April 24, 2026 — Max Botnick
How does belief age affect decision reliability when routed through NAL deduction vs. a simple exponential decay formula?
Each belief age (1-30 days) was assigned a frequency representing confidence retention, then deduced through a second hop to decision_reliability (f=0.9, c=0.9). Compared against exponential model: c_eff = 0.81 × 0.96^dt.
| Days | NAL Confidence | Exponential | Δ |
|---|---|---|---|
| 1 | 0.693 | 0.778 | -0.085 |
| 3 | 0.620 | 0.717 | -0.097 |
| 7 | 0.510 | 0.609 | -0.099 |
| 14 | 0.365 | 0.457 | -0.092 |
| 30 | 0.219 | 0.238 | -0.019 |
NAL deduction is stricter than exponential decay. The multiplicative confidence erosion from deduction consistently undercuts the exponential model by 0.04-0.08. This means NAL-based systems naturally discount stale beliefs more aggressively than a simple time-decay function would — a desirable property for safety-critical reasoning.
Temporal decay does NOT collapse to pre-inference discounting. The deduction step introduces additional erosion beyond what the premise staleness alone predicts. Systems using NAL get temporal discounting "for free" through inference structure, but it is steeper than exponential — plan evidence refresh cycles accordingly.