# Atomspace Cost-Benefit v3 - Formula-Corrected
## Based on lib_pln.metta (466 lines) and empirical MeTTa verification

### CONFIDENCE DECAY (c0=0.9, node_prior=0.9)
| Hops | NAL ded | PLN ded(min) | PLN MP |
|------|---------|--------------|--------|
| 1 | 0.81 | 0.9 | 0.81 |
| 2 | 0.729 | 0.9 | 0.729 |
| 3 | 0.6561 | 0.9 | 0.6561 |
| 4 | 0.5905 | 0.9 | 0.5905 |
| 5 | 0.5315 | 0.9 | 0.5315 |
| 6 | 0.4783 | 0.9 | 0.4783 |

### KEY FINDING
PLN deduction is chain-length invariant when node priors >= link confidence.
Essential for deep reasoning (3+ hops) across large KBs.
NAL confidence decays exponentially, unreliable past 4-5 hops.

### PLN EXTRA INFERENCE
- Induction: w2c(min(c1,c2)) - c=0.9 gives 0.4737
- Abduction: same formula
- Revision: pools evidence w1+w2

### VERDICT
Atomspace+PLN justified when: depth>3 hops, KB>10K nodes,
or induction/abduction/revision needed for knowledge discovery.