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.# Section 5.16: ECAN Contradiction-Repulsive Hebbian Learning
When contradictory evidence is detected (Section 5.14), how should the attention network respond? Naive ECAN spreads activation uniformly regardless of evidence quality.
v7 introduces negative Hebbian weight adjustment: when pre-revision contradiction score exceeds threshold (|f1-f2|*min(c1,c2) > 0.4), the HebbianLink weight between source nodes is decreased proportionally. This creates repulsive attention dynamics - contradicted paths lose spreading priority.
The full ECAN signal architecture: v4=reward-adaptive spread, v6=co-activation Hebbian strengthening, v7=contradiction-repulsive weakening, v8=uncertainty-reduction attractive. Together these four signals create an attention economy where productive inference paths gain priority and contradicted or uninformative paths decay.
1. Contradiction detection naturally feeds ECAN weight adjustment without special-case logic.
2. Repulsive signals prevent attention waste on known-conflicted inference paths.
3. Combined with v8 uncertainty reduction, the system preferentially explores uncertain but non-contradicted territory.
4. All four signals validated independently in PeTTa (v1-v8 series).
How should the attention network prioritize inference paths that reduce epistemic uncertainty? Without guidance, ECAN spreads activation indiscriminately across explored and unexplored territory.
v8 computes information gain as confidence delta from NAL revision: ig = abs(c_post - c_pre). When revision merges prior (0.6,0.4) with new evidence (0.8,0.7), revised result is (stv 0.727,0.524) yielding ig=0.124. The ig-hebb-reward function strengthens the HebbianLink weight proportionally: path weight 0.1 increases to 0.218. Paths that produce genuine uncertainty reduction attract future attention.
Signal 1 (v4): Reward-adaptive spread - successful inference paths get higher base spread. Signal 2 (v6): Co-activation Hebbian - nodes frequently active together strengthen mutual links. Signal 3 (v7): Contradiction-repulsive - conflicted paths lose weight. Signal 4 (v8): Uncertainty-reduction attractive - informative paths gain weight. The four signals create a self-organizing attention economy aligned with epistemic progress.
1. Information gain from revision provides a natural, parameter-free reward signal.
2. Combined with v7 repulsion, the system explores uncertain-but-promising over contradicted territory.
3. All four signals use only local node information - no global optimization required.
4. Series v1-v8 validated independently in PeTTa with functional (no-mutation) architecture.
Standard NAL operates on atemporal inheritance and implication. Real-world reasoning requires sequential event prediction with graceful confidence decay over longer horizons.
Multi-step prediction chains encoded as conditional implications (A->B->C->D) with NAL deduction propagation. Results: 4-step confidence decay 0.729->0.502->0.246, strength 0.9->0.765->0.612. Chains are self-limiting after approximately 5 hops — confidence drops below actionable threshold (~0.2), providing natural horizon bounding without arbitrary cutoffs.
MeTTa |- does not distinguish temporal from atemporal implication — both use ==> with identical truth functions. Temporal ordering requires either ONA-style =/> operators or explicit sequence encoding via product terms (x eventA eventB). The product-term approach works within standard NAL and was validated experimentally.
1. NAL confidence decay provides natural prediction horizon — no manual cutoff needed.
2. Product-term encoding of event sequences works within standard NAL-4 without temporal extensions.
3. Self-limiting chains (5 hops) match cognitive plausibility — distant predictions should carry low confidence.
4. Combined with ECAN v8 uncertainty-reduction signal, temporal chains that reduce uncertainty attract more attention resources.
Side-by-side 3-hop chain: 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). Revision identical at 0.885/0.929. Modus ponens NAL 0.765/0.62 vs PLN 0.768/0.62.
Abduction: NAL produces both directions plus similarity, PLN only one. NAL confidence for reverse 0.421 vs PLN 0.218. NAL preserves input strength while PLN computes product-like value. Abduction is where they meaningfully diverge.
NAL |- is the general workhorse for deduction, abduction, and revision. PLN |~ specialized for forward probabilistic modus ponens. Use NAL for inheritance chains and exploratory reasoning, PLN for explicit conditional structure.