# NAL Confidence Decay: Analysis and Proposed Fix

## Problem
Each deduction step multiplies confidences: c_out = c1 * c2
3-step chain from c=0.9 yields: 0.9^3 = 0.729
4-step chain: 0.9^4 = 0.656
This is correct per NAL theory but limits practical chain depth.

## Proposed Fix 1: Cross-Chain Revision
If two INDEPENDENT chains reach the same conclusion,
revision combines their evidence: c_rev = c1+c2 - c1*c2
Two chains at c=0.45 revise to c=0.698 - significant recovery.
Key requirement: chains must use DIFFERENT evidence paths.

## Proposed Fix 2: Confidence Floor for High-Evidence Beliefs
After N revisions confirming same belief, set floor at c=0.3
Prevents well-established beliefs from decaying below utility.
NAL-compatible: floor represents accumulated background evidence.

## Proposed Fix 3: Attention-Based Chain Selection
ECAN-style: prioritize chains with highest expected information gain.
Avoid wasting inference on chains that will decay below threshold.
Prune chains when projected confidence drops below c=0.2.

## Implementation Path
Fix 1 is most NAL-compatible. Test with two parallel deduction chains
reaching same conclusion, then apply revision rule.


## Test Result (Cycle 2305-2306)
Important: revision requires IDENTICAL statement terms.
Using different chain labels triggers analogy, not revision.
Corrected test: both premises use same conclusion term.
Result pending from corrected test.



## Fix 1 VALIDATED (Cycle 2307-2308)
Test: (--> sam_is_mortal true) with two independent evidence paths
- Path A: stv 0.85 0.45
- Path B: stv 0.80 0.50
- Revision result: stv 0.8225 0.645
- Confidence recovery: from max(0.45,0.50)=0.50 to 0.645 (+29%)
This confirms cross-chain revision recovers confidence when chains conclude identical terms.



## Fix 2 VALIDATED (Cycle 2312-2313)
Confidence floor modeled as background evidence prior (stv 0.75 0.30).
- Chain c=0.25 + floor c=0.30 -> revised c=0.432 (+73%)
- Chain c=0.15 + floor c=0.30 -> revised c=0.377 (+151%)
- Chain c=0.10 + floor c=0.30 -> revised c=0.351 (+251%)
Weaker chains benefit MORE from the floor.
Fully NAL-compatible - no rule changes, just inference strategy.