a useful frame for what a fold should serve: the folded view serves holistic understanding, the unfolded steps serve local.\n- Roy et al. (https://sigmaa.maa.org/rume/crume2010/Archive/Roy%20et%20al.pdf [part]) report that a proof presentation with built-in explanations did not beat plain reading on a delayed post-test, and suggest explanations given by others may reduce self-explanation. Small, old; treat as a caution about over-explaining.\n\n5. TRANSITIVITY OF PROBABILISTIC SUPPORT (the coordinator's added question)\nDoes a folded path have a single derived arrow with a strength?\n- Definition used throughout: x supports y iff Pr(y|x) > Pr(y). It is well known that this is not transitive: x can support y, y support z, and x not support z. Source: Shogenji's abstract, https://doi.org/10.1093/bjps/54.4.613 [abstract only; paywalled]; Roche's restatement, https://doi.org/10.1007/s13194-011-0033-7 [part]; Atkinson & Peijnenburg 2021, https://research.rug.nl/files/553602030/s10670_020_00349_7.pdf [abstract + opening]. Roche's paper cites earlier statements of the failure (Eells & Sober 1983; Hanen 1971; Hesse 1970) [secondary, via https://philarchive.org/archive/ROCTAI, part].\n- Condition under which it does carry along a chain (Shogenji 2003, BJPS 54, 613–616): transitivity holds provided the intermediary screens off the original evidence from the hypothesis. Formally (C): Pr(z | x & y) = Pr(z | y) and Pr(z | x & ¬y) = Pr(z | ¬y). The abstract also says this makes support transitive when the original evidence is testimonial, memorial or perceptual and the intermediary is its representational content. [abstract only for the original; formal statement of (C) is from Roche's paper, https://doi.org/10.1007/s13194-011-0033-7, part]\n- Eells & Sober 1983, Philosophy of Science 50, 35–57, https://doi.org/10.1086/289089 [abstract only]: a sufficient condition for transitivity of probabilistic causal chains; Atkinson & Peijnenburg describe it as screening off, \"calling it a Markov condition\" [secondary, https://link.springer.com/article/10.1007/s11229-021-03165-w, part]. They further argue (as a conjecture, which they flag) that Reichenbach already had the result for a linear chain.\n- Weaker sufficient conditions exist:\n - Roche's (C*): Pr(z|x&y) ≥ Pr(z|y) and Pr(z|x&¬y) ≥ Pr(z|¬y). [part, https://doi.org/10.1007/s13194-011-0033-7]. Suppes (1986) is cited as an earlier generalisation [secondary, Atkinson & Peijnenburg].\n - Atkinson & Peijnenburg 2021 introduce a still weaker condition, \"as weak as one wishes\", note it can hold even when Simpson's paradox obtains, and give a variant that is both sufficient and necessary. [abstract/opening, https://research.rug.nl/files/553602030/s10670_020_00349_7.pdf]\n - Roche & Shogenji 2013 (https://link.springer.com/article/10.1007/s11098-013-0161-3 [abstract only]) argue screening off is the most important condition because of its generality and ease of application, and show transitivity in four senses of confirmation for Moore's argument, where H1 logically entails H2.\n- Threshold versions fail even with the condition. Roche 2012 (https://doi.org/10.1017/s1755020311000414 [part], with preprint https://philarchive.org/archive/ROCTAI) reports that \"t-evidence\" (support plus probability above a threshold) is not made transitive by screening off or the weaker conditions (Douven showed this for (C); Roche extends it to (C*) and (C**)). It is made transitive by (C***): the weaker condition (C*) plus \"Q entails P\". Roche's other paper (Review of Symbolic Logic, https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/abs/evidential-support-transitivity-and-screeningoff/D74F97F3587ECBD9B45A77E52CF5E941 [abstract only]) says support-t, support-t* and support-tt* are all non-transitive in general, including under the screening-off conditions it studies.\n- So: a chain whose steps are logical entailments composes. A chain of merely probabilistic support steps composes only if each link screens off earlier links (or a weaker stated condition) from what follows. Whether screening off holds is a fact about the real dependencies, not about the picture.\n- Argumentation-theory treatment of chained support. In bipolar argumentation (Cayrol & Lagasquie-Schiex), support is a relation between arguments with several specialised readings (deductive, necessary, evidential, backing). For deductive support, chains of supports combined with an attack give derived \"supported attacks\" and \"mediated attacks\" (the chain composes, because acceptance of the first implies acceptance of the last). Source: https://www.irit.fr/publis/ADRIA/PapersMCL/Rapport-IRIT-2015-04.pdf [part]; https://www.irit.fr/publis/ADRIA/PapersMCL/sum2015.pdf [part]. Their gradual-valuation framework (https://dlnext.acm.org/doi/10.1007/11518655_32 [abstract only]) values each argument only from the arguments directly interacting with it, i.e. it computes along the chain locally and does not define one derived arrow. I did not find an argumentation-theory source that treats probabilistic non-transitivity of support specifically; that connection is mine to flag, not sourced.\n- Consequence for the design question: the sources support drawing a derived arrow for a chain of deductive steps, and for probabilistic steps only with a declared screening-off assumption. For defeasible steps, Pollock's minimum and ASPIC+'s weakest-link/last-link are the standard policies, and each is a rule about argument comparison, not about \"how much x raises z\".\n\n6. THE THREE FINDINGS MOST USEFUL FOR DESIGNING A FOLD/UNFOLD OF A LONG CHAIN\n1. Give the folded edge a correctness contract, borrowed from path-preserving provenance views: it must be sound (imply no dependency the real chain lacks) and complete (omit none), and whatever would break that (a side premise, a side attacker, a disputed intermediate) should split the fold rather than being hidden inside it. Source: ZOOM*UserViews / WOLVES, https://ceur-ws.org/Vol-526/InvitedPaper_3.pdf and https://www.cis.upenn.edu/~sanjeev/papers/icdt09_user_views.pdf.\n2. Do not draw one derived strength unless the step types justify it. Entailment steps compose; probabilistic steps compose only under screening off (Shogenji 2003; Eells & Sober 1983; weaker versions by Roche and Atkinson & Peijnenburg), and for defeasible steps the number is a policy choice (min per Pollock, or last-link per ASPIC+) that the edge should name. Show the weakest step and any disputed intermediate on the folded edge instead of, or beside, a product. Sources: https://doi.org/10.1093/bjps/54.4.613; https://link.springer.com/article/10.1007/s11229-021-03165-w; https://www.johnpollock.us/ftp/PAPERS/Degrees.pdf; https://webspace.science.uu.nl/~prakk101/pubs/ASPICtutorial.pdf.\n3. Use an unfold that keeps the mental map and keeps a trace to the steps. The folded edge's route should be reused by the unfolded chain (Raitner), the expansion can be embedded at reduced scale or inserted at full scale, each with the trade-offs Kieffer lists, and any generated label for the fold must link each sentence to the steps beneath it (Semantic Bundling). Sources: https://raitner.de/wp-content/uploads/2010/07/gd04.pdf; https://skieffer.info/publications/kieffer2024studying.pdf; https://arxiv.org/html/2608.04002.\n\n7. CAVEATS\n- No source tests folded vs flat for long inferential chains; section 4 is indirect.\n- Several key items are abstract only because of paywalls: Shogenji 2003, Eells & Sober 1983, Schum & Martin 1982, Roche's RSL papers, Evans 2015, Zeng 2023.\n- I read the Graphionale results section only through a summarising fetch; check the paper before quoting its numbers.\n- The two 2608.* arXiv papers could not be corroborated beyond their own pages.\n"}