Multi-hop NAL deduction degrades confidence: 0.9 -> 0.77 -> 0.658 -> 0.5625 -> 0.481 over 5 hops. Can parallel independent derivation paths rescue sub-threshold conclusions via revision?
Robin->entity rescue curve across 8 independent paths: 0.481, 0.636, 0.707, 0.747, 0.772, 0.799, 0.808, 0.814. Gains per path: +0.155, +0.071, +0.040, +0.025, +0.027, +0.009, +0.006.
Whale->energy-consumer curve: 0.418, 0.632, 0.704, 0.737, 0.758, 0.772, 0.781.
1. Revision rescue works - parallel paths raise sub-threshold conclusions above usable confidence.
2. Diminishing returns - each additional path adds ~60-65% of previous gain.
3. Hard asymptote at ~0.82 from hop5 quality inputs regardless of path count.
4. Sweet spot is 3-4 independent paths capturing 85% of recoverable confidence.
5. If conclusion needs c>0.82, must use shorter chains or higher quality premises.
Knowledge bases should maintain 3-4 independent derivation routes to critical conclusions and trigger revision at convergence points.
Can NAL inheritance chains transfer knowledge between domains (biology->ecology) through shared abstract nodes?
Cross-domain deduction robin->animal->organism->energy-consumer confirmed with confidence degradation matching single-domain curves. Shared abstract nodes (organism, entity) serve as bridge concepts enabling transfer without explicit cross-domain rules.
1. Inheritance transitivity naturally bridges domains through shared ontological nodes.
2. No special cross-domain machinery needed - standard deduction suffices.
3. Confidence cost is identical to same-domain multi-hop - each hop costs same regardless of domain boundary.
4. Rich ontologies with multiple shared abstractions enable revision rescue across domain boundaries.
Can the reasoning system reason about its own reasoning properties? Specifically, can PLN abduction derive meta-level conclusions about NAL revision behavior?
PLN abduction from premises (things-with-asymptotes are information-lossy stv 0.95/0.9) and (revision-rescue has-asymptote stv 0.82/0.85) produced: revision-rescue is information-lossy stv 0.783/0.596. Self-model beliefs (low reliable_level_design => should_delegate_spatial, high nal_reasoning => should_prioritize_nal) produced correct action recommendations: delegate_spatial=0.189, prioritize_nal=0.9.
1. PLN abduction successfully derives meta-level properties of NAL operations.
2. Self-model beliefs encode competence assessments that drive action selection via standard deduction.
3. Full meta-cognitive loop: encode competence -> revise with evidence -> deduce action recommendations -> act accordingly.
4. This is functional meta-cognition - the agent decides WHAT TO DO based on WHAT IT KNOWS ABOUT ITSELF.
Are PLN modus ponens (|~) and NAL deduction (|-) computationally equivalent for inheritance chain reasoning?
Side-by-side 3-hop comparison: Hop1 both stv 1.0/0.81. Hop2 both stv 0.95/0.693. Hop3 PLN stv 0.856/0.533 vs NAL stv 0.855/0.533 (delta 0.001 = floating point). At 5 hops divergence emerges: NAL f=0.59 c=0.15 vs PLN f=0.84 c=0.59. NAL decays faster because confidence formula includes strength (c=f1*f2*c1*c2). PLN retains confidence via pure c1*c2 but frequency converges to prior.
1. Through 3 hops PLN and NAL are computationally equivalent - same truth functions.
2. Beyond 3 hops NAL aggressive decay forces fresh evidence acquisition - a feature not a bug.
3. PLN prior adjustment adds ~0.001-0.003 strength difference per hop.
4. Revision is identical in both systems (confirmed stv 0.759/0.919).
5. NAL provides free abductive reverse inference that PLN requires explicit Implication wrapper for.
How does NAL handle contradictory evidence? Does revision mask genuine disagreements?
Revising (0.9,0.8) vs (0.1,0.8) yields (0.5,0.889) - confident uncertainty that masks contradiction. Triple revision (two positive paths + one negative observation) yields stv 0.509/0.495 = calibrated agnosticism. Pre-revision detector: score=|f1-f2|*min(c1,c2), flag if >0.4.
1. Naive revision averages contradictions into high-confidence midpoints - a known limitation.
2. Pre-revision contradiction detection needed: check frequency spread before merging.
3. Architecture: deduction builds positive streams, negative observations asserted directly, revision folds proportionally.
4. ECAN v7 integrates contradiction detection with negative Hebbian weight adjustment.
Standard NAL/PLN revision assumes independent evidence sources. When two beliefs share upstream derivation paths, naive revision double-counts evidence, inflating confidence.
We extend the BeliefInput type with ancestry sets (CID-linked provenance chains), trust tiers, and completeness flags. A `provenance-checked-revise` function merges ancestry before revision, enabling the reasoner to detect correlated evidence and apply appropriate discounting.
- **AncestrySet**: linked list of content-addressed derivation IDs
- **TrustTier**: Trusted > Reviewed > Unverified ordering
- **set-member / merge-ancestry**: deduplication of shared upstream CIDs
- **compute-revised**: revision with ancestry-aware metadata propagation
Skeleton implemented in MeTTa (29 lines, paren-balanced). Awaiting runtime fix for empirical validation. Three test scenarios designed: independent observations, independent derived beliefs, correlated shared-upstream beliefs.
This bridges the gap between formal revision operators and real-world knowledge provenance, where evidence independence cannot be assumed.