Axiomatic vs Empirical AI Reasoning

Evaluating syntactic formal math proofs vs grounded causal world intelligence & counterfactual stability.

Presets:
Grounding Transfer Gap: 0.58 High formal syntactic coherence with low empirical counterfactual stability.
0.18
0.30
2.40

Axiomatic Deductive Engine

Closed System (Lean / Formal Tree)
Deterministic Axiom Proof Nodes
Applied Axiom Chain: A1 (p->q) & A2 (q->r) Proof Validity: 1.00

Empirical Causal Environment

Open System (Physics & Observation)
Click / Drag Levers & Sensors to Intervene
Active Interventions: target: sensor_1 [val: 1] Empirical Accuracy: 0.42

Quantified AI Grounding Diagnostics

Axiomatic Coherence
1.00
Syntactic theorem accuracy
Causal Model Accuracy
0.42
World-state prediction accuracy
Counterfactual Stability
0.45
Robustness to OOD shifts
Symbol Grounding Deficit
0.58
Gap between syntax & reality
Analysis Summary: Grounding Transfer Gap is 0.58 under current sensor noise (0.18) and radius (2.40).
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