NAL Belief Revision

How Independent Evidence Merges to Strengthen or Weaken Beliefs — With Real Experimental Data

NAL revision: same proposition + independent evidence → pooled confidence. Formula: w=c/(1-c), f_rev=weighted avg, c_rev=w_total/(w_total+1) Evidence Af=0.40 c=0.50Weak positive signalEvidence Bf=0.30 c=0.60Independent observation REVISIONResult: f=0.34 c=0.71Confidence UP (evidence pooled), freq DOWN (B pulled it) CONTRADICTION CASEf=0.90 c=0.80f=0.10 c=0.70Revised: f=0.54 c=0.93Strong conflict: moderate freq, HIGH confidenceRevision never discards — it weighs all evidence proportionally REAL EXPERIMENTAL DATA: reliable_agent confidence recovery1.00.0Revision steps0.4840.7660.899~0.95asymptote

What this diagram shows: NAL belief revision merges independent evidence about the same proposition. Unlike Bayesian updating, it tracks confidence (how much evidence) separately from frequency (what the evidence says).

Formula: Convert confidence to evidence weight w=c/(1-c). Revised frequency is the weighted average. Revised confidence pools all evidence: c_rev = (w1+w2)/(w1+w2+1). Confidence always increases with more evidence.

Real data: The reliable_agent belief started at c=0.484 after initial observation, rose to 0.766 after second confirming evidence, then 0.899 after third. Each revision approaches but never reaches 1.0 — the asymptotic bound ensures epistemic humility.

Contradiction case: When evidence conflicts (f=0.9 vs f=0.1), revision does NOT discard either. It produces moderate frequency with HIGH confidence — the system is very sure the truth is ambiguous.