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Phase 6: TheoryNet Projection

Overview

Phase 6 formalizes the mined argumentation and conceptual graph into a mathematically rigorous TheoryNet (\(\rho, \alpha\)). It evaluates argument acceptability, assigns node plausibility and edge weights, and verifies empirical content bounds through bipartite partition analysis (\(A\)-atoms vs. \(B\)-atoms).

Purpose

While earlier phases extract textual discourse units and local/global relations, Phase 6 performs the formal epistemological projection:

  1. Translates extracted argument components into formal theory atoms (\(\rho\)) with assigned plausibility scores.
  2. Projects relations into weighted dialectical edges (\(\alpha\)).
  3. Asserts the structuralist empirical content condition: ensuring theoretical hypotheses (\(A\)-partition) connect meaningfully to empirical observations (\(B\)-partition).

Theoretical Foundation

See Formal Graph Schema (TheoryNet) and Theory-Nets, Posets & Topologies:

  • Formal representation: \(T = \langle \mathcal{A}, \mathcal{R}, \rho, \alpha \rangle\)
  • Bipartite partitioning: Theoretical Hypotheses (\(A\)-atoms) vs. Empirical Observations (\(B\)-atoms)
  • Empirical content criteria (\(Z_1\) connectivity)
  • Gradual semantics and Quaternary Bipolar Argumentation Frameworks (QBAF)

Components

1. TheoryNet Projector (TheoryNetProjector)

  • Projects the cumulative Phase4ArtifactsView into a formal TheoryNet domain contract.
  • Maps component classifications to formal theoretical partitions:
    • Partition A (Theoretical Core): THEORETICAL_HYPOTHESIS, AXIOM, LAW.
    • Partition B (Empirical Grounding): EMPIRICAL_STATEMENT, OBSERVATION_UNIT.

2. Plausibility & Edge Weight Formalization

  • Node Plausibility: Initializes atom.plausibility from extraction confidence (defaulting to 1.0 when unweighted).
  • Edge Weights: Populates relation.weight from relation confidence scores, maintaining scope annotations ("local" vs. "global").

3. Empirical Content & \(Z_1\) Connectivity Verification

  • Builds an adjacency projection over the theoretical partition (\(A\)-atoms).
  • Identifies \(Z_1\)-connected components: theoretical atoms directly connected to empirical \(B\)-atoms or reachable through connected \(A\)-hypotheses.
  • Computes empirical content coverage and verifies that theoretical constructs maintain grounding in the empirical manifold.

Workflow

flowchart TD
    A[Phase4ArtifactsView<br>TheoryAtoms & TheoryRelations] --> B[TheoryNetProjector.project<br>Formal Graph Formalization]
    B --> C[Compute Node Plausibility<br>atom.plausibility = confidence]
    C --> D[Compute Relation Weights<br>relation.weight = confidence]
    D --> E[Bipartite Partitioning<br>Partition A: Hypotheses / Partition B: Observations]
    E --> F[Verify Z_1 Empirical Connectivity<br>Path Reachability to B-Atoms]
    F --> G[Graph Commit:<br>upsert_argument_components & upsert_relations]
    G --> H[Final Theory Graph Ready in Neo4j]

Implementation Details

  • pipeline_explanation.md - Detailed step-by-step implementation walkthrough
  • Runner: Phase6Runner in pipeline/phases/phase6_theorynet/__init__.py
  • Projector: TheoryNetProjector in pipeline/projection/theorynet_projector.py
  • Configuration: Phase6Config in pipeline/config.py

Configuration

Configuration is managed via Phase6Config in pipeline/config.py:

Parameter Type Default Description
enabled bool True Whether to execute the formal TheoryNet projection pass.

Phase Contract

Inputs:

  • Phase4ArtifactsView: Cumulative collection of TheoryAtom and TheoryRelation artifacts across the pipeline run.

Outputs:

  • ArtifactCollection containing formal TheoryNet artifacts.
  • Neo4j graph updates:
    • Updated ArgumentComponent / TheoryAtom nodes with .plausibility.
    • Updated TheoryRelation edges with .weight.

Invariants:

  • Plausibility and edge weights are bounded in \([0.0, 1.0]\).
  • Every \(A\)-atom's empirical grounding is verifiable via \(Z_1\) paths.