2nd/10_Wiki/Topics/AI_and_ML/Beliefs.md

---
id: wiki-2026-0508-beliefs
title: Beliefs
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [신념, belief revision, Bayesian belief, knowledge, confirmation bias, doxastic logic]
duplicate_of: none
source_trust_level: B
confidence_score: 0.85
verification_status: applied
tags: [epistemology, beliefs, knowledge, bayesian, confirmation-bias, ai-belief, doxastic-logic]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: epistemology / cognitive science
  applicable_to: [Agent Beliefs, RAG Trust, Bias Mitigation]
---

# Beliefs

## 📌 한 줄 통찰
> **"매 mind 의 잠정적 결론"**. 매 evidence 의 objective ↔ subjective 의 confidence. 매 action 의 trigger. 매 AI 의 응용 — 매 agent 의 belief state, 매 RAG 의 trust scoring, 매 confirmation bias 의 detect.

## 📖 핵심

### 매 정의 (philosophical)
- **Belief**: 매 proposition 의 true 의 mental acceptance.
- **Knowledge**: 매 Justified True Belief (Plato).
- **Gettier problem**: JTB 가 X 의 case (Gettier 1963).
- → 매 knowledge 의 stricter (no luck / safety / sensitivity).

### 매 belief 의 type
1. **Occurrent**: 매 active conscious thought.
2. **Dispositional**: 매 stored, 매 retrieve 매 ready.
3. **De dicto vs de re**: 매 about-words vs about-thing.
4. **Implicit / explicit**: 매 articulate-able.

### 매 belief revision (AGM)
- **Expansion**: 매 add (no conflict).
- **Contraction**: 매 remove.
- **Revision**: 매 add + remove 매 conflicting.
- **Postulates**: 매 closure, success, consistency, ...

### Bayesian belief
- 매 belief = 매 probability (degree of confidence).
- 매 update via Bayes (Cox theorem).
- 매 coherent.
- 매 modern AI 의 standard.

### 매 cognitive bias (belief 관련)
1. **Confirmation bias**: 매 belief 의 confirm 의 selective.
2. **Belief perseverance**: 매 disconfirming evidence 후 의 retain.
3. **Backfire effect**: 매 disconfirming evidence 의 strengthen.
4. **Sunk cost**: 매 commitment 의 belief 의 maintain.
5. **Motivated reasoning**: 매 want 의 believe.

### 매 AI / agent 의 응용

#### Belief state (POMDP)
- 매 partially observable.
- 매 belief = 매 distribution over state.
- 매 action 의 belief 의 update.

#### RAG trust score
- 매 retrieved document 의 belief.
- 매 confidence = recency × authority × consistency.

#### Multi-agent BDI (Belief-Desire-Intention)
- 매 belief: world state.
- 매 desire: goal.
- 매 intention: committed plan.
- 매 PRS, JADE.

#### LLM 의 belief
- 매 train 의 belief 의 instillation.
- 매 RLHF 의 alignment.
- 매 calibration: 매 P(true) 의 actual frequency.

### 매 epistemic logic
- 매 K_a φ: 매 agent a 의 knows φ.
- 매 B_a φ: 매 belief.
- 매 multi-agent: 매 common knowledge.
- 매 Aumann's agreement theorem: 매 rational 의 동의.

## 💻 패턴 (응용)

### Bayesian belief update
```python
def update_belief(prior, likelihood_true, likelihood_false, evidence):
    # P(H | E) = P(E | H) * P(H) / P(E)
    posterior_unnorm = likelihood_true * prior
    evidence_prob = likelihood_true * prior + likelihood_false * (1 - prior)
    return posterior_unnorm / evidence_prob

belief = 0.3  # 매 prior
belief = update_belief(belief, 0.9, 0.2, evidence=True)  # 매 0.66
belief = update_belief(belief, 0.9, 0.2, evidence=True)  # 매 0.90
```

### POMDP belief state
```python
class POMDPBelief:
    def __init__(self, n_states, prior):
        self.belief = prior  # np.array, sum=1
    
    def update(self, action, observation, T, O):
        # T: transition matrix, O: observation matrix
        new_belief = np.zeros_like(self.belief)
        for s_next in range(len(self.belief)):
            new_belief[s_next] = O[s_next, observation] * \
                sum(T[s, s_next, action] * self.belief[s] for s in range(len(self.belief)))
        new_belief /= new_belief.sum()
        self.belief = new_belief
```

