Q&A: Phase 24.1 — BeliefTracker

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Q&A: Phase 24.1 — BeliefTracker 🧠

Q1: Why use log-odds instead of raw probabilities for Bayesian updates?

A: Log-odds provide numerical stability. With raw probabilities, repeated strong evidence (LR=1000) can push posteriors to floating-point limits (1.0 or 0.0), creating degenerate beliefs that can never be revised. Log-odds spread the range to (-∞, +∞), and the sigmoid function maps back cleanly. We additionally clamp to [ε, 1-ε] where ε=1e-6 as a safety net.

Q2: What happens when a new observation contradicts an agent's established beliefs?

A: The AGM belief revision module activates. Depending on the operation:

• Expansion: If no conflict, simply add the new belief.
• Revision: If conflict exists, apply partial meet contraction—identify the minimal set of existing beliefs to retract (ordered by entrenchment = evidence_count × posterior), then add the new belief.
• Contraction: Remove a belief and close under logical consequences.

The key AGM postulate is minimal change—we retract as little as possible to restore consistency.

Q3: How does common knowledge differ from "everyone knows X"?

A: "Everyone knows X" (mutual knowledge level 1) means each agent individually knows X. Common knowledge requires the infinite recursion: everyone knows X, everyone knows that everyone knows X, everyone knows that everyone knows that everyone knows X... and so on. In practice, we approximate by iterating to a fixed-point or a configurable depth (default 3). The difference matters for coordination—common knowledge of a meeting time means everyone shows up; mere mutual knowledge doesn't guarantee it.

Q4: How does belief decay work, and why is it important?

A: Without decay, belief models become stale—an agent observed cooperating 1000 steps ago may have changed strategy. The exponential decay formula:

posterior_new = prior + (posterior_old - prior) × exp(-λ × Δt)

pulls posteriors back toward the prior as time passes without new evidence. λ (decay_rate) controls speed: higher = faster forgetting. This implements the principle that absence of evidence is weak evidence of absence in a non-stationary world.

Q5: How does BeliefTracker integrate with WorldModel (13.1)?

A: WorldModel provides ground truth—the actual state of the world. BeliefTracker models what agents believe about the world, which may differ from truth (false beliefs). The integration:

1. WorldModel updates → evidence source for our own belief model
2. Periodic validation: compare agent's believed state with ground truth to detect false beliefs
3. False belief detection feeds PerspectiveTaker (24.3) for Sally-Anne reasoning

Q6: What is the entrenchment ordering and why does it matter for revision?

A: Entrenchment (Gärdenfors 1988) determines which beliefs are "stickier"—more resistant to retraction during revision. We compute entrenchment as evidence_count × posterior, meaning beliefs with strong evidence from many observations resist retraction, while weakly-supported beliefs are retracted first. This ensures AGM revision respects the principle of informational economy—retract the least valuable information.

Q7: Can BeliefTracker handle contradictory evidence from different sources?

A: Yes. Each evidence source (observation, communication, inference) contributes a likelihood ratio to the Bayesian update. Contradictory evidence from different sources will push the posterior in opposite directions, naturally resulting in high uncertainty (posterior ≈ 0.5). The source tag on each BeliefEntry enables downstream components to weight sources differently—e.g., direct observation > communicated claim > inference.