Narrative Path

Here’s how Christine Müller’s paper grounds and sharpens the “narrative path” idea we’ve been using: [dmx](https://dmx.ralfbarkow.ch/systems.dmx.webclient/#/topicmap/874648/topic/899529/related) * #What a narrative path is In Müller’s model, topics are nodes in a **variant graph**; edges can be **semantic dependencies**, **narrative flows**, or **variant relations**. A **narrative walk** is any sequence of nodes connected by narrative-flow edges that share the same flow reference “#”. A **narrative path** is the *simple* (no repeated nodes) version of that walk. In short: a narrative path is the linear story you get by following one labeled narrative flow through distinct topic nodes. * #Why it matters The system *produces documents by traversing narrative paths*, not just hyperlink trails. Narrative edges may carry **transitional text** (“as we now define…”) so the linearization reads coherently, something plain topic chains usually lack. Variants on content and on narrative flows let the system pick the best storyline for a given reader. * #How a path is chosen (algorithmic gist) The hybrid traversal builds a global path **P** by repeatedly grabbing the **longest narrative path** that best matches the user’s **adaptation context** Λ (an ordered set of preference constraints). The match score for a candidate path is the average of node-level weights derived from how each node’s context annotations satisfy Λ. If no narrative option fits, it falls back to a path over semantic dependencies (and, if needed, to a context-based sequencing). Listings 1–3 specify this precisely. * #How to map this to our topicmap/DMX backend 1. **Types & IDs:** Represent associations of type `narrative` with a required property `flowRef` (= Müller’s “#”) so multiple alternative flows can coexist; keep `semantic` and `variant` as separate association types. Store optional `transitionText` on `narrative` edges. 2. **Context annotations:** Put node/edge annotations as key–value sets; preserve order/priority from Λ to compute weights exactly like Müller’s `w(P)` (average over nodes). 3. **Path selection:** Given current tail node `n` of P, search for the longest simple path that: (a) follows `narrative` edges with equal `flowRef`, (b) maximizes the match score under Λ, and (c) doesn’t revisit nodes. If none starts at `n`, allow any start; if still none, compute a semantic path/topological segment as fallback. 4. **Granularity passes:** First traverse container topics (e.g., theories/sections) to lay out the chapter sequence; then, for each section, traverse constituent graphs (definitions, proofs, examples) to linearize the inner narrative—exactly the two-level iteration Müller uses. * #Practical litmus tests (for our “narrative path” concept) * **Distinctness:** Does our story route forbid node repetition? If yes, we have a path (not just a walk). * **Flow identity:** Are consecutive edges in the story tagged with the same `flowRef`? That’s a single narrative path rather than a stitched set of flows. * **Personalization:** Can we rank competing paths by Λ and pick the top-scoring path segment when extending P? That’s Müller’s selection logic. * **Coherence:** Do we render edge-level `transitionText` when crossing edges? That’s how the path produces readable narrative, not just an ordered list. If we implement those four pieces, our “narrative path” matches Müller’s formalism: a maximal, context-best, distinct-node route along a single labeled narrative flow, with variants and fallbacks ensuring both personalization and coverage.

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