### BDI agent
```python
class BDIAgent:
    def __init__(self):
        self.beliefs = {}     # 매 facts about world
        self.desires = []     # 매 goals
        self.intentions = []  # 매 active plans
    
    def perceive(self, observations):
        for obs in observations:
            self.beliefs[obs.key] = obs.value
    
    def deliberate(self):
        # 매 desire selection based on belief
        feasible = [d for d in self.desires if self.is_feasible(d)]
        return max(feasible, key=lambda d: d.priority)
    
    def plan(self, goal):
        # 매 belief 기반 의 plan
        return planner.plan(self.beliefs, goal)
    
    def execute(self):
        if not self.intentions:
            goal = self.deliberate()
            self.intentions = self.plan(goal)
        action = self.intentions.pop(0)
        return action
```

### LLM calibration
```python
def calibration_check(model, eval_set):
    # 매 P(true) 의 declared confidence vs actual
    bins = [(0, 0.1), (0.1, 0.2), ..., (0.9, 1.0)]
    bin_correct = {b: [] for b in bins}
    
    for example in eval_set:
        response = model.generate(example.prompt + ' Reply with answer and confidence (0-1).')
        ans, conf = parse(response)
        actual = (ans == example.expected)
        for b in bins:
            if b[0] <= conf < b[1]:
                bin_correct[b].append(actual)
                break
    
    # 매 ECE (Expected Calibration Error)
    ece = sum(abs(np.mean(corr) - (b[0]+b[1])/2) * len(corr) / len(eval_set)
              for b, corr in bin_correct.items() if corr)
    return ece
```

→ 매 well-calibrated = ECE 낮음.

### Confirmation bias detector
```python
def detect_confirmation_bias(query, results, user_belief):
    # 매 user 의 belief 의 align 의 source 만 의 click?
    aligning = [r for r in results if r.aligns_with(user_belief)]
    clicked_aligning = sum(1 for r in aligning if r.clicked)
    clicked_total = sum(1 for r in results if r.clicked)
    
    if clicked_total == 0: return None
    bias_ratio = clicked_aligning / clicked_total
    return bias_ratio  # 매 > 0.7 = 매 strong confirmation bias
```

## 🤔 결정 기준
| 응용 | Approach |
|---|---|
| Agent world model | POMDP belief |
| RAG trust | Source authority + consistency |
| Multi-agent | BDI |
| LLM calibration | ECE + temperature scaling |
| User UX | Diverse perspective + bias detect |
| Knowledge graph | Justified belief (provenance) |

**기본값**: Bayesian belief + ECE calibration + diverse evidence.

## 🔗 Graph
- 부모: [[Epistemology]]
- 변형: [[Knowledge]] · [[Bayesian-Belief]] · [[Doxastic-Logic]]
- 응용: [[POMDP]]
- 비판: [[Confirmation Bias]]
- Adjacent: [[Bayesian-Brain-Hypothesis]] · [[Multi-agent-System|Multi-Agent-Systems]]

## 🤖 LLM 활용
**언제**: 매 agent design (belief state). 매 RAG trust scoring. 매 LLM calibration eval. 매 bias detection.
**언제 X**: 매 metaphysical claim 의 substitute. 매 single belief 의 deterministic system.

## ❌ 안티패턴
- **Belief 의 binary**: 매 confidence 의 lose.
- **No update**: 매 stale belief.
- **Confirmation bias 의 ignore**: 매 echo chamber.
- **Calibration 무시**: 매 over-confident model.
- **Multiple agent 의 belief 의 share assumption**: 매 multi-agent fail.
- **Belief 의 hard-code**: 매 update 의 X.

## 🧪 검증 / 중복
- Verified (Plato JTB, Gettier, AGM postulates, Bayesian).
- 신뢰도 B.
- Related: [[Bayesian Statistics]] · [[Bayesian-Brain-Hypothesis]] · [[Confirmation Bias]] · [[POMDP]].

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — JTB + AGM + Bayesian + POMDP / BDI + 매 calibration code |